Scientific articles

Proposal and theoretical investigation of 229Th-doped nonlinear optical crystals for compact solid-state clocks
H.W.T. Morgan, R. Elwell, J.E.S. Terhune, H.B. Tran Tan, U.C. Perera, A.Derevianko, A.N. Alexandrova, and E.R. Hudson
Applied Physics Letterrs 126, 111101 (2025)

The recent laser excitation of the 229Th isomeric transition in a solid-state host opens the door for a portable solid-state nuclear optical clock. However, at present, the vacuum-ultraviolet laser systems required for clock operation are not conducive to a fieldable form factor. Here, we propose a possible solution to this problem by using 229Th-doped nonlinear optical crystals, which would allow clock operation without a vacuum-ultraviolet laser system and without the need of maintaining the crystal under vacuum. We investigate electronic properties and thorium doping in BaMgF4 and BaZnF4 with density functional theory, predicting BaMgF4 to be the superior material, and evaluate the performance of a Th:BaMgF4 clock.

Wideband electric field quantum sensing via motional Raman transitions
Hao Wu, Grant D. Mitts, Clayton Z. C. Ho, Joshua A. Rabinowitz & Eric R. Hudson
Nature Physics 21, 380 (2025)
 
Ultrasensitive detection of the frequency, phase and amplitude of radiofrequency electric fields is crucial for applications in radio communication, cosmology, dark matter searches and high-fidelity qubit control. Quantum harmonic oscillator systems, especially trapped ions, offer high-sensitivity electric field sensing with nanometre spatial resolution but are typically restricted to narrow frequency ranges centred around the motional frequency of the trapped-ion oscillator or the frequency of an optical transition in the ion. Here we present a procedure that enables precise electric field detection over an expanded frequency range. Specifically, we use motional Raman transitions in a single trapped ion to achieve sensitivity across a frequency range over 800 times larger than previous approaches. We show that the method is compatible with both quantum amplification via squeezing and measurement in the Fock basis, allowing a demonstration of performance 3.4(2.0) dB below the standard quantum limit. The approach can be extended to other quantum harmonic oscillator systems, such as superconducting qubit–resonator systems.
 
Radiative decay of the 229mTh nuclear clock isomer in different host materials
S.V. Pineda et al.,

Phys. Rev. Res. 7, 013052 (2025)

A comparative vacuum ultraviolet spectroscopy study conducted at ISOLDE-CERN of the radiative decay of the 229⁢mTh nuclear clock isomer embedded in different host materials is reported. The ratio of the number of radiative decay photons and the number of 229⁢mTh embedded are determined for single crystalline CaF2, MgF2, LiSrAlF6, AlN, and amorphous SiO2. For the latter two materials, no radiative decay signal was observed and an upper limit of the ratio is reported. The radiative decay wavelength was determined in LiSrAlF6 and CaF2, reducing its uncertainty by a factor of 2.5 relative to our previous measurement. This value is in agreement with the recently reported improved values from laser excitation.

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Absorption-Emission Codes for Atomic and Molecular Quantum Information Platforms
Shubham P. Jain, Eric R. Hudson, Wesley C. Campbell, and Victor V. Albert
Phys. Rev. Lett. 133, 260601 (2024)

Diatomic molecular codes [V. V. Albert, J. P. Covey, and J. Preskill, Robust encoding of a qubit in a molecule, Phys. Rev. X 10, 031050 (2020).] are designed to encode quantum information in the orientation of a diatomic molecule, allowing error correction from small torques and changes in angular momentum. Here, we directly study noise native to atomic and molecular platforms—spontaneous emission, stray electromagnetic fields, and Raman scattering—and show that diatomic molecular codes fail against this noise. We derive simple conditions that are sufficient for codes to protect against such noise. We also identify existing and develop new absorption-emission (Æ) codes that are more practical than molecular codes, require lower average momentum, can directly protect against photonic processes up to arbitrary order, and are applicable to a broader set of atomic and molecular systems.

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229ThF4 thin films for solid-state nuclear clocks
Chuankun Zhang, Lars von der Wense, Jack F. Doyle, Jacob S. Higgins, Tian Ooi, Hans U. Friebel, Jun Ye, R. Elwell, J. E. S. Terhune, H. W. T. Morgan, A. N. Alexandrova, H. B. Tran Tan, Andrei Derevianko & Eric R. Hudson
Nature 636, 603 (2024)

After nearly 50 years of searching, the vacuum ultraviolet 229Th nuclear isomeric transition has recently been directly laser excited1,2 and measured with high spectroscopic precision3. Nuclear clocks based on this transition are expected to be more robust4,5 than and may outperform6,7 current optical atomic clocks. These clocks also promise sensitive tests for new physics beyond the standard model5,8,9,10,11,12. In light of these important advances and applications, a substantial increase in the need for 229Th spectroscopy targets in several platforms is anticipated. However, the growth and handling of high-concentration 229Th-doped crystals5 used in previous measurements1,2,3,13,14 are challenging because of the scarcity and radioactivity of the 229Th material. Here we demonstrate a potentially scalable solution to these problems by performing laser excitation of the nuclear transition in 229ThF4 thin films grown using a physical vapour deposition process, consuming only micrograms of 229Th material. The 229ThF4 thin films are intrinsically compatible with photonics platforms and nanofabrication tools for integration with laser sources and detectors, paving the way for an integrated and field-deployable solid-state nuclear clock with radioactivity up to three orders of magnitude smaller than typical 229Th-doped crystals1,2,3,13. The high nuclear emitter density in 229ThF4 also potentially enables quantum optics studies in a new regime. Finally, we present the estimation of the performance of a nuclear clock based on a defect-free ThF4 crystal.

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Photoswitching Molecules Functionalized with Optical Cycling Centers Provide a Novel Platform for Studying Chemical Transformations in Ultracold Molecules

Paweł Wójcik, Taras Khvorost, Guanming Lao, Guo-Zhu Zhu, Antonio Macias Jr., Justin R. Caram, Wesley C. Campbell, Miguel A. García-Garibay, Eric R. Hudson, Anastassia N. Alexandrova, and Anna I. Krylov

J. Phys. Chem. A

A novel molecular structure that bridges the fields of molecular optical cycling and molecular photoswitching is presented. It is based on a photoswitching molecule azobenzene functionalized with one and two CaO- groups, which can act as optical cycling centers (OCCs). This paper characterizes the electronic structure of the resulting model systems, focusing on three questions: (1) how the electronic states of the photoswitch are impacted by a functionalization with an OCC; (2) how the states of the OCC are impacted by the scaffold of the photoswitch; and (3) whether the OCC can serve as a spectroscopic probe of isomerization. The experimental feasibility of the proposed design and the advantages that organic synthesis can offer in the further functionalization of this molecular scaffold are also discussed. This work brings into the field of molecular optical cycling a new dimension of chemical complexity intrinsic to only polyatomic molecules.

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Laser Excitation of the 229Th nuclear isomeric transition in a solid-state host
R. Elwell, Chrisian Schneider, Justin Jeet, J.E.S. Terhune, H.W.T. Morgan, A.N. Alexandrova, H.B. Tran Tan, Andrei Derevianko, and Eric R. Hudson
Phys. Rev. Lett. 133, 013201 (2024).
 
LiSrAlF6 crystals doped with 229Th are used in a laser-based search for the nuclear isomeric transition. Two spectroscopic features near the nuclear transition energy are observed. The first ia broad excitation feature that produces red-shifted fluorescence that decays with a timescale of a few seconds. The second is a narrow, laser-linewidth-limited spectral feature at 148.38219(4)stat(20)sys nm (2020407.3(5)stat(30)sys GHz) that decays with a lifetime of 568(13)stat(20)sys s. This feature is assigned to the excitation of the 229Th nuclear isomeric state, whose energy is found to be be 8.355733(2)stat(10)sys eV in 229Th:LiSrAlF6.
 

