In a system of ac-driven condensed bosons we study a new type of Josephson effect occurring between states sharing the same region of space and the same internal atom structure. We first develop a technique to calculate the long-time dynamics of a driven interacting many body system. For resonant frequencies, this dynamics can be shown to derive from an effective time-independent Hamiltonian which is expressed in terms of standard creation and annihilation operators. Within the subspace of resonant states, and if the undriven states are plane waves, a locally repulsive interaction between bosons translates into an effective attraction. We apply the method to study the effect of interactions on the coherent ratchet current of an asymmetrically driven boson system. We find a wealth of dynamical regimes which includes Rabi oscillations, self trapping and chaotic behavior. In the latter case, a full many-body calculation deviates from the mean-field results by predicting large quantum fluctuations of the relative particle number.
In a system of ac-driven condensed bosons we study a new type of Josephson effect occurring between states sharing the same region of space and the same internal atom structure. We first develop a technique to calculate the long-time dynamics of a driven interacting many body system. For resonant frequencies, this dynamics can be shown to derive from an effective time-independent Hamiltonian which is expressed in terms of standard creation and annihilation operators. Within the subspace of resonant states, and if the undriven states are plane waves, a locally repulsive interaction between bosons translates into an effective attraction. We apply the method to study the effect of interactions on the coherent ratchet current of an asymmetrically driven boson system. We find a wealth of dynamical regimes which includes Rabi oscillations, self trapping and chaotic behavior. In the latter case, a full many-body calculation deviates from the mean-field results by predicting large quantum fluctuations of the relative particle number.
In a system of ac-driven condensed bosons we study a new type of Josephson effect occurring between states sharing the same region of space and the same internal atom structure. We first develop a technique to calculate the long-time dynamics of a driven interacting many-body system. For resonant frequencies, this dynamics can be shown to derive from an effective time-independent Hamiltonian which is expressed in terms of standard creation and annihilation operators. Within the subspace of resonant states, and if the undriven states are plane waves, a locally repulsive interaction between bosons translates into an effective attraction. We apply the method to study the effect of interactions on the coherent ratchet current of an asymmetrically driven boson system. We find a wealth of dynamical regimes which includes Rabi oscillations, self-trapping and chaotic behavior. In the latter case, a full many-body calculation deviates from the mean-field results by predicting large quantum fluctuations of the relative particle number.
We show that the orbital Josephson effect appears in a wide range of driven atomic Bose–Einstein condensed systems, including quantum ratchets, double wells and box potentials. We use three separate numerical methods: the Gross–Pitaevskii equation, exact diagonalization of the few-mode problem and the multi-configurational time-dependent Hartree for bosons algorithm. We establish the limits of mean-field and few-mode descriptions, demonstrating that the few-mode approximation represents the full many-body dynamics to high accuracy in the weak driving limit. Among other quantum measures, we compute the instantaneous particle current and the occupation of natural orbitals. We explore four separate dynamical regimes, the Rabi limit, chaos, the critical point and self-trapping; a favorable comparison is found even in the regimes of dynamical instabilities or macroscopic quantum self-trapping. Finally, we present an extension of the ( t , t ')-formalism to general time-periodic equations of motion, which permits a systematic description of the long-time dynamics of resonantly driven many-body systems, including those relevant to the orbital Josephson effect.
We show that the orbital Josephson effect appears in a wide range of driven atomic Bose-Einstein condensed systems, including quantum ratchets, double wells and box potentials. We use three separate numerical methods: the Gross-Pitaevskii equation, exact diagonalization of the few-mode problem and the multi-configurational time-dependent Hartree for bosons algorithm. We establish the limits of mean-field and few-mode descriptions, demonstrating that the few-mode approximation represents the full many-body dynamics to high accuracy in the weak driving limit. Among other quantum measures, we compute the instantaneous particle current and the occupation of natural orbitals. We explore four separate dynamical regimes, the Rabi limit, chaos, the critical point and self-trapping; a favorable comparison is found even in the regimes of dynamical instabilities or macroscopic quantum self-trapping. Finally, we present an extension of the (t, t')-formalism to general time-periodic equations of motion, which permits a systematic description of the long-time dynamics of resonantly driven many-body systems, including those relevant to the orbital Josephson effect.
