The speed of Markovian relaxation towards the ground state

TL;DR

This paper investigates how quantum systems relax to their ground state under decoherence, revealing that coherence and coupling details significantly influence relaxation speed, with superradiance as a special case.

Contribution

It provides a detailed analysis of relaxation dynamics for various Hamiltonians and coupling operators, highlighting the role of coherence and coupling matrix elements in relaxation speed.

Findings

Relaxation is faster when coherences are considered.

Relaxation speed depends on coupling matrix elements.

Dicke superradiance is a coherence-assisted relaxation phenomenon.

Abstract

For sufficiently low reservoir temperatures, it is known that open quantum systems subject to decoherent interactions with the reservoir relax towards their ground state in the weak coupling limit. Within the framework of quantum master equations, this is formalized by the Born-Markov-secular (BMS) approximation, where one obtains the system Gibbs state with the reservoir temperature as a stationary state. When the solution to some problem is encoded in the (isolated) ground state of a system Hamiltonian, decoherence can therefore be exploited for computation. The computational complexity is then given by the scaling of the relaxation time with the system size $n$. We study the relaxation behavior for local and non-local Hamiltonians that are coupled dissipatively with local and non-local operators to a bosonic bath in thermal equilibrium. We find that relaxation is generally more efficient when coherences of the density matrix in the system energy eigenbasis are taken into account. In addition, the relaxation speed strongly depends on the matrix elements of the coupling operators between initial state and ground state. We show that Dicke superradiance is a special case of our relaxation models and can thus be understood as a coherence-assisted relaxation speedup.