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arXiv:2306.02284 · New Journal of Physics

Quantum fluctuations in atomic Josephson junctions: the role of dimensionality

Andrea Bardin, Francesco Lorenzi, Luca Salasnich

Published Dec 5, 2023• 8 citations
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Abstract

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.

DOI
10.1088/1367-2630/ad127b

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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 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.
We investigate the fully quantum evolution of the population imbalance in a perfectly symmetric Bose-Josephson junction modeled by a two-mode Bose-Hubbard Hamiltonian, focusing on the validity of macroscopic quantum self-trapping beyond the mean-field theory. We show that for any finite number of particles, the exact quantum dynamics leads to the breakdown of macroscopic quantum self-trapping after a finite time, regardless of the initial state. Using the symmetries of the Bose-Hubbard Hamiltonian, we provide a mathematical demonstration of this result and analyze the spectral properties governing the dynamics. We identify a branching behavior in the eigenvalue differences and a nontrivial structure of the population-imbalance amplitudes. These features allow us to distinguish two clearly different dynamical regimes and to elucidate the mechanism leading to the emergence of a quasi–macroscopic quantum self-trapping regime for large particle numbers. These findings bridge the gap between mean-field predictions and exact quantum dynamics and provide insight into the emergence of classical nonlinear behavior from finite quantum many-body systems.
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.
In this paper we consider a bosonic Josephson junction described by a two-mode Bose-Hubbard model, and we thoroughly analyze a quantum phase transition occurring in the system in the limit of infinite bosonic population. We discuss the relation between this quantum phase transition and the dynamical bifurcation occurring in the spectrum of the discrete self-trapping equations describing the system at the semiclassical level. In particular, we identify five regimes depending on the strength of the effective interaction among bosons, and study the finite-size effects arising from the finiteness of the bosonic population. We devote special attention to the critical regime which reduces to the dynamical bifurcation point in the thermodynamic limit of infinite bosonic population. Specifically, we highlight an anomalous scaling in the population imbalance between the two wells of the trapping potential, as well as in two quantities borrowed from quantum information theory, i.e., the entropy of entanglement and the ground-state fidelity. Our analysis is not limited to the zero-temperature case, but considers thermal effects as well.
We explore the interplay between tunneling and interatomic interactions in the dynamics of a bosonic Josephson junction. We tune the scattering length of an atomic ^{39}K Bose-Einstein condensate confined in a double-well trap to investigate regimes inaccessible to other superconducting or superfluid systems. In the limit of small-amplitude oscillations, we study the transition from Rabi to plasma oscillations by crossing over from attractive to repulsive interatomic interactions. We observe a critical slowing down in the oscillation frequency by increasing the strength of an attractive interaction up to the point of a quantum phase transition. With sufficiently large initial oscillation amplitude and repulsive interactions, the system enters the macroscopic quantum self-trapping regime, where we observe coherent undamped oscillations with a self-sustained average imbalance of the relative well population. The exquisite agreement between theory and experiments enables the observation of a broad range of many body coherent dynamical regimes driven by tunable tunneling energy, interactions and external forces, with applications spanning from atomtronics to quantum metrology.
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.