Qubit decoherence in dissipative two-photon resonator: real-time instantons and Wigner function

TL;DR

This paper develops a theoretical framework combining phase-space methods, instantons, and the Wigner function to analyze decoherence and metastability in a driven-dissipative two-photon resonator, relevant for quantum information.

Contribution

It introduces a unified approach linking steady-state phase-space analysis with quantum activation dynamics using instantons and Wigner functions.

Findings

Identifies metastable states in the system due to quantum fluctuations.

Derives an analytical decoherence rate expression.

Connects quantum activation processes with phase-space representations.

Abstract

We study the quantum dynamics of a single bosonic cavity subject to two-photon driving and two-photon dissipation in the presence of finite detuning. Exploiting a hidden time-reversal symmetry, the Wigner representation and the WKB method, we introduce an effective phase-space potential for description of the steady state. It reveals two attracting points, which are metastable due to quantum fluctuations. By employing the Keldysh real-time path integral formalism, we compute the instanton trajectory governing the quantum activation process between these attractors and establish a fundamental connection with the Wigner representation. This relation unifies the steady-state phase-space description with dynamical quantum activation processes. We also derive an analytical expression for the decoherence rate of the system. Our work provides a coherent theoretical framework for analyzing quantum bistability, metastability, and decoherence in driven-dissipative nonlinear resonators, with direct implications for the design of bosonic qubits and quantum information processing.