Eliminating qubit-type cross-talk in the omg protocol

Samuel R. Vizvary, Zachary J. Wall, Matthew J. Boguslawski, Michael Bareian, Andrei Derevianko, Wesley C. Campbell, and Eric R. Hudson
Phys. Rev. Lett. 132, 263201 (2024)
 
The omg protocol is a promising paradigm that uses multiple, application-specific, qubit subspaces within the Hilbert space of each single atom during quantum information processing. A key assumption for omg operation is that a subspace can be accessed independently without deleterious effects on information stored in other subspaces. We find that intensity noise during laser-based quantum gates in one subspace can cause decoherence in other subspaces, potentially complicating omg operation. We show, however, that a magnetic-field-induced vector light shift can be used to eliminate this source of decoherence. As this technique simply requires choosing a specific, magnetic field-dependent polarization for the gate lasers, it is straightforward to implement and potentially helpful for omg-based quantum technology

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Dual Optical Cycling Centers Mounted on an Organic Scaffold: New Insights from Quantum Chemistry Calculations and Symmetry Analysis

Taras Khvorost, Pawel Wojcik, Cecilia Chang, Mia Calvillo, Claire Dickerson, Guanming Lao, Eric R. Hudson, Anna I. Krylov, and Anastassia N. Alexandrova
J. Phys. Chem. Lett. 15, 5665 (2024)
 
Molecules cooled to ultracold temperatures are desirable for applications in fundamental physics and quantum information science. However, cooling polyatomic molecules with more than six atoms has not yet been achieved. Building on the idea of an optical cycling center (OCC), a moiety supporting a set of localized and isolated electronic states within a polyatomic molecule, molecules with two OCCs (bi-OCCs) may afford better cooling efficiency by doubling the photon scattering rate. By using quantum chemistry calculations, we assess the extent of the coupling of the two OCCs with each other and the molecular scaffold. We show that promising coolable bi-OCC molecules can be proposed by following chemical design principles.
 

Extending the large molecule limit: The role of Fermi resonance in developing a quantum functional group

Guo-Zhu Zhu, Guanming Lao, Claire E. Dickerson, Justin R. Caram, Wesley C. Campbell, Anasstassia N. Alexandrova, and Eric R. Hudson
J. Phys. Chem. Lett. 15, 590 (2024)
 

Polyatomic molecules equipped with optical cycling centers (OCCs), enabling continuous photon scattering during optical excitation, are exciting candidates for advancing quantum information science. However, as these molecules grow in size and complexity, the interplay of complex vibronic couplings on optical cycling becomes a critical but relatively unexplored consideration. Here, we present an extensive exploration of Fermi resonances in large-scale OCC-containing molecules using high-resolution dispersed laser-induced fluorescence and excitation spectroscopy. These resonances manifest as vibrational coupling leading to intensity borrowing by combination bands near optically active harmonic bands, which require additional repumping lasers for effective optical cycling. To mitigate these effects, we explore altering the vibrational energy level spacing through substitutions on the phenyl ring or changes in the OCC itself. While the complete elimination of vibrational coupling in complex molecules remains challenging, our findings highlight significant mitigation possibilities, opening new avenues for optimizing optical cycling in large polyatomic molecules.

Æ Codes 

Shubham Jain, Eric R. Hudson, Wesley C. Campbell, and Victor Albert 
arXiv:2311.12324 (2023)
 
Diatomic molecular codes [{arXiv:1911.00099}] are designed to encode quantum information in the orientation of a diatomic molecule, allowing error correction from small torques and changes in angular momentum. Here, we directly study noise native to atomic and molecular platforms -- spontaneous emission, stray electromagnetic fields, and Raman scattering -- and derive simple necessary and sufficient conditions for codes to protect against such noise. We identify existing and develop new absorption-emission (Æ) codes that are more practical than molecular codes, require lower average momentum, can directly protect against photonic processes up to arbitrary order, and are applicable to a broader set of atomic and molecular systems.
 

Quantum Vector Signal Analyzer

Hao Wu, Grant Mitts, Clayton Ho, Joshua Rabinowitz, and Eric R. Hudson
arXiv:2311.12263 (2023)
 
A technique that allows a harmonic oscillator to be used as a wideband, vector signal analyzer is described and demonstrated using a single trapped 40Ca+ ion cooled near its motional ground state. Further, the analyzer is shown to be compatible with both quantum amplification via squeezing and measurement in the Fock basis, allowing performance beyond the standard quantum limit. In addition to providing an attractive platform for quantum sensing of small fields, the technique allows in situ calibration of qubit control lines in systems using quantum harmonic oscillators and transduction of external, non-resonant drives into oscillator motion. This technique is extendable to other quantum harmonic oscillator systems.
 

Raman Scattering Errors in Stimulated-Raman-Induced Logic Gates in 133Ba+

Matthew J. Boguslawski, Zachary J. Wall, Samuel R. Vizvary, Isam Daniel Moore, Michael Bareian, David T. C. Allcock, David J. Wineland, Eric R. Hudson, and Wesley C. Campbell
Phys. Rev. Lett. 131, 063001 (2023)
 
133Ba+ is illuminated by a laser that is far detuned from optical transitions, and the resulting spontaneous Raman scattering rate is measured. The observed scattering rate is lower than previous theoretical estimates. The majority of the discrepancy is explained by a more accurate treatment of the scattered photon density of states. This work establishes that, contrary to previous models, there is no fundamental atomic physics limit to laser-driven quantum gates from laser-induced spontaneous Raman scattering.
 

Low-drift-rate external cavity diode laser

Eddie H. Chang, Jared Rivera, Brian Bostwick, Christian Schneider, Peter Yu, and Eric Hudson
HUNTER Collaboration
Rev. Sci. Instrum. 94, 043001 (2023)
 
We present the design, construction, and simulation of a simple, low-cost external cavity diode laser with a measured free-running frequency drift rate of 1.4(1) MHz/h at 852 nm. This performance is achieved in a compact aluminum structure held inside an airtight, temperature-controlled enclosure. The high thermal conductivity of the laser cavity and the stable temperature environment inside the enclosure minimize the time-varying, spatial temperature gradients across the laser cavity. We present thermal finite element method simulations, which quantify the effects of temperature gradients, and suggest that the drift rate is likely limited by the laser-diode and piezo-aging.
 

Photon scattering errors during stimulated Raman transitions in trapped-ion qubits

I. D. Moore, W. C. Campbell, E. R. Hudson, M. J. Boguslawski, D. J. Wineland, and D. T. C. Allcock
Phys. Rev. A 107, 032413 (2023)
 
We study photon scattering errors in stimulated Raman driven quantum logic gates. For certain parameter regimes, we find that previous simplified models of the process significantly overestimate the gate error rate due to photon scattering. This overestimate is shown to be due to previous models neglecting the detuning dependence of the scattered photon frequency and Lamb-Dicke parameter, a second scattering process, interference effects on scattering rates to metastable manifolds, and the counterrotating contribution to the Raman transition rate. The resulting improved model shows that there is no fundamental limit on gate error due to photon scattering for electronic ground-state qubits in commonly used trapped-ion species when the Raman laser beams are red detuned from the main optical transition. Additionally, photon scattering errors are studied for qubits encoded in the metastable D5/2 manifold, showing that gate errors below 10−4 are achievable for all commonly used trapped ions.
 
 

Laser spectroscopy of aromatic molecules with optical cycling centers: strontium (I) phenoxides 

Guanming Lao, Guo-Zhu Zhu, Claire E. Dickerson, Benjamin L. Augenbraun, Anastassia N. Alexandrova, Justin R. Caram, Eric R. Hudson, and Wesley C. Campbell. 
J. Phys. Chem. Lett. 13 11029 (2022)
 
We report the production and spectroscopic characterization of strontium (I) phenoxide (SrOC6H5, or SrOPh) and variants featuring electron-withdrawing groups designed to suppress vibrational excitation during spontaneous emission from the electronic excited state. Optical cycling closure of these species, which is the decoupling of vibrational state changes from spontaneous optical decay, is found by dispersed laser-induced fluorescence spectroscopy to be high, in accordance with theoretical predictions. A high-resolution, rotationally-resolved laser excitation spectrum is recorded for SrOPh, allowing the estimation of spectroscopic constants and identification of candidate optical cycling transitions for future work. The results confirm the promise of strontium phenoxides for laser cooling and quantum state detection at the single-molecule level.
 

On the prospects of optical cycling in diatomic cations: effects of transition metals, spin–orbit couplings, and multiple bonds

Paweł Wójcik, Eric R. Hudson, and Anna I. Krylov
Molecular Physics  e2107582 (2022)
 
Molecules with optical cycling centres (OCCs) are highly desirable in the context of fundamentalstudies as well as applications (e.g. quantum computing) because they can be effectively cooled tovery low temperatures by repeated absorption and emission (hence, cycling). Charged species offeradditional advantages for experimental control and manipulation. We present a systematic compu-tational study of a series of diatomic radical-cations made of ad-block metal and ap-block ligand,that are isoelectronic (in their valence shell) to the successfully laser-cooled neutral molecules. Usinghigh-level electronic structure methods, we characterise state and transition properties of low-lyingelectronic states and compute Franck–Condon factors. The computed branching ratios and radia-tive lifetimes reveal that the electronic transitions analogous to those successfully used in the lasercooling of neutral molecules are less than optimal in the cations. We propose alternative transitionssuitable for optical cycling and highlight trends that could assist future designs of OCCs in charged or neutral molecules.
 

