Many-body Dynamics with Time-dependent Interaction

Abstract

Recent advances in optical Feshbach resonance technique have enabled the experimental investigation of atomic gases with time-dependent interaction. In this work, we study the many-body dynamics of weakly interacting bosons subject with an arbitrary time varying scattering length. By employing a variational ansatz, we derive an effective Hamiltonian that governs the dynamics of thermal particles. Crucially, we show that there exists a hidden symmetry in this Hamiltonian that can map the many-body dynamics to the precession of an SU(1,1) "spin". As a demonstration, we calculate the situation where the scattering length is sinusoidally modulated. We show that the non-compactness of the SU(1,1) group naturally leads to solutions with exponentially growth of Bogoliubov modes and causes instabilities.

arXiv comment5 pages, 3 figures

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• Geometric approach to inhomogeneous Floquet systems
• SU(1,1) echoes for breathers in quantum gases
• Geometrizing quantum dynamics of a Bose-Einstein condensate
• Complex contact interaction for systems with short-range two-body loss
• Quantum Dynamics of Cold Atomic Gas with $SU(1,1)$ Symmetry
• Topological Micromotion of Floquet Quantum Systems
• The Quantum Dynamics of Two-component Bose-Einstein Condensate: an $Sp(4,R)$ Symmetry Approach
• Weakly interacting Bose gas with two-body losses
• Quantum walk for SU(1,1)