Finite-temperature entanglement and coherence in asymmetric bosonic Josephson junctions

TL;DR

The paper addresses finite-temperature properties of an asymmetric bosonic Josephson junction described by a two-site Bose-Hubbard model. It develops a quantum phase model and a semiclassical framework with an effective temperature to describe thermal averages in the strong tunneling regime, enabling analytical insight alongside exact diagonalization. The authors compute spectral weights, thermodynamic and entanglement entropies, population imbalance, quantum Fisher information, and coherence visibility, and they analyze how temperature and on-site asymmetry modify entanglement and coherence. The results provide a detailed map of thermal effects on quantum correlations in BJJs and suggest that the effective-description approach can extend to related models and regimes relevant for atomtronics and precision sensing.

Abstract

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.

Figures (9)

• Figure 1: Spectral decomposition $\rho_{ii} = \langle |c_i|^2\rangle$ of the statistical ensemble of states for $\varepsilon=0$ as a function of $i/N$, plotted for $N=50$ and $U/J = 1.0$ (solid orange line), $0.0$ (dashed green line), $-0.2$ (dashed-dotted cyan line) at different temperatures.
• Figure 2: Spectral decomposition $\rho_{ii} = \langle |c_i|^2\rangle$ of the statistical ensemble of states for $\varepsilon/J = 0.2$ as a function of $i/N$, plotted for $N=50$ and $U/J = 1.0$ (solid orange line), $0.0$ (dashed green line), $-0.2$ (dashed-dotted cyan line) at different temperatures.
• Figure 3: Energy gap between $| E_0 \rangle$ and $| E_1 \rangle$ (upper panels) and thermodynamic entropy (lower panels) as functions of $U/J$, plotted for $N=50$ and $k_BT/J = 10^{-10}$ (solid blue line), $1.0$ (dashed-dotted green line), $5.0$ (dashed orange line). The energy asymmetry is $\varepsilon = 0$ (left panels) and $\varepsilon/J = 0.1$ (right panels).
• Figure 4: Entanglement entropy as a function of $U/J$, plotted for $N=20$ and $k_BT/J = 0$ (solid blue line), $10.0$ (dashed-dotted green line), $20.0$ (dashed orange line). The energy asymmetry is $\varepsilon = 0$ (upper panel) and $\varepsilon/J = 3.0$ (lower panel).
• Figure 5: (a) Population imbalance at $T=0$ as a function of $\varepsilon/JN$, plotted for $N=10$ and $U/JN = 0.05$ (cyan circles), $0.5$ (green squares), $2.0$ (orange triangles). The continuous lines are the corresponding semiclassical results [Eq. \ref{['ksemi']}]. (b) Population imbalance at $\varepsilon/JN = 0.1$ as a function of $U/JN$, plotted for $N=10$ and $k_BT/JN = 0$ (solid blue line), $0.5$ (dashed-dotted green line), $1.0$ (dashed orange line).