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arXiv:0801.3154 · Physical Review A

Number squeezing, quantum fluctuations, and oscillations in mesoscopic Bose Josephson junctions

Giulia Ferrini, Anna Minguzzi, F. W. J. Hekking

Published Aug 5, 2008• 78 citations
arXivHTMLPDF

Abstract

We use a two-mode Bose-Hubbard Hamiltonian to determine the ground state and dynamical evolution for a Bose Josephson junction realized by an ultracold Bose gas in a double-well trap. We identify Mott-like lobes where number fluctuations are suppressed and the interference fringes in the momentum distribution are strongly reduced. Different from superconducting Josephson junctions, the lobes size increases at increasing wells imbalance. Upon a sudden rise of the barrier between the two wells, an initially phase-coherent state evolves into a coherent superposition of phase states, leading to destructive interference in the time-dependent momentum distribution.

DOI
10.1103/physreva.78.023606

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We use a two-mode Bose-Hubbard Hamiltonian to determine the ground state and dynamical evolution for a Bose Josephson junction realized by an ultracold Bose gas in a double-well trap. We identify Mott-like lobes where number fluctuations are suppressed and the interference fringes in the momentum distribution are strongly reduced. Different from superconducting Josephson junctions, the lobes size increases at increasing wells imbalance. Upon a sudden rise of the barrier between the two wells, an initially phase-coherent state evolves into a coherent superposition of phase states, leading to destructive interference in the time-dependent momentum distribution.
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We study the quantum behaviour of a binary mixture of Bose–Einstein condensates in a double-well potential starting from a two-mode Bose–Hubbard Hamiltonian. We focus on the small tunnelling amplitude regime and apply perturbation theory up to second order. Analytical expressions for the energy eigenvalues and eigenstates are obtained. Then, the quantum evolution of the number difference of bosons between the two potential wells is fully investigated for two different initial conditions: completely localized states and coherent spin states. In the first case both the short- and the long-time dynamics is studied and a rich behaviour is found, ranging from small amplitude oscillations and collapses and revivals to coherent tunnelling. In the second case, the short-timescale evolution of number difference is determined and a more irregular dynamics is evidenced. Finally, the formation of Schrödinger cat states is considered and shown to affect the momentum distribution.
Understanding how coherent quantum dynamics give way to correlation-dominated behavior in low-dimensional systems remains a central challenge in quantum many-body physics. Here, we investigate a one-dimensional Bose-Josephson junction confined in a box trap using the multiconfigurational time-dependent Hartree method for bosons (MCTDHB). By varying the interaction strength and initial population imbalance, we identify distinct dynamical regimes governed by the competition between coherence and correlation-induced fragmentation. Weak interactions support coherent Josephson oscillations, whereas increasing imbalance leads to damping. At intermediate interaction strength, varying only the initial imbalance induces a crossover from nearly pure coherent oscillations to many-body dephasing with collapse-and-revival dynamics, and ultimately to equilibration accompanied by strong fragmentation and the saturation of many-body observables. In the strongly interacting regime, the system enters a dynamical freezing regime characterized by pronounced fragmentation, well-separated particle-resolved density peaks, and strongly suppressed tunneling. A systematic comparison with the Bose-Hubbard model reveals excellent agreement in the weakly interacting regime, while progressively larger deviations emerge as higher-orbital occupations beyond the two-mode approximation become significant. These results provide a unified picture of the emergence and competition of coherence, many-body dephasing, equilibration, and dynamical freezing, while delineating the regime of validity of the Bose-Hubbard description.
We study a Bose Josephson junction realized with a double-well potential. We propose a strategy to observe the coherent superpositions of phase states occurring during the time evolution after a sudden rise of the barrier separating the two wells. We show that their phase content can be obtained by the full counting statistics of the spin-boson operators characterizing the junction, which could be mapped out by repeated measurements of the population imbalance after rotation of the state. This measurement can distinguish between coherent superpositions and incoherent mixtures, and can be used for a two-dimensional tomographic reconstruction of the phase content of the state.
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 the role of interatomic interactions when a Bose gas, in a double-well potential with a finite tunneling probability (a ‘Bose–Josephson junction’), is exposed to external noise. We examine the rate of decoherence of a system initially in its ground state with equal probability amplitudes in both sites. The noise may induce two kinds of effects: firstly, random shifts in the relative phase or number difference between the two wells and secondly, loss of atoms from the trap. The effects of induced phase fluctuations are mitigated by atom–atom interactions and tunneling, such that the dephasing rate may be suppressed by half its single-atom value. Random fluctuations may also be induced in the population difference between the wells, in which case atom–atom interactions considerably enhance the decoherence rate. A similar scenario is predicted for the case of atom loss, even if the loss rates from the two sites are equal. We find that if the initial state is number-squeezed due to interactions, then the loss process induces population fluctuations that reduce the coherence across the junction. We examine the parameters relevant for these effects in a typical atom chip device, using a simple model of the trapping potential, experimental data, and the theory of magnetic field fluctuations near metallic conductors. These results provide a framework for mapping the dynamical range of barriers engineered for specific applications and set the stage for more complex atom circuits (‘atomtronics’).