Qubit thermometry for micromechanical resonators

TL;DR

This paper investigates quantum-limited temperature estimation of micromechanical resonators using a coupled qubit, demonstrating optimal measurement strategies and showing current technology can reach fundamental precision limits.

Contribution

It introduces a method to optimize qubit-based thermometry for resonators, identifying conditions where population measurements are optimal and achievable with existing technology.

Findings

Population measurement is optimal for temperature estimation.

Optimal qubit preparation and interaction time maximize Fisher information.

Current technology can reach the quantum limit of measurement precision.

Abstract

We address estimation of temperature for a micromechanical oscillator lying arbitrarily close to its quantum ground state. Motivated by recent experiments, we assume that the oscillator is coupled to a probe qubit via Jaynes-Cummings interaction and that the estimation of its effective temperature is achieved via quantum limited measurements on the qubit. We first consider the ideal unitary evolution in a noiseless environment and then take into account the noise due to non dissipative decoherence. We exploit local quantum estimation theory to assess and optimize the precision of estimation procedures based on the measurement of qubit population, and to compare their performances with the ultimate limit posed by quantum mechanics. In particular, we evaluate the Fisher information (FI) for population measurement, maximize its value over the possible qubit preparations and interaction times, and compare its behavior with that of the quantum Fisher information (QFI). We found that the FI for population measurement is equal to the QFI, i.e., population measurement is optimal, for a suitable initial preparation of the qubit and a predictable interaction time. The same configuration also corresponds to the maximum of the QFI itself. Our results indicate that the achievement of the ultimate bound to precision allowed by quantum mechanics is in the capabilities of the current technology.