Temporal nonlocality of a two-level system interacting with a dephasing environment

Abstract

Temporal nonlocality of a two-level system interacting with a thermal reservoir is studied in terms of the Leggett–Garg inequality and the quantum witness, where the dephasing coupling and the Ohmic-like spectral density are assumed for an system-reservoir interaction. When the whole system is initially in the thermal equilibrium state, which is a quantum-classical correlated state, violation of the Leggett–Garg inequality and the quantum witness are investigated in detail. It is shown how the time evolution of the temporal nonlocality depends on the system-reservoir coupling strength, the reservoir temperature and the Ohmicity parameter. The results are compared with those obtained for a non-correlated initial state, where the two-level system and the thermal reservoir are initially in their own thermal equilibrium states. The comparison reveals that ignoring the initial correlation yields an additional phase shift in two-time correlation functions of the two-level system. The effect of the system-reservoir initial correlation becomes more significant as the Ohmicity parameter is smaller.