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arXiv:2410.17666 · Physical Review A

Instability and particle-current control of a parametrically driven Bose-Einstein condensate in a ring-shaped lattice

L. Q. Lai

Published Jan 6, 2025• 1 citation
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Abstract

We investigate the dynamics of a Bose-Einstein condensate in a one-dimensional ring-shaped lattice with the Peierls phase and site-dependent modulations, where the condensate is confined in a single deep trap and the interparticle interaction strength is modulated by a time-periodic driving field. The system has a finite spectrum, which limits the excitation regimes, and the Peierls phase typically induces imbalanced complex hopping amplitudes in each direction, leading to nonzero net particle currents along the lattice chain, which can hold nearly persistent even when the driving field is turned off after half of the period. The configuration provides a specific way for the coherent control of particle currents in many-body quantum systems with the help of an external driving field and promotes the possible applications in future closed-loop atom circuits.

DOI
10.1103/physreva.111.013304

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We study the dynamics of persistent bosonic currents in closed-loop atom circuits in the form of ring lattices and under the action of time periodic driving. The closed-loop atom circuits are described by a Bose-Hubbard model in the presence of a Peierls phase and with periodic boundary conditions. We find that the motion of matter waves can be controlled with the help of an external driving only applied in one site of the ring lattice. For tuned values of the interaction strength between particles, we show that there exists a frequency range of the external driving where not only suppression but also reversion of the persistent bosonic currents is achieved. Applications of our results are discussed.
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We study the stability of persistent currents in a coherently coupled quasi-two-dimensional Bose-Einstein condensate confined in a ring trap at T=0T=0T=0. By numerically solving Gross-Pitaevskii equations and by analyzing the excitation spectrum obtained from diagonalization of the Bogoliubov--de Gennes matrix, we describe the mechanisms responsible for the decay of the persistent currents depending on the values of the interaction coupling constants and the Rabi frequency. When the unpolarized system decays due to an energetic instability in the density channel, the spectrum may develop a rotonlike minimum, which gives rise to the finite wavelength excitation necessary for vortex nucleation at the inner surface. When decay in the unpolarized system is driven by spin-density excitations, the finite wavelength naturally arises from the existence of a gap in the excitation spectrum. In the polarized phase of the coherently coupled condensate, there is a hybridization of the excitation modes that leads to complex decay dynamics. In particular, close to the phase transition, a state of broken rotational symmetry is found to be stationary and stable.
Time-periodic driving has been an effective tool in the field of nonequilibrium quantum dynamics, which enables precise control of the particle interactions. We investigate the collective emission of particles from a Bose–Einstein condensate in a one-dimensional lattice with periodic drives that are separate in modulation amplitudes and relative phases. In addition to the enhancement of particle emission, we find that amplitude imbalances lead to energy shift and band broadening, while typical relative phases may give rise to similar gaps. These results offer insights into the specific manipulations of nonequilibrium quantum systems with tone-varying drives.
We study a special dynamical regime of a Bose-Einstein condensate in a ring-shaped lattice where the populations in each site remain constant during the time evolution. The states in this regime are characterized by equal occupation numbers in alternate wells and nontrivial phases, while the phase differences between neighboring sites evolve in time yielding persistent currents that oscillate around the lattice. We show that the velocity circulation around the ring lattice alternates between two values determined by the number of wells and with a specific time period that is only driven by the on-site interaction energy parameter. In contrast to the self-trapping regime present in optical lattices, the occupation number at each site does not show any oscillation and the particle imbalance does not possess a lower bound for the phenomenon to occur. These findings are predicted with a multimode model and confirmed by full three-dimensional Gross-Pitaevskii simulations using an effective on-site interaction energy parameter.