Bose-Einstein condensates in toroidal traps: instabilities, swallow-tail loops, and self-trapping

Abstract

We study the stability and dynamics of an ultra-cold bosonic gas trapped in a toroidal geometry and driven by rotation, in the absence of dissipation. We first delineate, via the Bogoliubov mode expansion, the regions of stability and the nature of instabilities of the system for both repulsive and attractive interaction strengths. To study the response of the system to variations in the rotation rate, we introduce a "disorder" potential, breaking the rotational symmetry. We demonstrate the breakdown of adiabaticity as the rotation rate is slowly varied and find forced tunneling between the system's eigenstates. The non-adiabaticity is signaled by the appearance of a swallow-tail loop in the lowest-energy level, a general sign of hysteresis. Then, we show that this system is in one-to-one correspondence with a trapped gas in a double-well potential and thus exhibits macroscopic quantum self-trapping. Finally, we show that self-trapping is a direct manifestation of the behavior of the lowest-energy level.

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• Quantum simulation of non-trivial topology
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• Vortices in a toroidal Bose-Einstein condensate with a rotating weak link
• Impurity in a bosonic Josephson junction: swallowtail loops, chaos, self-trapping and the poor man's Dicke model
• Nonlinear Phenomena of Ultracold Atomic Gases in Optical Lattices: Emergence of Novel Features in Extended States
• Metastability, excitations, fluctuations, and multiple-swallowtail structures of a superfluid in a Bose-Einstein condensate in the presence of a uniformly moving defect
• Self trapping of a dipolar Bose-Einstein condensate in a double well
• Fine structure of the stripe phase in ring-shaped Bose-Einstein condensates with spin-orbital-angular-momentum coupling
• Bose-Einstein condensate confined in a 1D ring stirred with a rotating delta link
• Hysteresis and metastability of Bose-Einstein condensed clouds of atoms confined in ring potentials
• Spin-orbit-coupled spin-1 Bose-Einstein condensates in a toroidal trap: even-petal-number necklacelike state and persistent flow
• Superfluidity fraction of few bosons in an annular geometry in the presence of a rotating weak link
• Current production in ring condensates with a weak link
• Acoustic analogue of Hawking radiation in quantized circular superflows of Bose-Einstein condensates
• Hidden vortices and Feynman rule in Bose-Einstein condensates with density-dependent gauge potential
• Quasistatic transfer protocols for atomtronic superfluid circuits
• Quantum irreversibility of quasistatic protocols for finite-size quantized systems
• Protocol for nonlinear state discrimination in rotating condensate
• Mixture of two unequally charged superfluids in a magnetic field
• Metastability, chaos and spectrum tomography for Bose-Hubbard rings and chains
• Stochastic modeling of spreading and dissipation in mixed-chaotic systems that are driven quasistatically