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

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 Poincaré 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 Poincaré 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.

arXiv comment10 pages,4,figures

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Cited by in corpus (6)

• Quantum Echo in Two-Component Bose-Einstein Condensates
• Exact Dynamics and Shortcuts to Adiabaticity in the Tomonaga-Luttinger Liquid
• The Uhlmann Phase Winding in Bose-Einstein Condensates at Finite Temperature
• Transitionless Quantum Driving of the Tomonaga-Luttinger Liquid
• Interference-induced suppression of particle emission from a Bose-Einstein condensate in lattice with time-periodic modulations
• Phase transitions from Heating to non-heating in SU(1, 1) quantum dynamics: applications to Bose-Einstein condensates and periodically driven coupled oscillators