# Steady-state entanglement and coherence of the coupled qubit system in equilibrium and nonequilibrium environments

## TL;DR

This paper analyzes how steady-state entanglement and coherence in coupled qubits are affected by equilibrium and nonequilibrium environments, revealing conditions that optimize quantum correlations for quantum information applications.

## Contribution

It provides a comprehensive analytical and numerical study of steady-state entanglement and coherence beyond the secular approximation, highlighting the effects of nonequilibrium conditions and bath parameters.

## Key findings

- Steady-state coherence increases monotonically with nonequilibrium conditions.
- Weak inter-qubit coupling and high bath temperature suppress entanglement and coherence.
- Energy detuning can enhance entanglement when combined with nonequilibrium conditions.

## Abstract

We investigate analytically and numerically the steady-state entanglement and coherence of two coupled qubits each interacting with a local boson or fermion reservoir, based on the Bloch-Redfield master equation beyond the secular approximation. We find that there is non-vanishing steady-state coherence in the nonequilibrium scenario, which grows monotonically with the nonequilibrium condition quantified by the temperature difference or chemical potential difference of the two baths. The steady-state entanglement in general is a non-monotonic function of the nonequilibrium condition as well as the bath parameters in the equilibrium setting. We also find that weak inter-qubit coupling and high base temperature or chemical potential of the baths can strongly suppress the steady-state entanglement and coherence, regardless of the strength of the nonequilibrium condition. On the other hand, the energy detuning of the two qubits, when used in a compensatory way with the nonequilibrium condition, can lead to significant enhancement of the steady-state entanglement in some parameter regimes. In addition, the qubits typically have a stronger steady-state entanglement when coupled to fermion baths exchanging particle with the system than boson baths exchanging energy with the system under similar conditions. We also discussed the possible experimental realization of measuring the steady state entanglement and coherence for coupled qubits systems in nonequilibrium environments. These results offer some general guidelines for optimizing the steady-state entanglement and coherence in the coupled qubit system and may find potential applications in quantum information technology.