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arXiv:1208.2349 · Journal of Physics B Atomic Molecular and Optical Physics

Finite temperature effects in two-mode bosonic Josephson junctions

G. Mazzarella, Luca Salasnich, Flavio Toigo

Published Aug 30, 2012• 4 citations
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Abstract

We analyze the effects of temperature on a bosonic Josephson junction realized with ultracold and dilute atoms in a double-well potential. Starting from the eigenstates of the two-site Bose–Hubbard Hamiltonian, we calculate the coherence visibility and the fluctuation of the on-site occupation number and study them as functions of temperature. We show that, contrary to naive expectations, when the boson–boson interaction is suitably chosen thermal effects can increase the coherence visibility and reduce the on-site number fluctuation.

DOI
10.1088/0953-4075/45/18/185301

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We analyze the effects of temperature on a bosonic Josephson junction realized with ultracold and dilute atoms in a double-well potential. Starting from the eigenstates of the two-site Bose–Hubbard Hamiltonian, we calculate the coherence visibility and the fluctuation of the on-site occupation number and study them as functions of temperature. We show that, contrary to naive expectations, when the boson–boson interaction is suitably chosen thermal effects can increase the coherence visibility and reduce the on-site number fluctuation.
We investigate the finite-temperature properties of a bosonic Josephson junction composed of N interacting atoms confined by a quasi-one-dimensional asymmetric double-well potential, modeled by the two-site Bose-Hubbard Hamiltonian. We compute numerically the spectral decomposition of the statistical ensemble of states, the thermodynamic and entanglement entropies, the population imbalance, the quantum Fisher information, and the coherence visibility. We analyze their dependence on the system parameters, showing in particular how finite temperature and on-site energy asymmetry affect the entanglement and coherence properties of the system. Moreover, starting from a quantum phase model which accurately describes the system over a wide range of interactions, we develop a reliable description of the strong tunneling regime, where thermal averages may be computed analytically using a modified Boltzmann weight involving an effective temperature. We discuss the possibility of applying this effective description to other models in suitable regimes.
We study the coherence fluctuations in a Josephson junction created by two weakly coupled Bose-Einstein condensates. We apply the two-mode approximation in the full quantum theory analysis, and so that the system is described by a two-site Bose-Hubbard Hamiltonian. The coherence fluctuations are determined by the total number of particles N, charging energy EC, junction energy EJ, asymmetry δ and temperature T. For zero-temperature symmetric systems, the coherence fluctuations increase with EC/EJ, however, the number squeezing increases with N2EC/EJ. For zero-temperature asymmetric systems, the coherence fluctuations are suppressed by the balance effects between asymmetry and interparticle interaction and the single-atom resonance effects. The coherence fluctuations grow with temperature, and the formation of a self-trapping state will cause abnormal behaviors at high temperatures.
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.
We use the Bose-Hubbard Hamiltonian to study quantum fluctuations in canonical equilibrium ensembles of bosonic Josephson junctions at relatively high temperatures, comparing the results for finite particle numbers NNN to the classical limit that is attained as NNN approaches infinity. We consider both attractive and repulsive atom-atom interactions, with special focus on the behavior near the T=0T=0T=0 quantum phase transition that occurs, for large enough NNN, when attractive interactions surpass a critical level. Differences between Bose-Hubbard results for small NNN and those of the classical limit are quite small even when $N\ensuremath{\sim}100$, with deviations from the limit diminishing as 1/N1/N1/N.
We consider a bosonic Josephson junction made of NNN ultracold and dilute atoms confined by a quasi-one-dimensional double-well potential within the two-site Bose-Hubbard model framework. The behavior of the system is investigated at zero temperature by varying the interatomic interaction from the strongly attractive regime to the repulsive one. We show that the ground state exhibits a crossover from a macroscopic Schr\"odinger-cat state to a separable Fock state through an atomic coherent regime. By diagonalizing the Bose-Hubbard Hamiltonian we characterize the emergence of the macroscopic cat states by calculating the Fisher information FFF, the coherence by means of the visibility $\ensuremath{\alpha}$ of the interference fringes in the momentum distribution, and the quantum correlations by using the entanglement entropy SSS. Both Fisher information and visibility are shown to be related to the ground-state energy by employing the Hellmann-Feynman theorem. This result, together with a perturbative calculation of the ground-state energy, allows simple analytical formulas for FFF and $\ensuremath{\alpha}$ to be obtained over a range of interactions, in excellent agreement with the exact diagonalization of the Bose-Hubbard Hamiltonian. In the attractive regime the entanglement entropy attains values very close to its upper limit for a specific interaction strength lying in the region where coherence is lost and self-trapping sets in.
We consider a degenerate Bose gas confined in a double-well potential in interaction with a trapped ion in one dimension and investigate the impact of two relevant sources of imperfections in experiments on the system dynamics: ion motion and thermal excitations of the bosonic ensemble. Particularly, their influence on the entanglement generation between the spin state of the moving ion and the atomic ensemble is analyzed. We find that the detrimental effects of the ion motion on the entanglement protocol can be mitigated by properly choosing the double-well parameters as well as timings of the protocol. Furthermore, thermal excitations of the bosons affect significantly the system's tunneling and self-trapping dynamics at moderate temperatures; i.e., thermal occupation of a few double-well quanta reduces the protocol performance by about 10%. Hence, we conclude that finite temperature is the main source of decoherence in such junctions and we demonstrate the possibility to entangle the condensate motion with the ion vibrational state.