Periodically and Quasi-periodically Driven Dynamics of Bose-Einstein Condensates

Abstract

We study the quantum dynamics of Bose-Einstein condensates when the scattering length is modulated periodically or quasi-periodically in time within the Bogoliubov framework. For the periodically driven case, we consider two protocols where the modulation is a square-wave or a sine-wave. In both protocols for each fixed momentum, there are heating and non-heating phases, and a phase boundary between them. The two phases are distinguished by whether the number of excited particles grows exponentially or not. For the quasi-periodically driven case, we again consider two protocols: the square-wave quasi-periodicity, where the excitations are generated for almost all parameters as an analog of the Fibonacci-type quasi-crystal; and the sine-wave quasi-periodicity, where there is a finite measure parameter regime for the non-heating phase. We also plot the analogs of the Hofstadter butterfly for both protocols.

23 pages, 7 figures

References in corpus (8)

• Photovoltaic Hall effect in graphene
• Measuring the Chern number of Hofstadter bands with ultracold bosonic atoms
• Localization in one-dimensional incommensurate lattices beyond the Aubry-André model
• Collective emission of matter-wave jets from driven Bose-Einstein condensates
• Emergent Spatial Structure and Entanglement Localization in Floquet Conformal Field Theory
• The fine structure of heating in a quasiperiodically driven critical quantum system
• Operator Product Expansion and Conservation Laws in Non-Relativistic Conformal Field Theories
• Many-Body Echo

Cited by in corpus (7)

• Geometric approach to inhomogeneous Floquet systems
• Periodically, Quasi-periodically, and Randomly Driven Conformal Field Theories (II): Furstenberg's Theorem and Exceptions to Heating Phases
• Quantum Dynamics of Cold Atomic Gas with $SU(1,1)$ Symmetry
• Patterns, spin-spin correlations and competing instabilities in driven quasi-two-dimensional spin-1 Bose-Einstein condensates
• Quasi-localization dynamics in a Fibonacci quantum rotor
• The Uhlmann Phase Winding in Bose-Einstein Condensates at Finite Temperature
• Interference-induced suppression of particle emission from a Bose-Einstein condensate in lattice with time-periodic modulations