Testing randomness in quantum mechanics

It is possible to construct algorithms to produce random numbers. However, even the more advanced algorithms show cycling after a finite number of iterations: that is to say, the sequences of “random” numbers repeat themselves eventually, and in that sense the numbers are not truly random [1].

Two examples of natural processes that occur randomly are beta-decay in the nucleus and spontaneous decay from at atom in an excited electronic state. It is not possible to predict exactly when these decay events will occur, only that many decays will, overall, yield the measured half-life of that particular substance or lifetime of a specified electronic state.

The aim of the UCLA strontium ion trap experiment is to use Dehmelt’s electron shelving idea [2] to measure the randomness of decay from a long-lived excited electronic state in 88Sr+. A single atomic ion of strontium can be excited with a laser so that it fluoresces at that wavelength and emits photons in all directions and at a rate of about 10 million per second. A certain fraction of these photons can be collected by a lens and focused onto a photomultiplier tube, which might register, typically, 40,000 counts/sec. The ion, continually excited on this strong dipole transition, is said to be “bright”. Simultaneously, however, a second laser can be used to excite the ion on a weak transition to a long-lived (metastable) state with a lifetime of around one second. When the outer valence electron of the ion resides in this state it stops its process of absorbing and emitting on the strong transition and becomes “dark”. When the ion decays back to the ground state it can once again absorb on the strong transition and so it “switches back on” and becomes bright. The time intervals of these bright and dark periods are of random duration, but precisely how random are they? Over longer timescales can correlations be found between bright or dark periods or can cycling be observed in the sequences of dark state durations?

[1] D. E. Knuth. The art of computer programming, Volume 2. Addison-Wesley, 1981.

[2] H. Dehmelt. Bull. Am. Phys. Soc., 20:60, 1975.