Fundamental Limitation on Cooling under Classical Noise

Jun Jing,Ravindra W Chhajlany,Lian-Ao Wu

doi:10.1038/s41598-017-00194-9

Abstract

We prove a general theorem that the action of arbitrary classical noise or random unitary channels can not increase the maximum population of any eigenstate of an open quantum system, assuming initial system-environment factorization. Such factorization is the conventional starting point for descriptions of open system dynamics. In particular, our theorem implies that a system can not be ideally cooled down unless it is initially prepared as a pure state. The resultant inequality rigorously constrains the possibility of cooling the system solely through temporal manipulation, i.e., dynamical control over the system Hamiltonian without resorting to measurement based cooling methods. It is a substantial generalization of the no-go theorem claiming that the exact ground state cooling is forbidden given initial system-thermal bath factorization, while here we prove even cooling is impossible under classical noise.

Highlights

Cooling and, more generally, pure-state preparation [1,2,3,4,5] of a microscopic or mesoscopic open system [6] is of paramount importance to many intriguing quantum technologies and engineering of low temperature quantum phases, in general
One could hope that cooling might be realized with minimal resources, such as under the influence of classical noise
We have shown that even approximate cooling to the ground state is impossible under such conditions assuming no work is done on the system

Summary

INTRODUCTION

More generally, pure-state preparation [1,2,3,4,5] of a microscopic or mesoscopic open system (small thermal object) [6] is of paramount importance to many intriguing quantum technologies and engineering of low temperature quantum phases, in general. An example is the recently proposed “counterintuitive” protocols as cooling by heating [35, 36] with the help of “incoherent thermal quantum noise” from a high-temperature bath, where we know ”quantum noise” could be equivalent to a corresponding classical noise as long as the Born-Markov approximation is used. It has been recently proved that exact ground state cooling is forbidden when one assumes factorization of the initial state of the system from the bath state [37] This is remarkable since initial systembath product state factorization is a common condition adopted in the derivation of master equations or Kraus operator representations describing open system dynamics [6, 38]. We find that under such conditions, even approximate cooling is impossible

NO-GO THEOREM FOR COOLING AN OPEN SYSTEM UNDER CLASSICAL NOISE

A single two-level system

CONSEQUENCES OF THE NO-GO THEOREM

A three-level system

DISCUSSION AND CONCLUSION