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arXiv:2407.17080 · Physical Review Research

Massive-vortex realization of a Bosonic Josephson Junction

Alice Bellettini, Andrea Richaud, Vittorio Penna

Published Nov 25, 2024• 14 citations
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Abstract

We study the mass exchange between two rotating, quantum massive vortices in a two-component Bose-Einstein condensate. The vortices, in the majority component, exhibit a filled core, where the in-filling minority component undergoes a quantum tunneling effect. Remarkably, we observe that the two-vortex system features stable Josephson oscillations, as well as all the nonlinear phenomena, including the macroscopic quantum self-trapping, that characterize a Bosonic Josephson Junction. We propose an analytical model for describing the intervortex tunneling, obtained by implementing the coherent-state representation of the two-mode Bose-Hubbard model. This allows us to give the explicit expression of the model's parameters in terms of the physical macroscopic parameters of the two-vortex system. The comparison of the dynamical scenario predicted by the model with that emerging from the Gross–Pitaevskii equations is very good for sufficiently small atom numbers, while at larger atom numbers it grows less precise, presumably due to the partial exclusion of the many-body interactions from our model. The definition of an effective self-interaction parameter allows us to include the many-body effects, thus restoring a quite good agreement with the numerical results. Interestingly, the recognition of the bosonic Josephson dynamics paves the way to the investigation of new dynamical behaviors in multivortex configurations. Published by the American Physical Society 2024

DOI
10.1103/physrevresearch.6.043197

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We study the mass exchange between two rotating, quantum massive vortices in a two-component Bose-Einstein condensate. The vortices, in the majority component, exhibit a filled core, where the in-filling minority component undergoes a quantum tunneling effect. Remarkably, we observe that the two-vortex system features stable Josephson oscillations, as well as all the nonlinear phenomena, including the macroscopic quantum self-trapping, that characterize a Bosonic Josephson Junction. We propose an analytical model for describing the intervortex tunneling, obtained by implementing the coherent-state representation of the two-mode Bose-Hubbard model. This allows us to give the explicit expression of the model's parameters in terms of the physical macroscopic parameters of the two-vortex system. The comparison of the dynamical scenario predicted by the model with that emerging from the Gross–Pitaevskii equations is very good for sufficiently small atom numbers, while at larger atom numbers it grows less precise, presumably due to the partial exclusion of the many-body interactions from our model. The definition of an effective self-interaction parameter allows us to include the many-body effects, thus restoring a quite good agreement with the numerical results. Interestingly, the recognition of the bosonic Josephson dynamics paves the way to the investigation of new dynamical behaviors in multivortex configurations. Published by the American Physical Society 2024
We consider the mean-field vortex solutions and their stability within a two-component Bose-Einstein condensate in the immiscible limit. A variational approach is employed to study a system consisting of a majority component which contains a single quantized vortex and a minority component which fills the vortex core. We show that a super-Gaussian function is a good approximation of the two-component vortex solution for a range of atom numbers of the infilling component by comparing the variational solutions to the full numerical solutions of the coupled Gross-Pitaevskii equations. We subsequently examine the stability of the vortex solutions by perturbing the infilling component away from the center of the vortex core, thereby demonstrating their stability to small perturbations. Finally, we consider the dynamics of infilled vortices. Published by the American Physical Society 2024
© 2024 authors. Published by the American Physical Society. Published by the American Physical Society under the terms of the 'https://creativecommons.org/licenses/by/4.0/'Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.We consider the mean-field vortex solutions and their stability within a two-component Bose-Einstein condensate in the immiscible limit. A variational approach is employed to study a system consisting of a majority component which contains a single quantized vortex and a minority component which fills the vortex core. We show that a super-Gaussian function is a good approximation of the two-component vortex solution for a range of atom numbers of the infilling component by comparing the variational solutions to the full numerical solutions of the coupled Gross-Pitaevskii equations. We subsequently examine the stability of the vortex solutions by perturbing the infilling component away from the center of the vortex core, thereby demonstrating their stability to small perturbations. Finally, we consider the dynamics of infilled vortices.
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 propose a new scheme for observing Josephson oscillations and macroscopic quantum self-trapping in a toroidally confined Bose-Einstein condensate: a dipolar self-induced Josephson junction. Polarizing the atoms perpendicularly to the trap symmetry axis, an effective ring-shaped, double-well potential is achieved which is induced by the dipolar interaction. By numerically solving the three-dimensional time-dependent Gross-Pitaevskii equation we show that coherent tunneling phenomena such as Josephson oscillations and quantum self-trapping can take place. The dynamics in the self-induced junction can be qualitatively described by a two-mode model taking into account both s -wave and dipolar interactions.
We propose a new scheme for observing Josephson oscillations and macroscopic quantum self-trapping in a toroidally confined Bose-Einstein condensate: a dipolar self-induced Josephson junction. Polarizing the atoms perpendicularly to the trap symmetry axis, an effective ring-shaped, double-well potential is achieved which is induced by the dipolar interaction. By numerically solving the three-dimensional time-dependent Gross-Pitaevskii equation we show that coherent tunneling phenomena such as Josephson oscillations and quantum self-trapping can take place. The dynamics in the self-induced junction can be qualitatively described by a two-mode model taking into account both s-wave and dipolar interactions. © 2011 Europhysics Letters Association.
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