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arXiv:1901.11449 · Chinese Physics Letters

Angular Momentum Josephson Effect between Two Isolated Condensates

Wei-Feng Zhuang, Yue-Xin Huang, Ming Gong

Published Jun 1, 2021• 4 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1088/0256-307x/38/6/060301

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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.
The momentum space Josephson effect describes the supercurrent flow between weakly coupled Bose-Einstein condensates (BECs) at two discrete momentum states. Here, we experimentally observe this exotic phenomenon using a BEC with Raman-induced spin-orbit coupling, where the tunneling between two local band minima is implemented by the momentum kick of an additional optical lattice. A sudden quench of the Raman detuning induces coherent spin-momentum oscillations of the BEC, which is analogous to the ac Josephson effect. We observe both plasma and regular Josephson oscillations in different parameter regimes. The experimental results agree well with the theoretical model and numerical simulation and showcase the important role of nonlinear interactions. We also show that the measurement of the Josephson plasma frequency gives the Bogoliubov zero quasimomentum gap, which determines the mass of the corresponding pseudo-Goldstone mode, a long-sought phenomenon in particle physics. The observation of momentum space Josephson physics offers an exciting platform for quantum simulation and sensing utilizing momentum states as a synthetic degree.
The Josephson effect is a prominent phenomenon of quantum supercurrents that has been widely studied in superconductors and superfluids. Typical Josephson junctions consist of two real-space superconductors (superfluids) coupled through a weak tunneling barrier. Here we propose a momentum-space Josephson junction in a spin-orbit coupled Bose-Einstein condensate, where states with two different momenta are coupled through Raman-assisted tunneling. We show that Josephson currents can be induced not only by applying the equivalent of "voltages," but also by tuning tunneling phases. Such tunneling-phase-driven Josephson junctions in momentum space are characterized through both full mean field analysis and a concise two-level model, demonstrating the important role of interactions between atoms. Our scheme provides a platform for experimentally realizing momentum-space Josephson junctions and exploring their applications in quantum-mechanical circuits.
Abstract We consider matter-wave bright solitons in helicoidal spin-orbit coupled Bose–Einstein condensates in optical lattices with a view to study Josephson-type oscillation and self-trapping of population imbalance between two pseudo-spin states. For fixed values of nonlinear interaction and lattice parameters, the population imbalance executes Josephson-type oscillation and the frequency of oscillation decreases with the increase of helicoidal gauge potential. The frequency of oscillation, however, increases in presence of nonlinear optical lattices. We find that the population imbalance can oscillate about a non-zero value and result self-trapping for proper choices of parameters of the system. The self-trapping can be enhanced by the increase of helicoidal gauge potential and by properly tuning the lattice parameters.
Abstract We theoretically investigate the energy band structure and Josephson dynamics of a spin-orbit coupled Bose–Einstein condensate in a double-well potential. We study the energy band structure and the corresponding tunneling dynamics of the system by properly adjusting the SO coupling, Raman coupling, Zeeman field and atomic interactions. The coupled effects of SO coupling, Raman coupling, Zeeman field and atomic interactions lead to the appearance of complex energy band structure including the loop structure. Particularly, the emergence of the loop structure in energy band also depends on SO coupling, Raman coupling, Zeeman field and atomic interactions. Correspondingly, the Josephson dynamics of the system are strongly related to the energy band structure. Especially, the emergence of the loop structure results in complex tunneling dynamics, including suppression-revival transitions and self-trapping of atoms transfer between two spin states and two wells. This engineering provides a possible means for studying energy level and corresponding dynamics of two-species SO coupled BECs.
We discuss the coherent atomic oscillations between two weakly coupled Bose-Einstein condensates. The weak link is provided by a laser barrier in a (possibly asymmetric) double-well trap or by Raman coupling between two condensates in different hyperfine levels. The boson Josephson junction (BJJ) dynamics is described by the two-mode nonlinear Gross-Pitaevskii equation that is solved analytically in terms of elliptic functions. The BJJ, being a neutral, isolated system, allows the investigations of dynamical regimes for the phase difference across the junction and for the population imbalance that are not accessible with superconductor Josephson junctions (SJJ's). These include oscillations with either or both of the following properties: (i) the time-averaged value of the phase is equal to $\ensuremath{\pi} (\ensuremath{\pi}$-phase oscillations); (ii) the average population imbalance is nonzero, in states with macroscopic quantum self-trapping. The (nonsinusoidal) generalization of the SJJ ac and plasma oscillations and the Shapiro resonance can also be observed. We predict the collapse of experimental data (corresponding to different trap geometries and the total number of condensate atoms) onto a single universal curve for the inverse period of oscillations. Analogies with Josephson oscillations between two weakly coupled reservoirs of ${}^{3}\mathrm{He}\ensuremath{-}B$ and the internal Josephson effect in ${}^{3}\mathrm{He}\ensuremath{-}A$ are also discussed.
We investigate the stability and dynamics of the orbital angular momentum modes of a repulsive Bose-Einstein condensate trapped in two tunnel-coupled rings in a stack configuration. Within mean-field theory, we derive a two-state model for the system in the case in which we populate both rings equally with a single orbital angular momentum mode and include small perturbations in other modes. Analyzing the fixed-point solutions of the model and the associated classical Hamiltonian, we characterize the destabilization of the stationary states and the subsequent dynamics. By populating a single orbital angular momentum mode with an arbitrary population imbalance between the rings, we derive analytically the boundary between the regimes of Josephson oscillations and macroscopic quantum self-trapping and study numerically the stability of these solutions.