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Relaxation of Bosons in One Dimension and the Onset of Dimensional Crossover

by Chen Li, Tianwei Zhou, Igor Mazets, Hans-Peter Stimming, Frederik S. Møller, Zijie Zhu, Yueyang Zhai, Wei Xiong, Xiaoji Zhou, Xuzong Chen, Jörg Schmiedmayer

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Submission summary

Authors (as registered SciPost users): Chen Li · Frederik Skovbo Møller · Jörg Schmiedmayer
Submission information
Preprint Link:  (pdf)
Date accepted: 2020-10-13
Date submitted: 2020-10-06 12:43
Submitted by: Li, Chen
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
  • Atomic, Molecular and Optical Physics - Experiment
  • Quantum Physics
Approach: Experimental


We study ultra-cold bosons out of equilibrium in a one-dimensional (1D) setting and probe the breaking of integrability and the resulting relaxation at the onset of the crossover from one to three dimensions. In a quantum Newton's cradle type experiment, we excite the atoms to oscillate and collide in an array of 1D tubes and observe the evolution for up to 4.8 seconds (400 oscillations) with minimal heating and loss. By investigating the dynamics of the longitudinal momentum distribution function and the transverse excitation, we observe and quantify a two-stage relaxation process. In the initial stage single-body dephasing reduces the 1D densities, thus rapidly drives the 1D gas out of the quantum degenerate regime. The momentum distribution function asymptotically approaches the distribution of quasimomenta (rapidities), which are conserved in an integrable system. In the subsequent long time evolution, the 1D gas slowly relaxes towards thermal equilibrium through the collisions with transversely excited atoms. Moreover, we tune the dynamics in the dimensional crossover by initializing the evolution with different imprinted longitudinal momenta (energies). The dynamical evolution towards the relaxed state is quantitatively described by a semiclassical molecular dynamics simulation.

Author comments upon resubmission

We thank the referees for the constructive suggestions. Their comments are addressed with the changes listed below. And more details are described in our replies to the referees.

List of changes

- According to Referee 1's comments, in Sec. 1 Para. 1-2, we replaced the term 'relax' with 'thermalize' and revised the relevant statements to eliminate any possible confusion.
- According to Referee 2's comment 1, in Sec. 1 Para. 5, a general introduction of molecular dynamics (MD) and Ref [35] were added to satisfy a broad audience. Additionally, Sec. 6 Para. 2 was formulated to improve the description of our molecular dynamics method.
- According to Referee 2's comment 2, in Sec. 5 Para. 2 and Sec. 6 Para. 2, we offered the justification of our statement that the dynamics mostly happened in the non-degenerate regime.
- According to Referee 2's comment 3, in the caption of Fig.3, it was clarified that the plots showed experimental measurements.
- According to Referee 2's comment 4, in Sec. 2.1 Para. 1 and Appendix A.1 Para. 2, the variations of ω_∥ and ω_⊥ over the occupied tubes were clarified.
- According to Referee 2's comment 5, in Sec. 1 Para. 1, an inappropriate statement was removed.
- According to Referee 2's comment 6, in Sec. 3 Para. 1, we declared that the results shown in Fig. 4 were consistent with the expectations.
- According to Referee 2's comment 7, we replaced 'rapidity' with 'quasimomentum' so that the terminology is consistent throughout the manuscript.
- Typos were corrected.
- The affiliation and funding information of Igor Mazets and Hans-Peter Stimming have been updated.

Published as SciPost Phys. 9, 058 (2020)

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