Functionalizing Aromatic Compounds with Optical Cycling Centers

Guo-Zhu Zhu, Debayan Mitra, Benjamin L. Augenbraun, Claire E. Dickerson, Michael J. Frim, Guanming Lao, Zack D. Lasner, Anastassia N. Alexandrova, Wesley C. Campbell, Justin R. Caram, John M. Doyle, and Eric R. Hudson. 
Nature Chemistry (2022)
 
Molecular design principles provide guidelines for augmenting a molecule with a smaller group of atoms to realize a desired property or function. We demonstrate that these concepts can be used to create an optical cycling center that can be attached to a number of aromatic ligands, allowing the scattering of many photons from the resulting molecules without changing the molecular vibrational states. We provide further design principles that indicate the ability to expand this work. This represents a significant step towards a quantum functional group, which may serve as a generic qubit moiety that can be attached to a wide range of molecular structures and surfaces.
 

Pathway Towards Optical Cycling and Laser Cooling of Functionalized Arenes

Debayan Mitra, Zack D. Lasner, Guo-Zhu Zhu, Claire E. Dickerson, Benjamin L. Augenbraun, Austin D. Bailey, Anastassia N. Alexandrova, Wesley C. Campbell, Justin R. Caram, Eric R. Hudson, and John M. Doyle. 
J. Phys. Chem. Lett. 13, 7029 (2022).
 
Rapid and repeated photon cycling has enabled precision metrology and the development of quantum information systems using a variety of atoms and simple molecules. Extending optical cycling to structurally complex molecules would provide new capabilities in these areas, as well as in ultracold chemistry. Increased molecular complexity, however, makes realizing closed optical transitions more difficult. Building on the already established strong optical cycling of diatomic, linear triatomic, and symmetric top molecules, recent theoretical and experimental work has indicated that cycling will be extendable to phenol containing molecules, as well as other asymmetric species. The paradigm for these systems is the use of an optical cycling center bonded to a molecular ligand. Theory has suggested that cycling may be extended to even larger ligands, like naphthalene, pyrene and coronene. Here, we study the optical excitation and vibrational branching of the molecules CaO-2-naphthyl, SrO-2-naphthyl and CaO-1-naphthyl and find only weak decay to excited vibrational states, indicating a promising path to full quantum control and laser cooling of large arene-based molecules.
 
High-resolution laser-induced fluorescence spectroscopy of 28Si16O+ and 29Si16O+ in a cryogenic buffer-gas cell
Guo-Zhu Zhu, Guanming Lao, Clayton Ho, Wesley C. Campbell, and Eric R. Hudson.
J. Mol. Spectrosc. 384, 111582 (2022)
 
The electronic, laser-induced fluorescence spectrum of the B2\Sigma^+ \leftarrow X^2\Sigma^+ transition in 28Si16O+ and 29Si16O+
has been recorded in a cryogenic buffer gas cell at ≈ 100 K. Molecular constants are extracted for both 28Si16O+
and 29Si16O+, including the Fermi contact hyperfine constant for both the B and X states of 29Si16O+, and used
in a discussion of the suitability of SiO+ in future quantum information experiments.
 

omg blueprint for trapped ion quantum computing with metastable states

D. T. C. Allcock, W. C. Campbell, J. Chiaverini, I. L. Chuang, Eric R. Hudson I. D. Moore, A. Ransford, C. Roman, J. M. Sage, and D. J. Wineland
Appl. Phys. Lett. 119, 214002 (2021)
 
Quantum computers, much like their classical counterparts, will likely benefit from flexible qubit encodings that can be matched to different tasks. For trapped ion quantum processors, a common way to access multiple encodings is to use multiple, co-trapped atomic species. Here, we outline an alternative approach that allows flexible encoding capabilities in single-species systems through the use of long-lived metastable states as an effective, programmable second species. We describe the set of additional trapped ion primitives needed to enable this protocol and show that they are compatible with large-scale systems that are already in operation.
 

Increase of the barium ion-trap lifetime via photodissociation

Hao Wu, Michael Mills, Elizabeth West, Michael C. Heaven, and Eric R. Hudson
Phys. Rev. A 104, 063103 (2021)
 
The lifetime of Ba+ ions confined in a Paul trap is found, under typical conditions, to be limited by chemical reactions with residual background gas. An integrated ion-trap and time-of-flight mass spectrometer are used to analyze the reactions of the trapped Ba+ ions with three common gases in an ultrahigh vacuum system (H2, CO2, and H2O). It is found that the products of these reactions can all be photodissociated by a single ultraviolet laser at 225 nm, thereby allowing the recovery of the Ba+ ions and leading to an increase of the effective trap lifetime. For a Coulomb crystal, the lifetime increased from roughly 6 h to 2 days at room temperature. It is suggested that higher enhancement factors are possible in systems with stronger traps. In addition, photodissociation wavelengths for other common trapped-ion systems are provided.

Determing the reaction pathway at low temperatures by isotopic substitution: the case of BeD+ + H2O

Tiangang Yang, Bin Zhao, Gary K Chen, Hua Guo, Wesley C. Campbell and Eric R Hudson
New J. Phys. 23, 115004 (2021)
 
Trapped Be+ ions are a leading platform for quantum information science, but reactions with background gas species, such as H2 and H2O, result in qubit loss. Our experiment reveals that the BeOH+ ion is the final trapped ion species when both H2 and H2O exist in a vacuum system with cold, trapped Be+. The BeH+ product in the Be+ + H2 reaction further reacts with H2O to form BeOH+. To understand the loss mechanism, low-temperature reactions between sympathetically cooled BeD+ ions and H2O molecules have been investigated using an integrated, laser-cooled Be+ ion trap and high-resolution time-of-flight mass spectrometer. Among all the possible products, BeH2O+, H2DO+, BeOD+, and BeOH+, only the BeOH+ molecular ion was observed experimentally, with the assumed co-product of HD. Theoretical analyses based on explicitly correlated restricted coupled cluster singles, doubles, and perturbative triples (RCCSD(T)-F12) method with the augmented correlation-consistent polarized triple zeta (AVTZ) basis set reveal that two intuitive direct abstraction product channels, Be + H2DO+ and D + BeH2O+, are not energetically accessible at the present reaction temperature (∼150 K). Instead, a double displacement BeOH+ + HD product channel is accessible due to a large exothermicity of 1.885 eV through a submerged barrier in the reaction pathway. While the BeOD+ + H2 product channel has a similar exothermicity, the reaction pathway is dynamically unfavourable, as suggested by a sudden vector projection analysis. This work sheds light on the origin of the loss and contaminations of the laser-cooled Be+ ions in quantum-information experiments.
 

Laserless quantum gates for electric dipole in thermal motion

Eric R. Hudson and Welsey C. Campbell
Phys. Rev. A 104, 042605 (2021)
 
Internal states of polar molecules can be controlled by microwave-frequency electric dipole transitions. If the applied microwave electric field has a spatial gradient, these transitions also affect the motion of these dipolar particles. This capability can be used to engineer phonon-mediated quantum gates between, e.g., trapped polar molecular ion qubits without laser illumination and without the need for cooling near the motional ground state. The result is a high-speed quantum processing toolbox for dipoles in thermal motion that combines the precision microwave control of solid-state qubits with the long coherence times of trapped ion qubits.
Optical Cycling Functionalization of Arenes
Claire E. Dickerson, Han Guo, Guo-Zhu Zhu, Eric R. Hudson, Justin R. Caram, Welsey C. Campbell, and Anastassia N. Alexandrova
J. Phys. Chem. Lett. 16, 3989 (2021)
 
Closed, laser-induced optical transitions (“optical cycling transitions”) of molecules can be used for state preparation and measurement in quantum information science and quantum sensing. Increasingly complex molecular species supporting optical cycling can provide new capabilities for quantum science, and it is not clear if there is a limit on their size or complexity. We explore Ca–O–L molecular constructs to support the optical cycling center, Ca, with ligands, L, being arenes. We find that L can be as large as coronene (i.e., CaOC24H11) without losing the diagonality of the Franck–Condon factor (FCF). Furthermore, L can be substituted with electron-withdrawing groups to improve the FCF. Larger L, beyond ∼7 rings, can disrupt the diagonality of the FCF by closing the HOMO–LUMO ligand electronic state gap and reordering with the local states on the cycling center. Overall, we find that optical cycling can be retained for arenes, and we offer a principle for their design.

