Simulating and Optimising Quantum Thermometry Using Single Photons

A classical thermometer typically works by exchanging energy with the system being measured until it comes to equilibrium, at which point the readout is related to the final energy state of the thermometer. A recent paper noted that different-temperature baths lead not only to different equilibrium states but also to different equilibration rates. In some cases this means that temperature discrimination is better achieved by comparing the rates than the asymptotic states -- and should therefore be carried out at finite times rather than once equilibration is essentially complete. The theory work also noted that for a \emph{quantum} thermometer, the difference between the relaxation rates for populations and coherences means that for intermediate time regimes (before full equilibration but after some characteristic time that depends on the temperatures of the baths), optimal discrimination is achieved not by probing energy only but by using quantum coherence as well. In this work, we study these effects experimentally. Implementing a recent proposal for efficiently emulating an arbitrary quantum channel, we use the quantum polarisation state of individual photons as models of "single-qubit thermometers" which evolve for a certain time in contact with a thermal bath. We investigate the optimal thermometer states for temperature discrimination, and the optimal interaction times, confirming that there is a broad regime where quantum coherence provides a significant improvement. We also discuss the more practical question of thermometers composed of a finite number of spins/qubits (greater than one), and characterize the performance of an adaptive protocol for making optimal use of all the qubits.