Non-Markovian dynamics of mixed-state geometric phase of dissipative qubits

TL;DR

This paper studies how non-Markovian effects and counter-rotating terms influence the geometric phase of a dissipative qubit, revealing significant differences from approximate models that neglect these terms.

Contribution

It demonstrates that counter-rotating terms critically affect the geometric phase in non-Markovian dynamics, challenging previous approximations that predict phase jumps.

Findings

Exact results show no $ ext{pi}$-phase jump in geometric phase.

Counter-rotating terms significantly alter the geometric phase.

RWA-based models predict phase jumps not observed in exact solutions.

Abstract

We investigate the geometric phase of a two-level atom (qubit) coupled to a bosonic reservoir with Lorentzian spectral density, and find that for the non-Markovian dynamics in which rotating-wave approximation (RWA) is performed, geometric phase has a $\pi$-phase jump at the nodal point. However, the exact result without RWA given by hierarchy equation of motion method shows that there is no such a phase jump or nodal structure in geometric phase. Thus our results demonstrate that the counter-rotating terms significantly contribute to the geometric phase in multi-mode Hamiltonian under certain circumstances.