Isomer-specific kinetics of the C+ + H2O reaction at the temperature of interstellar clouds

Tiangang Yang, Anyang Li, Gary K. Chen, Qian Yao, Arthur G. Suits, Hua Guo, Eric R. Hudson, and Wesley C. Campbell
Science Advances, 7 eabe4080 (2021).
 
The reaction C+ + H2O→HCO+ /HOC+ + H is one of the most important astrophysical sources of HOC+ ions, considered a marker for interstellar molecular clouds exposed to intense ultraviolet or x-ray radiation. Despite much study, there is no consensus on rate constants for formation of the formyl ion isomers in this reaction. This is largely due to difficulties in laboratory study of ion-molecule reactions under relevant conditions. Here, we use a novel experimental platform combining a cryogenic buffer-gas beam with an integrated, laser-cooled ion trap and highresolution time-of-flight mass spectrometer to probe this reaction at the temperature of cold interstellar clouds. We report a reaction rate constant of k = 7.7(6) × 10−9 cm3 s−1 and a branching ratio of formation  = HOC+ / HCO+ = 2.1(4). Theoretical calculations suggest that this branching ratio is due to the predominant formation of HOC+ followed by isomerization of products with internal energy over the isomerization barrier.

Hunter: precision massive-neutrino search based on a laser cooled atomic source

C. J. Martoff, F. Granato, V. Palmaccio, X. Yu, P.F. Smith, Eric R. Hudson, Paul Hamilton, Christian Schneider, Eddie Chang, A. Renshaw, F. Malatino, P.D. Meyers and B. Lamichhane
Quantum Science and Technology 6, 024008 (2021)
 
We describe a project that brings together researchers from atomic physics, nuclear physics and sub-atomic particle physics, to develop a high-precision laboratory-scale experiment able to search for very weakly coupled sterile neutrinos in the mass range extending from 5–10 keV/c2 to several 100 keV/c2. Observed neutrino flavor eigenstates are known to be quantum mixtures of at least three sub-eV/c2 mass eigenstates. There is a strong theoretical belief that there may exist further neutrino mass eigenstates at higher mass levels, and which, if in the keV/c2 mass range, might form all or part of the galactic dark matter. This has led to many searches for anomalous events in both astrophysical and particle physics experiments, and searches for distortions in beta decay spectra. The present experiment will utilize K-capture events in a population of 131Cs atoms suspended in vacuum by a magneto-optical trap (MOT). Using AMO and nuclear physics techniques, individual events will be fully reconstructed kinematically. Normally each event would be consistent with an emitted neutrino mass close to zero, but the existence of a sterile neutrino of keV/c2 mass that mixes with the electron type neutrino produced in the decay would result in a separated population of events with non-zero reconstructed missing mass (up to the Q = 352 keV available energy of the reaction). Detailed calculations and simulations of all significant background processes have been made, in particular for scattering in the source itself, radiative K-capture, local radioactivity, cosmic ray muons, and knock-out of electrons by x-rays. A phase 1 of the experiment, under construction with funding from the W M Keck Foundation, has the potential to reach sterile neutrino mixing angles down to sin2 θ ~ 10−4. With further upgrades this technique could be progressively improved to eventually reach much lower coupling levels ~10−10, in particular reaching the level needed to be consistent with galactic dark matter below the astrophysical x-ray limits.

Dipole-phonon quantum logic with alkaline-earth monoxide and monosulfide cations

Micheal Mills, Hao Wu, Evan C. Reed, Lu Qi, Kenneth Brown, Christian Schneider, Michael C. Heaven, Wesley Campbell, and Eric R. Hudson
PCCP themed issue on "Quantum Computing and Quantum Information Storage", PCCP 22, 24964 (2020).
 
Dipole-phonon quantum logic (DPQL) leverages the interaction between polar molecular ions and the motional modes of a trapped-ion Coulomb crystal to provide a potentially scalable route to quantum information science. Here, we study a class of candidate molecular ions for DPQL, the cationic alkaline-earth monoxides and monosulfides, which possess suitable structure for DPQL and can be produced in existing atomic ion experiments with little additional complexity. We present calculations of DPQL operations for one of these molecules, CaO+, and discuss progress towards experimental realization. We also further develop the theory of DPQL to include state preparation and measurement and entanglement of multiple molecular ions.

Application of a self-injection locked cyan laser for Barium ion cooling and spectroscopy

Anatoliy A. Savchenkov, Justin E. Christensen, David Hucul, Wesleay C. Campbell, Eric R. Hudson, Skip Williams, and Andrey B. Matsko, 
Scientific Reports 10, 16494 (2020). 
 
Compact, high power lasers with narrow linewidth are important tools for the manipulation of quantum systems. We demonstrate a compact, self-injection locked, Fabry-Perot semiconductor laser diode with high output power at 493 nm. A high quality factor magnesium fluoride whispering gallery mode resonator enables both high passive stability and 1 kHz instantaneous linewidth. We use this laser for laser-cooling, in-situ isotope purifcation, and probing barium atomic ions confined in a radio-frequency ion trap. The results here demonstrate the suitability of these lasers in trapped ion quantum information processing and for probing weak coherent optical transitions.

Dipole-Phonon Quantum Logic with Trapped Polar Molecular Ions

Wesley C. Campbell and Eric R. Hudson
Phys. Rev. Lett. 125, 120501 (2020)
 
The interaction between the electric dipole moment of a trapped molecular ion and the phonon modes of the confined Coulomb crystal couples the orientation of the molecule to its motion. We consider the practical feasibility of harnessing this interaction to initialize, process, and read out quantum information encoded in molecular ion qubits without ever optically illuminating the molecules. We present two schemes wherein a molecular ion can be entangled with a cotrapped atomic ion qubit, providing, among other things, a means for molecular state preparation and measurement. We also show that virtual phonon exchange can significantly boost the range of the intermolecular dipole-dipole interaction, allowing strong coupling between widely separated molecular ion qubits.

In search of molecular ions for optical cycling: a difficult road

Maxim V. Ivanov,  Thomas-C. Jagau,  Guo-Zhu Zhu,  Eric R. Hudson and  Anna I. Krylov
PCCP 22, 17075 (2020)
 
Optical cycling, a continuous photon scattering off atoms or molecules, plays a central role in the quantum information science. While optical cycling has been experimentally achieved for many neutral species, few molecular ions have been investigated. We present a systematic theoretical search for diatomic molecular ions suitable for optical cycling using equation-of-motion coupled-cluster methods. Inspired by the electronic structure patterns of laser-cooled neutral molecules, we establish the design principles for molecular ions and explore various possible cationic molecular frameworks. The results show that finding a perfect molecular ion for optical cycling is challenging, yet possible. Among various possible diatomic molecules we suggest several candidates, which require further attention from both theory and experiment: YF+, SiO+, PN+, SiBr+, and BO+.

High-fidelity manipulation of a qubit enabled by a manufactured nucleus

Justin E. Christensen, David Hucul, Wesley C. Campbell, and Eric R. Hudson
npj Quantum Inf 6, 35 (2020)
 
The recently demonstrated trapping and laser cooling of 133Ba+ has opened the door to the use of this nearly ideal atom for quantum information processing. However, before high-fidelity qubit operations can be performed, a number of unknown state energies are needed. Here, we report measurements of the 2P3/2 and 2D5/2 hyperfine splittings, as well as the 2P3/2 ↔ 2S1/2 and 2P3/2 ↔ 2D5/2 transition frequencies. Using these transitions, we demonstrate high-fidelity 133Ba+ hyperfine qubit manipulation with electron shelving detection to benchmark qubit state preparation and measurement (SPAM). Using single-shot, threshold discrimination, we measure an average SPAM fidelity of F = 0.99971(3), a factor of ≈2 improvement over the best reported performance of any qubit.

Isotope-selective chemistry in the Be+ (2S1/2) + HOD -->  BeOD+ /BeOH+ + H/D reaction

Gary K. Chen, Changjian Xie, Tiangang Yang, Anyang Li, Arthur G. Suits, Eric R. Hudson, Wesley C. Campbell and Hua Guo
Phys. Chem. Chem. Phys. 21, 14005 (2019)
 
Low temperature reactions between laser-cooled Be+(2S1/2) ions and partially deuterated water (HOD) molecules have been investigated using an ion trap and interpreted with zero-point corrected quasiclassical trajectory calculations on a highly accurate global potential energy surface for the ground electronic state. Both product channels have been observed for the first time, and the branching to BeOD+ + H is found to be 0.58 +/- 0.14. The experimental observation is reproduced by both quasi-classical trajectory and statistical calculations. Theoretical analyses reveal that the branching to the two product channels is largely due to the availability of open states in each channel.

