Abstract
With subrecoil-laser-cooled atoms, one may reach nanokelvin temperatures while the ergodic properties of these systems do not follow usual statistical laws. Instead, due to an ingenious trapping mechanism in momentum space, power-law-distributed sojourn times are found for the cooled particles. Here, we show how this gives rise to a statistical-mechanical framework based on infinite ergodic theory, which replaces ordinary ergodic statistical physics of a thermal gas of atoms. In particular, the energy of the system exhibits a sharp discontinuous transition in its ergodic properties. Physically, this is controlled by the fluorescence rate, but, more profoundly, it is a manifestation of a transition for any observable, from being an integrable to becoming a nonintegrable observable, with respect to the infinite (non-normalized) invariant density.
Highlights
With subrecoil-laser-cooled atoms, one may reach nanokelvin temperatures while the ergodic properties of these systems do not follow usual statistical laws
We show how this gives rise to a statistical-mechanical framework based on infinite ergodic theory, which replaces ordinary ergodic statistical physics of a thermal gas of atoms
The energy of the system exhibits a sharp discontinuous transition in its ergodic properties. This is controlled by the fluorescence rate, but, more profoundly, it is a manifestation of a transition for any observable, from being an integrable to becoming a nonintegrable observable, with respect to the infinite invariant density
Summary
With subrecoil-laser-cooled atoms, one may reach nanokelvin temperatures while the ergodic properties of these systems do not follow usual statistical laws. In the context of subrecoil-laser cooling, this time diverges, and, no matter how long one measures, deviations from standard ergodic theory are prominent. Our goal is to show how tools of infinite ergodic theory describe the statistical properties of the ensemble and corresponding time averages of the subrecoil-laser-cooled atoms.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
