Precise measurement of coupling strength and high temperature quantum effect in a nonlinearly coupled qubit-oscillator system

TL;DR

This paper investigates the coherence dynamics of a qubit coupled to a harmonic oscillator with both linear and quadratic interactions, revealing how quadratic coupling influences coherence decay and revival, enabling precise measurement of coupling strength at high temperatures.

Contribution

It provides a detailed analysis of coherence behavior in a nonlinearly coupled qubit-oscillator system, highlighting the role of quadratic coupling and its measurement advantages without cooling.

Findings

Coherence revives periodically at 2π/g₂

Coherence peak width decreases with temperature

Quadratic coupling effects persist beyond classical limits

Abstract

We study the coherence dynamics of a qubit coupled to a harmonic oscillator with both linear and quadratic interactions. As long as the linear coupling strength is much smaller than the oscillator frequency, the long time behavior of the coherence is dominated by the quadratic coupling strength $g_2$. The coherence decays and revives at a period $2\pi/g_2$, with the width of coherence peak decreases as the temperature increases, hence providing a way to measure $g_2$ precisely without cooling. Unlike the case of linear coupling, here the coherence dynamics never reduces to the classical limit in which the oscillator is classical. Finally, the validity of linear coupling approximation is discussed and the coherence under Hahn-echo is evaluated