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arXiv:2604.27809

Bosonic Josephson junction dynamics: interplay between quantum and thermal fluctuations

Andrea Bardin, Francesco Lorenzi, Luca Salasnich

Published Apr 30, 2026• 0 citations
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Abstract

We investigate the superfluid dynamics of a Josephson junction beyond the mean-field description, incorporating the role of thermal fluctuations as well as quantum fluctuations. Using a formalism that accounts for the fluctuations in a homogeneous gas, and under the assumption that the transport of the non-condensed component is negligible, we derive a corrected equation of motion within the two-site approximation. The resulting corrections for the typical dynamical quantities, like the Josephson frequency, the strength of macroscopic quantum self-trapping, and the threshold for spontaneous symmetry breaking, allow us to predict the effects of both types of fluctuations and assess their relative importance in different regimes in a semianalytical fashion. For all the dynamical quantities, the quantum fluctuations are shown to play an opposite role with respect to the thermal fluctuations. Josephson frequency is decreased by thermal fluctuations and both the critical strenghts of macroscopic quantum self trapping and spontaneous symmetry breaking are increased. We assess the experimentally accessible regimes by calculating the relevant parameters of recent experimental realizations of Bosonic Josephson junction and show that the expected regime is dominated by quantum fluctuations.

DOI
10.48550/arxiv.2604.27809

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We investigate the superfluid dynamics of a Josephson junction beyond the mean-field description, incorporating the role of thermal fluctuations as well as quantum fluctuations. Using a formalism that accounts for the fluctuations in a homogeneous gas, and under the assumption that the transport of the non-condensed component is negligible, we derive a corrected equation of motion within the two-site approximation. The resulting corrections for the typical dynamical quantities, like the Josephson frequency, the strength of macroscopic quantum self-trapping, and the threshold for spontaneous symmetry breaking, allow us to predict the effects of both types of fluctuations and assess their relative importance in different regimes in a semianalytical fashion. For all the dynamical quantities, the quantum fluctuations are shown to play an opposite role with respect to the thermal fluctuations. Josephson frequency is decreased by thermal fluctuations and both the critical strenghts of macroscopic quantum self trapping and spontaneous symmetry breaking are increased. We assess the experimentally accessible regimes by calculating the relevant parameters of recent experimental realizations of Bosonic Josephson junction and show that the expected regime is dominated by quantum fluctuations.
Abstract We investigate the role of quantum fluctuations in the dynamics of a bosonic Josephson junction in D spatial dimensions, by using beyond-mean-field Gaussian corrections. We derive some key dynamical properties in a systematic way for D = 3 , 2 , 1 . In particular, we compute the Josephson frequency in the regime of low population imbalance. We also obtain the critical strength of the macroscopic quantum self-trapping. Our results show that quantum corrections increase the Josephson frequency in spatial dimensions D = 2 and D = 3, but they decrease it in the D = 1 case. The critical strength of macroscopic quantum self-trapping is instead reduced by quantum fluctuations in D = 2 and D = 3 cases, while it is enhanced in the D = 1 configuration. We show that the difference between the cases of D = 2 and D = 3 on one side, and D = 1 on the other, can be related to the qualitatively different dependence of the interaction strength on the scattering length in the different dimensions.
We investigate finite-size quantum effects in the dynamics of NNN bosonic particles which are tunneling between two sites adopting the two-site Bose-Hubbard model. By using time-dependent atomic coherent states (ACSs) we extend the standard mean-field equations of this bosonic Josephson junction, which are based on time-dependent Glauber coherent states. In this way we find 1/N1/N1/N corrections to familiar mean-field (MF) results: the frequency of macroscopic oscillation between the two sites, the critical parameter for the dynamical macroscopic quantum self-trapping (MQST), and the attractive critical interaction strength for the spontaneous symmetry breaking (SSB) of the ground state. To validate our analytical results we perform numerical simulations of the quantum dynamics. In the case of Josephson oscillations around a balanced configuration we also find that, for a few atoms, the numerical results are in good agreement with the predictions of time-dependent ACS variational approach, provided that the time evolution is not too long. Also, the numerical results of SSB are better reproduced by the ACS approach than with the MF approach. Instead, the onset of MQST is correctly reproduced by ACS theory only in the large NNN regime and, for this phenomenon, the 1/N1/N1/N correction to the MF formula is not reliable.
