Taking the temperature of a pure quantum state

TL;DR

This paper introduces a quantum interferometry method to measure the temperature of isolated pure quantum states, using a qubit probe's decoherence rate, validated through numerical simulations on a thermalising quantum spin chain.

Contribution

It presents a novel interferometric scheme to determine temperature in pure quantum states based on qubit decoherence, requiring minimal assumptions about the system.

Findings

Decoherence rate of the qubit correlates with the system's temperature.

Numerical simulations confirm the method's effectiveness on a quantum spin chain.

The approach works under assumptions of eigenstate thermalisation and hydrodynamics.

Abstract

Temperature is a deceptively simple concept that still raises deep questions at the forefront of quantum physics research. The observation of thermalisation in completely isolated quantum systems, such as cold-atom quantum simulators, implies that a temperature can be assigned even to individual, pure quantum states. Here, we propose a scheme to measure the temperature of such pure states through quantum interference. Our proposal involves interferometry of an auxiliary qubit probe, which is prepared in a superposition state and subsequently decoheres due to weak coupling with a closed, thermalised many-body system. Using only a few basic assumptions about chaotic quantum systems -- namely, the eigenstate thermalisation hypothesis and the emergence of hydrodynamics at long times -- we show that the qubit undergoes pure exponential decoherence at a rate that depends on the temperature of its surroundings. We verify our predictions by numerical experiments on a quantum spin chain that thermalises after absorbing energy from a periodic drive. Our work provides a general method to measure the temperature of isolated, strongly interacting systems under minimal assumptions.