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Journal of Physics B Atomic Molecular and Optical Physics

A bosonic Josephson junction

Rudolf Gati, Markus K. Oberthaler

Published May 1, 2007• 392 citations
Publisher

Abstract

We review the experimental realization of a single bosonic Josephson junction for ultracold gases, which was made possible by the generation of a precisely controllable double-well potential for Bose–Einstein condensates. We will focus on the comparison of the experimentally obtained data with the predictions of a many-body two-mode model and a mean-field description and show that the observed static, thermal and dynamical properties can be described in terms of classical equations.

DOI
10.1088/0953-4075/40/10/r01

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We review the experimental realization of a single bosonic Josephson junction for ultracold gases, which was made possible by the generation of a precisely controllable double-well potential for Bose–Einstein condensates. We will focus on the comparison of the experimentally obtained data with the predictions of a many-body two-mode model and a mean-field description and show that the observed static, thermal and dynamical properties can be described in terms of classical equations.
We study atomic Josephson junctions (AJJs) with one and two bosonic species confined by a double-well potential. Proceeding from the second quantized Hamiltonian, we show that it is possible to describe the zero-temperature AJJ microscopic dynamics by means of extended Bose–Hubbard (EBH) models, which include usually neglected nonlinear terms. Within the mean-field approximation, the Heisenberg equations derived from such two-mode models provide a description of AJJ macroscopic dynamics in terms of ordinary differential equations (ODEs). We discuss the possibility of distinguishing the Rabi, Josephson and Fock regimes in terms of the macroscopic parameters which appear in the EBH Hamiltonians, and then in the ODEs. We compare the predictions for the relative populations of the Bose gas atoms in the two wells obtained from the numerical solutions of the two-mode ODEs, with those deriving from the direct numerical integration of the Gross–Pitaevskii equations (GPEs). Our investigations show that the nonlinear terms of the ODEs are crucial to achieve a good agreement between the ODE and GPE approaches, and in particular to give quantitative predictions of the self-trapping regime.
The subject of this work is the experimental implementation of a single bosonic Josephson junction and the discussion of the performed investigations. To generate this new kind of Josephson junction a 87-Rubidium Bose-Einstein condensate is split in a double well potential into two matter wave packets, which are coupled coherently to each other via quantum mechanical tunneling of atoms through the barrier. The state of the system can be described by two dynamical variables, the population imbalance of the two wells and their phase difference. The investigation of the dynamical response of the Josephson junction shows, that two dynamical regimes can be identified, the plasma oscillation regime, where atoms tunnel back and forth between the wells, and the self trapping regime, where no tunneling is found. Furthermore, the investigation at finite temperature reveals, that the relative phase in steady state is not locked to zero but fluctuates according to its temperature and the tunneling coupling. By measuring the fluctuations and calculating the tunneling coupling it is possible to deduce the temperature of the atomic cloud. With this a new method for thermometry is realized, which also works in a regime, where the standard methods can not be applied.
One of the most striking manifestations of the quantum collective behavior of matter is the Josephson effect: it allows for a classically forbidden current to flow without dissipation [125]. Traditional Josephson junctions are built by means of superconductors separated by thin non-conducting oxide barriers and they have drawn an intense interest for their striking phenomenology. A bosonic analog is the so-called Bosonic Josephson junction (BJJ) where two macroscopic populations of bosons are trapped in a double well geometry. Bose-Einstein condensation of dilute atomic gases has allowed for the demonstration of BJJs by trapping two condensates in double wells [126],[127].
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
In ultracold atoms, bosons tunneling in a double-well potential can produce a typical Josephson junction in real space. A major advancement in quantum matter and simulations is anticipated by the recently found momentum-space Josephson junctions, which elucidates the supercurrent flow between spin-orbit coupled Bose-Einstein condensates at two distinct independent momentum states. For the first time, our study unveils specific protocols to engineer momentum-space Josephson dynamics for scalar bosons (or a single-component condensate) in a rotating frame through modulation of the geometry of a double-well trapping potential and rotation frequencies. In this setup, the rotation simultaneously results in effective double wells both in position and in momentum spaces, and the dynamics of the corresponding Josephson junctions is hosted in these double wells. Consequently, it is observed that the rotation generates momentum-space Josephson dynamics of the condensate along the transverse direction and position-space Josephson dynamics along the longitudinal direction; these effects are particularly noticeable for high rotation frequencies. Additionally, the rotation-induced momentum-space junctions are highly significant in both the mean-field and many-body dynamics. Our protocols offer a framework for investigating momentum-space Josephson junctions for single-component condensates in both theoretical and experimental contexts, as well as their significant applications in quantum mechanical devices.
Abstract In the framework of the stochastic projected Gross–Pitaevskii equation we investigate finite-temperature dynamics of a bosonic Josephson junction (BJJ) formed by a Bose–Einstein condensate of atoms in a two-well trapping potential. We extract the characteristic properties of the BJJ from the stationary finite-temperature solutions and compare the dynamics of the system with the resistively shunted Josephson model. Analyzing the decay dynamics of the relative population imbalance we estimate the effective normal conductance of the junction induced by thermal atoms. The calculated normal conductance at various temperatures is then compared with predictions of the noise-less model and the model of ballistic transport of thermal atoms.