Geometrizing quantum dynamics of a Bose-Einstein condensate

Abstract

We show that quantum dynamics of Bose-Einstein condensates in the weakly interacting regime can be geometrized by a Poincaré disk. Each point on such a disk represents a thermofield double state, the overlap between which equals the metric of this hyperbolic space. This approach leads to a unique geometric interpretation of stable and unstable modes as closed and open trajectories on the Poincaré disk, respectively. The resonant modes that follow geodesics naturally equate fundamental quantities including the time, the length, and the temperature. Our work suggests a new geometric framework to coherently control quantum systems and reverse their dynamics using SU(1,1) echoes. In the presence of perturbations breaking the SU(1,1) symmetry, SU(1,1) echoes deliver a new means to measure these perturbations such as the interactions between excited particles.

arXiv comment6 pages (4 figures) + 3 pages (2 figures)

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Cited by in corpus (13)

• Geometric approach to inhomogeneous Floquet systems
• SU(1,1) echoes for breathers in quantum gases
• Many-body Dynamics with Time-dependent Interaction
• Quantum Dynamics of Cold Atomic Gas with $SU(1,1)$ Symmetry
• Quantum Echo in Two-Component Bose-Einstein Condensates
• The Quantum Dynamics of Two-component Bose-Einstein Condensate: an $Sp(4,R)$ Symmetry Approach
• The Uhlmann Phase Winding in Bose-Einstein Condensates at Finite Temperature
• Quantum walk for SU(1,1)
• Echoes and defects in the Calogero model
• Interference-induced suppression of particle emission from a Bose-Einstein condensate in lattice with time-periodic modulations
• Ferroelectricity in a magnon Bose-Einstein condensate: Nonreciprocal superfluidity, exceptional points, and Majorana bosons
• Tailored generation of quantum states in an entangled spinor interferometer to overcome detection noise
• Phase transitions from Heating to non-heating in SU(1, 1) quantum dynamics: applications to Bose-Einstein condensates and periodically driven coupled oscillators