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arXiv · 2201.04304

Quantum Dynamics of Cold Atomic Gas with $SU(1,1)$ Symmetry

Jing Zhang·Xiaoyi Yang·Chenwei Lv·Shengli Ma·Ren Zhang
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Abstract

Motivated by recent advances in quantum dynamics, we investigate the dynamics of the system with $SU(1,1)$ symmetry. Instead of performing the time-ordered integral for the evolution operator of the time-dependent Hamiltonian, we show that the time evolution operator can be expressed as an $SU(1,1)$ group element. Since the $SU(1,1)$ group describes the "rotation" on a hyperbolic surface, the dynamics can be visualized on a Poincar\'e disk, a stereographic projection of the upper hyperboloid. As an example, we present the trajectory of the revival of Bose-Einstein condensation and that of the scale-invariant Fermi gas on the Poincar\'e disk. Further considering the quantum gas in the oscillating lattice, we also study the dynamics of the system with time-dependent single-particle dispersion. Our results are hopefully to be checked in current experiments.

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Jing Zhang, Xiaoyi Yang, Chenwei Lv, Shengli Ma, Ren Zhang. 2022-01-12. Quantum Dynamics of Cold Atomic Gas with $SU(1,1)$ Symmetry. https://doi.org/10.1103/physreva.106.013314

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