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
We investigate the effect of dissipation in a Bose-Josephson junction (BJJ) coupled to baths of bosons at its two sites. Apart from the dynamical transition due to repulsive interactions, the BJJ undergoes a quantum phase transition by increasing the coupling strength with the bath modes. We analyze this system by mapping to an equivalent spin model coupled to the bosonic modes. The excitation energies and fluctuation of number imbalance are obtained within a Holstein-Primakoff approximation, which exhibits vanishing of the energy gap and enhanced quantum fluctuations at the critical point. We study the dynamics of BJJ using a time-dependent variational method and analyze stability of different types of steady states. As a special case we study in detail the phase space dynamics of BJJ coupled to a single mode, which reveals diffusive and incoherent behavior with increasing coupling to the bath mode. The dynamical steady states corresponding to the π oscillation and self-trapped state become unstable when their oscillation frequencies are in resonance with the bath modes. We study the Josephson dynamics in the presence of an Ohmic bath with Gaussian noise to incorporate the thermal fluctuations and obtain the Josephson oscillation frequency and damping analytically. We also observe the transition to the symmetry-broken state for strong coupling as well as decay of π oscillation and a self-trapped state to the ground state due to dissipation. Variation of the phase fluctuation with temperature of the bath shows similar behavior as observed in experiment. Finally we discuss the experimental setup to study the observable effects of dissipation in BJJ.
Bosonic Josephson junctions can be realized by confining ultracold gases of bosons in multiwell traps and studied theoretically with the MMM-site Bose-Hubbard model. We show that canonical equilibrium states of the MMM-site Bose-Hubbard model may be approximated by mixtures of coherent states, provided the number of atoms is large and the total energy is comparable to kBT{k}_{B}TkB​T. Using this approximation, we study thermal fluctuations in bosonic Josephson junctions in the mean-field regime. Statistical estimates of the fluctuations of relative phase and number, obtained by averaging over many replicates of an experiment, can be used to estimate the temperature and the tunneling parameter or to test whether the experimental procedure is effectively sampling from a canonical thermal equilibrium ensemble.
© 2025 by the authors.We investigate how collisional interactions between the condensate and the thermal cloud influence the distinct dynamical regimes (Josephson plasma, phase-slip-induced dissipative regime, and macroscopic quantum self-trapping) emerging in ultracold atomic Josephson junctions at non-zero subcritical temperatures. Specifically, we discuss how the self-consistent dynamical inclusion of collisional processes facilitating the exchange of particles between the condensate and the thermal cloud impacts both the condensate and the thermal currents, demonstrating that their relative importance depends on the system’s dynamical regime. Our study is performed within the full context of the Zaremba–Nikuni–Griffin (ZNG) formalism, which couples a dissipative Gross–Pitaevskii equation for the condensate dynamics to a quantum Boltzmann equation with collisional terms for the thermal cloud. In the Josephson plasma oscillation and vortex-induced dissipative regimes, collisions markedly alter dynamics at intermediate-to-high temperatures, amplifying damping in the condensate imbalance mode and inducing measurable frequency shifts. In the self-trapping regime, collisions destabilize the system even at low temperatures, prompting a transition to Josephson-like dynamics on a temperature-dependent timescale. Our results show the interplay between coherence, dissipation, and thermal effects in a Bose–Einstein condensate at a finite temperature, providing a framework for tailoring Josephson junction dynamics in experimentally accessible regimes.