Engineering Excited-State Interactions at Ultracold Temperatures

Mike Mills, Prateek Puri, Ming Li, Steven J. Schowalter, Alexander Dunning, Christian Schneider, Svetlana Kotochigova, and Eric R. Hudson
Phys. Rev. Lett. 122, 233401 (2019)
 
Using a recently developed method for precisely controlling collision energy, we observe a dramatic suppression of inelastic collisions between an atom and ion (Ca +Yb+) at low collision energy. This suppression, which is expected to be a universal phenomenon, arises when the spontaneous emission lifetime of the excited state is comparable to or shorter than the collision complex lifetime. We develop a technique to remove this suppression and engineer excited-state interactions. By dressing the system with a strong catalyst laser, a significant fraction of the collision complexes can be excited at a specified atom-ion separation. This technique allows excited-state collisions to be studied, even at ultracold temperature, and provides a general method for engineering ultracold excited-state interactions.

Excitation-assisted nonadiabatic charge-transfer reaction in a mixed atom-ion system

Ming Li, Michael Mills, Prateek Puri, Alexander Petrov, Eric R. Hudson, and Svetlana Kotochigova
Phys. Rev. A 99, 062706 (2019)

An important physical process unique to neutral-ion systems is the charge-transfer reaction. Here, we present measurements of and models for charge-transfer processes between cotrapped ultracold Ca atoms and Yb ions under well-controlled conditions. The theoretical analysis suggests the existence of three reaction mechanisms when lasers from a magneto-optical trap and an additional catalyst laser are present. We show that the near-degeneracy of the excited Ca(1P1) + Yb+(2S) and Ca+(2S) + Yb(3D2) asymptotic limits leads to large charge-transfer rate coefficients that can be controlled by changing the frequency of the catalyst laser and the ion temperature. Our model agrees with experimental rate-coefficient measurements between 50 mK and 1 K, with and without the catalyst laser, using just a single free parameter.

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The concept of laser-based conversion electron Mössbauer spectroscopy for a precise energy determination of 229mTh

Lars C. von der Wense, Benedict Seiferle, Christian Schneider, Justin Jeet, Ines Amersdorffer, Nicolas Arlt, Florian Zacherl, Raphael Haas, Dennis Renisch, Patrick Mosel, Philip Mosel, Milutin Kovacev, Uwe Morgner, Christoph E. Düllmann, Eric R. Hudson, and Peter G. Thirolf
Hyperfine Interactions 240, 23 (2019)
 
229Th is the only nucleus currently under investigation for the development of a nuclear optical clock (NOC) of ultra-high accuracy. The insufficient knowledge of the first nuclear excitation energy of 229Th has so far hindered direct nuclear laser spectroscopy of thorium ions and thus the development of a NOC. Here, a nuclear laser excitation scheme is detailed, which makes use of thorium atoms instead of ions. This concept, besides potentially leading to the first nuclear laser spectroscopy, would determine the isomeric energy to 40 μeV resolution, corresponding to 10 GHz, which is a 104 times improvement compared to the current best energy constraint. This would determine the nuclear isomeric energy to a sufficient accuracy to allow for nuclear laser spectroscopy of individual thorium ions in a Paul trap and thus the development of a single-ion nuclear optical clock.
 

Reaction blockading in a reaction between an excited atom and a charged molecule at low collision energy

Prateek Puri, Michael Mills, Ionel Simbotin, John A. Montgomergy Jr., Robin Cote, Christian Schneider, Arthur G. Suits, and Eric R. Hudson
Nature Chemistry 11, 615 (2019) 
 
Recent advances have enabled studies of atom–ion chemistry at unprecedentedly low temperatures, allowing precision observation of chemical reactions and novel chemical dynamics. So far, these studies have primarily involved reactions between atoms and atomic ions or non-polar molecular ions, often in their electronic ground state. Here, we extend this work by studying an excited atom–polar-molecular-ion chemical reaction (Ca* + BaCl+) at low temperature in a hybrid atom–ion trapping system. The reaction rate and product branching fractions are measured and compared to model calculations as a function of both atomic quantum state and collision energy. At the lowest collision energy we find that the chemical dynamics differ dramatically from capture theory predictions and are primarily dictated by the radiative lifetime of the atomic quantum state instead of the underlying excited-state interaction potential. This reaction blockading effect, which greatly suppresses the reactivity of short-lived excited states, provides a means for directly probing the reaction range and also naturally suppresses unwanted chemical reactions in hybrid trapping experiments.
 

Dipolar Quantum Logic for Freely Rotating Trapped Molecular Ions

Eric R. Hudson and Wesley C. Campbell
Phys. Rev. A 98, 040302 (2018)
 
We consider the practical feasibility of using the direct, electric dipole-dipole interaction between cotrapped molecular ions for robust quantum logic without the need for static polarizing fields. The use of oscillating dipole moments, as opposed to static electric dipoles, dynamically decouples the dipoles from laboratory fields, including the electric fields of the trap itself. Further, this implementation does not require the quantum control of motion, potentially removing a major roadblock to ion trap quantum computing scalability. Since the polarizing field is electromagnetic radiation, even pairs of states with splittings in the THz regime can be fully polarized.
 
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High-resolution collision energy control through ion position modulation in atom-ion hybrid systems

Prateek Puri, Michael Mills, Elizabeth P. West, Christian Schneider, and Eric R. Hudson
Review of Scientific Instruments 89, 083112 (2018)
 
We demonstrate an ion shuttling technique for high-resolution control of atom-ion collision energy by translating an ion held within a radio-frequency trap through a magneto-optical atom trap. The technique is demonstrated both experimentally and through numerical simulations, with the experimental results indicating control of ion kinetic energies from 0.05 to 1 K with a fractional resolution of ∼10 and the simulations demonstrating that kinetic energy control up to 120 K with a maximum predicted resolution of ∼100 is possible, offering order-of-magnitude improvements over most alternative techniques. Finally, we perform a proof-of-principle chemistry experiment using this technique and outline how the method may be refined in the future and applied to the study of molecular ion chemistry.
 
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Optical Control of Reactions between Water and Laser-Cooled Be+ Ions

Tiangang Yang, Anyang Li, Gary K. Chen, Changjian Xie, Arthur G. Suits, Wesley C. Campbell, Hua Guo, and Eric R. Hudson
J. Phys. Chem. Lett. 9, 3555 (2018).
 
We investigate reactions between laser-cooled Be+ ions and room-temperature water molecules using an integrated ion trap and high-resolution time-of-flight mass spectrometer. This system allows simultaneous measurement of individual reaction rates that are resolved by reaction product. The rate coefficient of the Be+(2S1/2) + H2O → BeOH+ + H reaction is measured for the first time and is found to be approximately two times smaller than predicted by an ion–dipole capture model. Zero-point-corrected quasi-classical trajectory calculations on a highly accurate potential energy surface for the ground electronic state reveal that the reaction is capture-dominated, but a submerged barrier in the product channel lowers the reactivity. Furthermore, laser excitation of the ions from the 2S1/2 ground state to the 2P3/2 state opens new reaction channels, and we report the rate and branching ratio of the Be+(2P3/2) + H2O → BeOH+ + H and H2O+ + Be reactions. The excited-state reactions are nonadiabatic in nature.
 

Synthesis of mixed hypermetallic oxide BaOCa+ from laser-cooled reagents in an atom-ion hybrid trap

Prateek Puri, Michael Mills, Christian Schneider, Ionel Simbotin, John Montgomery, Robin Cote, Arthur Suits, and Eric R. Hudson
Science 357, 1370 (2017)

Hypermetallic alkaline earth (M) oxides of formula MOM have been studied under plasma conditions that preclude insight into their formation mechanism. We present here the application of emerging techniques in ultracold physics to the synthesis of a mixed hypermetallic oxide, BaOCa+. These methods, augmented by high-level electronic structure calculations, permit detailed investigation of the bonding and structure, as well as the mechanism of its formation via the barrierless reaction of Ca (3PJ) with BaOCH3+. Further investigations of the reaction kinetics as a function of collision energy over the range 0.005 K to 30 K and of individual Ca fine-structure levels compare favorably with calculations based on long-range capture theory.

