Scientific articles

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 mm = 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, 0.66×10s eV3≤ τ ≤ 2.2×10s eV33, 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 DyClis 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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