We investigate the collective dynamics of two-component Bose-Einstein condensates in a double well potential. By taking into account the Lee-Huang-Yang (LHY) correction from quantum fluctuation, we find that the LHY term, though much smaller than the mean field interactions, can significantly change the coherent oscillating behaviors of the bosonic Josephson junction in the regime of g12≃−g11g22 . Besides the quantitative renormalization to the plasma frequencies of the Josephson oscillations, a series of unexpected nonzero fixed points beyond mean field emerges in the stationary state. More remarkably, unique macroscopic self-trapping states, which are usually absent in the mean field dynamics, can be sustained by the LHY nonlinearity. Our results reveal the nontrivial LHY effect on the Josephson dynamics, which can be tested in the current experiment. Published by the American Physical Society 2024
The dynamics of a two-dimensional Bose-Einstein condensate mixture, loaded into a dual-core trap, when the beyond-mean-field effects are taken into account, are considered. The effects of quantum fluctuations are described by the Lee-Huang-Yang correction terms in the extended coupled Gross-Pitaevskii equations (GPE). The spatially uniform and inhomogeneous condensate cases are studied. In the first case, the parameter regimes associated with macroscopic quantum tunneling, macroscopic self-trapping, and revival-like localization dynamics are found. The Josephson oscillation frequencies for both the zero-phase and the π -phase modes are derived. As the total atom number is varied, the dynamics exhibit a nontrivial bifurcation structure: along the zero-phase branch, two successive pitchfork bifurcations generate bistability and hysteresis, while the π -phase branch shows a single pitchfork bifurcation. In the second case, the Josephson dynamics for quantum droplets and vortices are investigated. The analytical predictions for the oscillation frequencies of the atomic population between quantum droplets are found, and results are validated by direct numerical simulations of the system of coupled extended GPE. The existence of the Andreev-Bashkin nondissipative drag through simulations of droplet-droplet interactions is shown. The Josephson dynamics of vortex states are studied. It was found that vortices with topological charge S and sufficiently small particle number are typically unstable, breaking up into S + 1 (and occasionally S + 2 ) fundamental, nonvortical fragments, with the time to breakup increasing as the particle number grows. It is also found that unstable asymmetric vortices exhibit the splitting and/or crescentlike instability. For vortices with sufficiently large norms, long-time simulations confirm robust stability against small perturbations. In this stable regime, the properties of Josephson oscillations and Andreev-Bashkin-type entrainment for vortex states with charges S = 1 , 2 , and 3 are investigated.
We demonstrate that the two degenerate energy levels in spin–orbit coupled trapped Bose gases, coupled by a quenched Zeeman field, can be used for angular momentum Josephson effect. In a static quenched field, we can realize a Josephson oscillation with a period ranging from millisecond to hundreds of milliseconds. Moreover, by a driven Zeeman field, we realize a new Josephson oscillation, in which the population imbalance may have the same expression as the current in the direct-current Josephson effect. When the dynamics of the condensate cannot follow up the modulation frequency, it is in the self-trapping regime. This new dynamic is understood from the time-dependent evolution of the constant-energy trajectory in the phase space. This model has several salient advantages compared to the previous ones. The condensates are isolated from their excitations by a finite gap, thus can greatly suppress the damping effect induced by thermal atoms and Bogoliubov excitations. The oscillation period can be tuned by several orders of magnitude without influencing other parameters. In experiments, the dynamics can be mapped out from spin and momentum spaces, thus it is not limited by the spatial resolution in absorption imaging. This system can serve as a promising platform for matter wave interferometry and quantum metrology.