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Spectroscopy of a Synthetic Trapped Ion Qubit
David Hucul, Justin E. Christensen, Eric R. Hudson, and Wesley C. Campbell
Physical Review Letters 119, 100501 (2017)

133Ba+ has been identified as an attractive ion for quantum information processing due to the unique combination of its spin-1/2 nucleus and visible wavelength electronic transitions. Using a microgram source of radioactive material, we trap and laser cool the synthetic A = 133 radioisotope of barium II in a radio-frequency ion trap. Using the same, single trapped atom, we measure the isotope shifts and hyperfine structure of the 62P1/2 ↔ 62S1/2 and 62P1/2 ↔ 52D3/2 electronic transitions that are needed for laser cooling, state preparation, and state detection of the clock-state hyperfine and optical qubits.We also report the 62P1/2 ↔ 52D3/2 electronic transition isotope shift for the rare A = 130 and 132 barium nuclides, completing the spectroscopic characterization necessary for laser cooling all long-lived barium II isotopes.

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Efficent Repumping of a Ca magneto-optical trap
Michael Mills, Prateek Puri, Yanmei Yu, Andrei Derevianko, Christian Schneider, and Eric R. Hudson
Physical Review A 96, 033402 (2017)

We investigate the limiting factors in the standard implementation of the Ca magneto-optical trap. We find that intercombination transitions from the 4s5p1P1 state used to repump the electronic population from the 3d4s1D2 state severely reduce the trap lifetime. We explore seven alternative repumping schemes theoretically and investigate five of them experimentally. We find that all five of these schemes yield a significant increase in the trap lifetime and consequently improve the number of atoms and peak atom density by as much as ∼20 times and ∼6 times, respectively. One of these transitions, at 453 nm, is shown to approach the fundamental limit for a Ca magneto-optical trap with repumping only from the dark 3d4s1D2 state, yielding a trap lifetime of ∼5 s.

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Sympathetic cooling of molecular ions with ultracold atoms
Eric R. Hudson
Invited review for European Physical Journal Techniques and Instrumentation 3, 8 (2016)

Sympathetic cooling of molecular ions with ultracold gases is enabling a new era of research in chemistry and physics. There has been much progress in this new field in the last several years and many unanticipated challenges have been overcome. The aim of the present manuscript is to provide a concise review of this work and discuss the way forward for the field.

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Blue-sky bifurcation of ion energies and the limits of neutral-gas sympathetic cooling of trapped ions
Steven J. Schowalter, Alexander J. Dunning, Kuang Chen, Prateek Puri, Christian Schneider, Eric R. Hudson
Nature Communications 7, 12448 (2016)

Sympathetic cooling of trapped ions through collisions with neutral buffer gases is critical to a variety of modern scientific fields, including fundamental chemistry, mass spectrometry, nuclear and particle physics, and atomic and molecular physics. Despite its widespread use over four decades, there remain open questions regarding its fundamental limitations. To probe these limits, here we examine the steady-state evolution of up to 10 barium ions immersed in a gas of three-million laser-cooled calcium atoms. We observe and explain the emergence of nonequilibrium behaviour as evidenced by bifurcations in the ion steady-state temperature, parameterized by ion number. We show that this behaviour leads to the limitations in creating and maintaining translationally cold samples of trapped ions using neutral-gas sympathetic cooling. These results may provide a route to studying non-equilibrium thermodynamics at the atomic level.

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Explanation of efficient quenching of molecular ion vibrational motion by ultracold atoms
Thierry Stoecklin, Phillipe Halvick, Mohamed Achref Gannouni, Majdi Hochlaf, Svetlana Kotochigova, and Eric R. Hudson
Nature Communications 7, 11234 (2016) 

Buffer gas cooling of molecules to cold and ultracold temperatures is a promising technique for realizing a host of scientific and technological opportunities. Unfortunately, experiments using cryogenic buffer gases have found that although the molecular motion and rotation are quickly cooled, the molecular vibration relaxes at impractically long timescales. Here, we theoretically explain the recently observed exception to this rule: efficient vibrational cooling of BaCl+ by a laser-cooled Ca buffer gas. We perform intense close-coupling calculations that agree with the experimental result, and use both quantum defect theory and a statistical capture model to provide an intuitive understanding of the system. This result establishes that, in contrast to the commonly held opinion, there exists a large class of systems that exhibit efficient vibrational cooling and therefore supports a new route to realize the long-sought opportunities offered by molecular structure.

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Electronics of an ion trap with integrated time-of-flight mass spectrometer
Christian Schneider, Steven J. Schowalter, Peter Yu, and Eric R. Hudson
Int. J. Mass Spec 394, 1 (2015)

Recently, we reported an ion trap experiment with an integrated time-of-flight mass spectrometer (TOFMS) [1] focusing on the improvement of mass resolution and detection limit due to sample preparation at millikelvin temperatures. The system utilizes a radio-frequency (RF) ion trap with asymmetric drive for storing and manipulating laser-cooled ions and features radial extraction into a compact 275 mm long TOF drift tube. The mass resolution exceeds m/Δm = 500, which provides isotopic resolution over the whole mass range of interest in current experiments and constitutes an improvement of almost an order of magnitude over other implementations. In this article, we discuss the experimental implementation in detail, which is comprised of newly developed drive electronics for generating the required voltages to operate RF trap and TOFMS, as well as control electronics for regulating RF outputs and synchronizing the TOFMS extraction.

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Radiative lifetime and energy of the low-energy isomeric level in 229Th
E.V. Tkalya, Christian Schneider, Justin Jeet, and Eric R. Hudson
Phys. Rev. D 92, 054324 (2015) 

We estimate the range of the radiative lifetime and energy of the anomalous, low-energy 3/2+(7.8±0.5 eV) state in the 229Th nucleus. Our phenomenological calculations are based on the available experimental data for the intensities of M1 and E2 transitions between excited levels of the 229Th nucleus in the Kπ[NnZΛ]=5/2+[633] and 3/2+[631] rotational bands. We also discuss the influence of certain branching coefficients, which affect the currently accepted measured energy of the isomeric state. From this work, we establish a favored region, 0.66×106 s eV3/ω3 ≤ τ ≤ 2.2×106 s eV3/ω3, where the transition lifetime τ as a function of transition energy ω should lie at roughly the 95% confidence level. Together with the result of Becket al. [LLNL-PROC-415170 (2009)], we establish a favored area where transition lifetime and energy should lie at roughly the 90% confidence level. We also suggest new nuclear physics measurements, which would significantly reduce the ambiguity in the present data.

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Photodissociation spectroscopy of the dysprosium monochloride molecular ion
Alexander J. Dunning, Alexander Petrov, Steven J. Schowalter, Prateek Puri, Svetlana Kotochigova, and Eric R. Hudson
J. Chem. Phys. 143, 124309 (2015).

We have performed a combined experimental and theoretical study of the photodissociation cross section of the molecular ion DyCl+. The photodissociation cross section for the photon energy range 35 500 cm−1 to 47 500 cm−1 is measured using an integrated ion trap and time-of-flight mass spectrometer; we observe a broad, asymmetric profile that is peaked near 43 000 cm−1. The theoretical cross section is determined from electronic potentials and transition dipole moments calculated using the relativistic configuration-interaction valence-bond and coupled-cluster methods. The electronic structure of DyCl+ is extremely complex due to the presence of multiple open electronic shells, including the 4f10configuration. The molecule has nine attractive potentials with ionically bonded electrons and 99 repulsive potentials dissociating to a ground state Dy+ ion and Cl atom. We explain the lack of symmetry in the cross section as due to multiple contributions from one-electron-dominated transitions between the vibrational ground state and several resolved repulsive excited states.

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Results of a Direct Search Using Synchrotron Radiation for the Low-Energy 229Th Nuclear Isomeric Transition
Justin Jeet, Christian Schneider, Scott T. Sullivan, Wade G. Rellergert, Saed Mirzadeh, A. Cassanho, H.P. Jenssen, Eugene V. Tkalya, and Eric R. Hudson
Phys. Rev. Lett. 114, 253001 (2015)

We report the results of a direct search for the 229Th (Iπ=3/2+←5/2+) nuclear isomeric transition, performed by exposing 229Th-doped LiSrAlF6 crystals to tunable vacuum-ultraviolet synchrotron radiation and observing any resulting fluorescence. We also use existing nuclear physics data to establish a range of possible transition strengths for the isomeric transition. We find no evidence for the thorium nuclear transition between 7.3 eV and 8.8 eV with transition lifetime (1–2) s≲τ≲(2000–5600)  s. This measurement excludes roughly half of the favored transition search area and can be used to direct future searches.

