Investigation of Quantum Mpemba Effect through Symmetry Restoration by Quantum Trajectory Approach

Abstract

Quantum Mpemba Effect (QME) is a counterintuitive phenomenon in which the systems further away from the equilibrium tend to relax more quickly than if they were closer. There are different measures by which you can quantify how distant the system is from the equilibria or the “distance from equilibrium”. In the literature, many mathematical norms have been proposed for quantifying this distance, for example: Hilbert-Schmidt distance, Frobenius norm, Beta-Weighted Norm, etc. Other quantities, such as Non-Equilibrium Free Energy and Ergotropy, have been used in the Quantum Thermodynamic sense as well. However, in this work, we look at QME from the perspective of symmetry restoration (the higher symmetry-broken state will restore faster). We focus on U(1) symmetry, using Renyi Entanglement Asymmetry as our measure of symmetry breaking, which quantitatively determines the amount of symmetry breaking at the level of subsystem. Recent works have been done in observing QME through this quantity, but they remain severely limited to closed quantum systems. Here, we probe the application of this quantity in the more general case of open quantum systems where we introduce local dephasing on each site of a 1D lattice chain. We use the quantum trajectory approach called Stochastic Unitary Unravelling (SUU) to unravel the Lindbladian, in order to model this noise. We start with an initial Gaussian state having comfortable tunable parameters, which have a correspondence to Rényi entanglement Asymmetry that directly controls the asymmetry in the state. We then evolve them under a noisy Hamiltonian (corresponding to the SUU protocol), which preserves U(1) symmetry. This Hamiltonian restores U(1) symmetry in the defined subsystem asymptotically in the large time limit. We find that Rényi Entanglement Asymmetry shows QME under specific situations and also depicts interesting power law behaviours in the late time regime.