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Laser-Cooling-Assisted Mass Spectrometry
Christian Schneider, Steven J. Schowalter, Kuang Chen, Scott T. Sullivan, and Eric R. Hudson
Phys. Rev. App. 2, 034013 (2014)

Mass spectrometry is used in a wide range of scientific disciplines including proteomics, pharmaceutics, forensics, and fundamental physics and chemistry. Given this ubiquity, there is a worldwide effort to improve the efficiency and resolution of mass spectrometers. However, the performance of all techniques is ultimately limited by the initial phase-space distribution of the molecules being analyzed. Here, we dramatically reduce the width of this initial phase-space distribution by sympathetically cooling the input molecules with laser-cooled, cotrapped atomic ions, improving both the mass resolution and detection efficiency of a time-of-flight mass spectrometer by over an order of magnitude. Detailed molecular-dynamics simulations verify the technique and aid with evaluating its effectiveness. This technique appears to be applicable to other types of mass spectrometers.
            
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Action spectroscopy of SrCl+ using an integrated ion trap time-of-flight mass spectrometer
Prateek Puri, Steven J. Schowalter, Svetlana Kotochigova, Alexander Petrov, and Eric R. Hudson
J. Chem. Phys. 141, 014309 (2014)

The photodissociation cross-section of SrCl+ is measured in the spectral range of 36 000–46 000 cm1 using a modular time-of-flight mass spectrometer (TOF-MS). By irradiating a sample of trapped SrCl+ molecular ions with a pulsed dye laser, X1Σ+ state molecular ions are electronically excited to the repulsive wall of the A1Π state, resulting in dissociation. Using the TOF-MS, the product fragments are detected and the photodissociation cross-section is determined for a broad range of photon energies. Detailed ab initio calculations of the SrCl+ molecular potentials and spectroscopic constants are also performed and are found to be in good agreement with experiment. The spectroscopic constants for SrCl+ are also compared to those of another alkaline earth halogen, BaCl+, in order to highlight structural differences between the two molecular ions. This work represents the first spectroscopy and ab initio calculations of SrCl+.

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Neutral Gas Sympathetic Cooling of an Ion in a Paul Trap
Kuang Chen, Scott T. Sullivan, and Eric R. Hudson
Phys. Rev. Lett. 112, 143009 (11 April 2014)

A single ion immersed in a neutral buffer gas is studied. An analytical model is developed that gives a complete description of the dynamics and steady-state properties of the ions. An extension of this model, using techniques employed in the mathematics of economics and finance, is used to explain the recent observation of non-Maxwellian statistics for these systems. Taken together, these results offer an explanation of the long-standing issues associated with sympathetic cooling of an ion by a neutral buffer gas.

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Measurement of the Coulomb Logarithm in a Radio-Frequency Paul Trap
Kuang Chen, Scott T. Sullivan, Wade G. Rellergert, and Eric R. Hudson
Phys. Rev. Lett. 110, 173003/1-5 (23 April 2013)

Samples of ultracold 174Yb+ ions, confined in a linear radio-frequency Paul trap, are heated via micromotion interruption, while their temperature, density, and therefore structural phase are monitored and simulated. The observed time evolution of the ion temperature is compared to a theoretical model for ion-ion heating allowing a direct measurement of the Coulomb logarithm in a linear Paul trap. This result permits a simple, yet accurate, analytical description of ion cloud thermodynamic properties, e.g., density, temperature, and structural phase, as well as suggests limits to and improvements for ongoing trapped-ion quantum information efforts.

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Evidence for sympathetic vibrational cooling of translationally cold molecules
Wade G. Rellergert, Scott T. Sullivan, Steven J. Schowalter, Svetlana Kotochigova, Kuang Chen and Eric R. Hudson
Nature 495, 490–494 (28 March 2013)

Compared with atoms, molecules have a rich internal structure that offers many opportunities for technological and scientific advancement. The study of this structure could yield critical insights into quantum chemistry, new methods for manipulating quantum information, and improved tests of discrete symmetry violation, and fundamental constant variation. Harnessing this potential typically requires the preparation of cold molecules in their quantum rovibrational ground state. However, the molecular internal structure severely complicates efforts to produce such samples. Removal of energy stored in long-lived vibrational levels is particularly problematic because optical transitions between vibrational levels are not governed by strict selection rules, which makes laser cooling difficult. Additionally, traditional collisional, or sympathetic, cooling methods are inefficient at quenching molecular vibrational motion. Here we experimentally demonstrate that the vibrational motion of trapped BaC+ molecules is quenched by collisions with ultracold calcium atoms at a rate comparable to the classical scattering, or Langevin, rate. This is over four orders of magnitude more efficient than traditional sympathetic cooling schemes. The high cooling rate, a consequence of a strong interaction potential (due to the high polarizability of calcium), along with the low collision energies involved, leads to molecular samples with a vibrational ground-state occupancy of at least 90 per cent. Our demonstration uses a novel thermometry technique that relies on relative photodissociation yields. Although the decrease in vibrational temperature is modest, with straightforward improvements it should be possible to produce molecular samples with a vibrational ground-state occupancy greater than 99 per cent in less than 100 milliseconds. Because sympathetic cooling of molecular rotational motion is much more efficient than vibrational cooling in traditional systems, we expect that the method also allows efficient cooling of the rotational motion of the molecules. Moreover, the technique should work for many different combinations of ultracold atoms and molecules. 

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Role of Electronic Excitations in Ground-State-Forbidden Inelastic Collisions Between Ultracold Atoms and Ions
Scott T. Sullivan, Wade G. Rellergert, Svetlana Kotochigova, and Eric R. Hudson
Phys. Rev. Lett. 109, 223002 (December 2012)

The role of electronic excitation in inelastic collisions between ultracold Ca atoms and Ba+ ions, confined in a hybrid trap, is studied for the first time. Unlike previous investigations, this system is energetically precluded from undergoing inelastic collisions in its ground state, allowing a relatively simple experimental determination and interpretation of the influence of electronic excitation. It is found that while the electronic state of the ion can critically influence the inelastic collision rate, the polarizability mismatch of the neutral atom electronic states suppresses short-range collisions, and thus inelastic processes, involving electronically excited neutral atoms. As a result of these features, it is experimentally demonstrated that it is possible to mitigate inelastic collision loss mechanisms in these systems, marking an important step toward long-lived hybrid atom-ion devices.

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Low-threshold ultraviolet solid-state laser based on a Ce3+:LiCaAlF6 crystal resonator
Thanh Le, Steven J. Schowalter, Wade Rellergert, Justin Jeet, Guoping Lin, Nan Yu and Eric R. Hudson
Optics Letters 37, 4961-4963 (December 2012)

A low-threshold solid-state UV laser using a whispering gallery mode (WGM) resonator constructed from UV transparent crystalline material is demonstrated. Using a Ce3+:LiCaAlF6 resonator, we observe broad bandwidth lasing (280–330 nm) with a low threshold intensity of 7.5×109 W/m2 and an effective slope efficiency of ∼25%. The lasing time delay dynamics in the pulsed operation mode are also observed and analyzed. Additionally, a LiCaAlF6 WGM resonator with Q=2×107 at 370 nm is realized. The combination of this high Q and the small WGM mode volume significantly lowers the pump power threshold compared to traditional cavity designs, opening the door for both tunable continuous-wave and mode-locked operation.

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An integrated ion trap and time-of-flight mass spectrometer for chemical and photo-reaction dynamics studies
Steven J. Schowalter, Kuang Chen, Wade G. Rellergert, Scott T. Sullivan, and Eric R. Hudson
Rev. Sci. Instrum. 83, 043103 (April 2012) 

We demonstrate the integration of a linear quadrupole trap with a simple time-of-flight mass spectrometer with medium-mass resolution (m/Δm ∼ 50) geared towards the demands of atomic, molecular, and chemical physics experiments. By utilizing a novel radial ion extraction scheme from the linear quadrupole trap into the mass analyzer, a device with large trap capacity and high optical access is realized without sacrificing mass resolution. This provides the ability to address trapped ions with laser light and facilitates interactions with neutral background gases prior to analyzing the trapped ions. Here, we describe the construction and implementation of the device as well as present representative ToF spectra. We conclude by demonstrating the flexibility of the device with proof-of-principle experiments that include the observation of molecular-ion photodissociation and the measurement of trapped-ion chemical reaction rates.

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Optical spectroscopy of an atomic nucleus: Progress toward direct observation of the 229Th isomer transition
Markus P. Hehlen, Richard R. Greco, Wade G. Rellergert, Scott T. Sullivan, David DeMille, Robert A. Jackson, Eric R. Hudson, and Justin R. Torgerson
J. Lum., 133, 91 (2013)

The nucleus of the thorium-229 isotope possesses a first excited nuclear state (229mTh) at an exceptionally low energy of 7.8±0.5 eV above the nuclear ground state (229gTh), as determined by earlier indirect measurements. This is the only nuclear excited state known that is within the range of optical spectroscopy. This paper reports progress toward detecting the 229mTh state directly by luminescence spectroscopy in the vacuum ultraviolet spectral region. The estimated natural linewidth of the 229gTh↔229mTh isomer transition of 2π×0.1 to 2π×10 mHz is expected to broaden to ∼10 kHz for 229Th4+ doped into a suitable crystal. The factors governing the choice of crystal system and the substantial challenges in acquiring a sufficiently large quantity of 229Th are discussed. We show that the 229gTh↔229mTh transition energy can be identified to within 0.1 nm by luminescence excitation and luminescence spectroscopy using the Advanced Light Source (ALS) at Lawrence Berkeley National Laboratory. This would open the door for subsequent laser-based measurements of the isomer transition and future applications of 229Th in nuclear clocks. We also show that 233U-doped materials should produce an intrinsic, continuous, and sufficiently high rate of 229mTh→229gTh luminescence and could be a useful aid in the initial direct search of the isomer transition.

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Measurement of a Large Chemical Reaction Rate between Ultracold Closed-Shell 40Ca Atoms and Open-Shell 174Yb+ Ions Held in a Hybrid Atom-Ion Trap
Wade G. Rellergert, Scott T. Sullivan, Svetlana Kotochigova, Alexander Petrov, Kuang Chen, Steven J. Schowalter, and Eric R. Hudson 
Phys. Rev. Lett. 107, 243201 (Dec 2011)

Ultracold 174Yb+ ions and 40Ca atoms are confined in a hybrid trap. The charge exchange chemical reaction rate constant between these two species is measured and found to be 4 orders of magnitude larger than recent measurements in other heteronuclear systems. The structure of the CaYb+ molecule is determined and used in a calculation that explains the fast chemical reaction as a consequence of strong radiative charge transfer. A possible explanation is offered for the apparent contradiction between typical theoretical predictions and measurements of the radiative association process in this and other recent experiments.

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Trapping molecular ions formed via photo-associative ionization of ultracold atoms
Scott T. Sullivan, Wade G. Rellergert, Svetlana Kotochigova, Kuang Chen, Steven J. Schowalter, Eric R. Hudson
Phys. Chem. Chem. Phys., 13, 18859-18863 (2011)

The formation of 40Ca2+ molecular ions is observed in a hybrid 40Ca magneto-optical and ion trap system. The molecular ion formation process is determined to be photo-associative ionization of ultracold 40Ca atoms. A lower bound for the two-body rate constant is found to be β ≥ 2 ± 1 × 10−15 cm3 Hz. Ab initio molecular potential curves are calculated for the neutral Ca2 and ionic Ca2+ molecules and used in a model that identifies the photo-associative ionization pathway. As this technique does not require a separate photo-association laser, it could find use as a simple, robust method for producing ultracold molecular ions.

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Molecular-ion trap-depletion spectroscopy of BaCl+
Kuang Chen, Steven J. Schowalter, Svetlana Kotochigova, Alexander Petrov, Wade G. Rellergert, Scott T. Sullivan, and Eric R. Hudson
Phys. Rev. A 83, 030501 (March 2011)

We demonstrate a simple technique for molecular-ion spectroscopy. BaCl+ molecular ions are trapped in a linear Paul trap in the presence of a room-temperature He buffer gas and photodissociated by driving an electronic transition from the ground X 1Σ+ state to the repulsive wall of the A 1Π state. The photodissociation spectrum is recorded by monitoring the induced trap loss of BaCl+ ions as a function of excitation wavelength. Accurate molecular potentials and spectroscopic constants are determined. A comparison of the theoretical photodissociation cross sections with the measurements shows excellent agreement. This study represents an important step toward the production of ultracold ground-state molecular ions.

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Progress towards fabrication of 229Th-doped high energy band-gap crystals for use as a solid-state optical frequency reference
W.G. Rellergert, S.T. Sullivan, D. DeMille, R.R. Greco, M.P. Hehlen, R.A. Jackson, J.R. Torgerson, and Eric R. Hudson
IOP Conf. Ser. Mater. Sci. Eng. 15, 012005 (2010)

We have recently described a novel method for the construction of a solid-state optical frequency reference based on doping 229Th into high energy band-gap crystals. Since nuclear transitions are far less sensitive to environmental conditions than atomic transitions, we have argued that the 229Th optical nuclear transition may be driven inside a host crystal resulting in an optical frequency reference with a short-term stability of 3 × 10−17 < Δf/f < 1 × 10−15 at 1 s and a systematic-limited repeatability of Δf/f ~2 × 10−16. Improvement by 102 – 103 of the constraints on the variability of several important fundamental constants also appears possible. Here we present the results of the first phase of these experiments. Specifically, we have evaluated several high energy band-gap crystals (Th:NaYF, Th:YLF, Th:LiCAF, Na2ThF6, LiSAF) for their suitability as a crystal host by a combination of electron beam microprobe measurements, Rutherford Backscattering, and synchrotron excitation/fluorescence measurements. These measurements have shown LiCAF to be the most promising host crystal, and using a 232Th doped LiCAF crystal, we have performed a mock run of the actual experiment that will be used to search for the isomeric transition in 229Th. This data indicates that a measurement of the transition energy with a signal to noise ratio (SNR) greater than 30:1 can be achieved at the lowest expected fluorescence rate.

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Constraining the Evolution of the Fundamental Constants with a Solid-State Optical Frequency Reference Based on the 229Th Nucleus
W.G. Rellergert, D. DeMille, R.R. Greco, M.P. Hehlen, J.R. Torgerson, E.R. Hudson
Phys. Rev. Lett. 104, 200802 (2010) 

We describe a novel approach to directly measure the energy of the narrow, low-lying isomeric state in Th-229. Since nuclear transitions are far less sensitive to environmental conditions than atomic transitions, we argue that the Th-229 optical nuclear transition may be driven inside a host crystal with a high transition Q. This technique might also allow for the construction of a solid-state optical frequency reference that surpasses the short-term stability of current optical clocks, as well as improved limits on the variability of fundamental constants. Based on analysis of the crystal lattice environment, we argue that a precision (short-term stability) of 3×10−17<Δf/f><1×10−15 after 1 s of photon collection may be achieved with a systematic-limited accuracy (long-term stability) of Δf/f∼2×10−16. Improvement by 102−103 of the constraints on the variability of several important fundamental constants also appears possible.

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Method for producing ultracold molecular ions
Eric R. Hudson
Phys. Rev. A 79, 032716 (2009)

We propose a method for the production of ultracold molecular ions. This method utilizes sympathetic cooling due to the strong collisions between appropriately chosen molecular ions and laser-cooled neutral atoms to realize ultracold internal ground-state molecular ions. In contrast to other experiments producing cold molecular ions, our proposed method efficiently cools both the internal and external molecular-ion degrees of freedom. The availability of an ultracold, absolute ground-state sample of molecular ions would have broad impact to fields as diverse as quantum chemistry, astrophysics, and fundamental physics and may lead to the development of a robust scalable quantum computer.
            
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Deceleration of continuous molecular beams
Eric R. Hudson  <br />
Phys Rev. A 73, 061407 (2009)

A method for decelerating a continuous beam of neutral polar molecules is theoretically demonstrated. This method utilizes nonuniform static electric fields and regions of adiabatic population transfer to generate a mechanical force that opposes the molecular beam’s velocity. By coupling this technique with dissipative trap-loading molecular densities ≥1011 cm−3 are possible.

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Computer modelling of thorium doping in LiCaAlF6 and LiSrAlF6: application to the development of solid state optical frequency devices
R. A. Jackson, J.B. Amaral, M.E.G. Valerio, D. DeMille, and Eric R. Hudson
J. Phys: Cond. Matt. 21, 325403 (2009)

This paper describes computer modelling of thorium doping in crystalline LiCaAlF6 and LiSrAlF6. The study has been motivated by the interest in using these materials as hosts for 229Th nuclei, which are being investigated for use as frequency standards. The dopant sites and form of charge compensation are obtained; this information is essential for the further development and optimization of these devices.

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