Quantum Simulation of Single-Qubit Thermometry Using Linear Optics

Abstract

Standard thermometry employs the thermalization of a probe with the system of interest. This approach can be extended by incorporating the possibility of using the nonequilibrium states of the probe and the presence of coherence. Here, we illustrate how these concepts apply to the single-qubit thermometer introduced by Jevtic et al. [Phys. Rev. A 91, 012331 (2015)PLRAAN1050-294710.1103/PhysRevA.91.012331] by performing a simulation of the qubit-environment interaction in a linear-optical device. We discuss the role of the coherence and how this affects the usefulness of nonequilibrium conditions. The origin of the observed behavior is traced back to how the coherence affects the propensity to thermalization. We discuss this aspect by considering the availability function.

Bridging thermodynamics and metrology in nonequilibrium quantum thermometry

“…Some paradigmatic examples of nanoscale thermometry involve nanomechanical resonators [19], quantum harmonic oscillators [20] or atomic condensates [21][22][23] (also in conjunction with estimation of chemical potential [24]). In this context the analysis of quantum properties needs to be taken into account in order to establish, and eventually enhance, metrological precision [18,[25][26][27][28][29].In a conventional approach to thermometry, an external bath B at thermal equilibrium is typically indirectly probed via an ancillary system, the thermometer S, that is placed into weak-interaction with the former. Assuming hence that the thermometer reaches the thermal equilibrium configuration without perturbing B too much, the Einstein Theory of Fluctuations (ETF) can be used to characterize the sensitivity of the procedure in terms of the heat capacity of S which represents its thermal susceptibility to the perturbation imposed by the bath [30][31][32].…”

“…However thermometry schemes that do not need a full thermalization of the probe have been recognized to offer higher sensitivities in temperature estimation [33].Thus, if on the one hand the QCRB can still be used as the proper tool to gauge the measurement uncertainty on the bath temperature, on the other hand establishing a direct link between this approach and the thermodynamic properties of the probe is still an open question. Furthermore, the advantages pointed out in [33] are conditional on precisely addressing the probe during its evolution, a task which might be demanding in real experiments [28]. Here S is assumed to be a quantum system characterized by a local Hamiltonian H that, after being initialized into some proper input state ρ(0), weakly interacts for some time τ with the bath B of assigned, but unknown, temperature T , before been measured.…”

“…The previous decomposition depicts the GAD as a weighted sum of two different processes, an AD and an IAD with weights respectively equal to N +1 2N +1 and 1 2N +1 . This last property is crucial for implementing a quantum optical simulation of the process: after reproducing the AD and the IAD channel through a succession of optical logic gates, is possible to reconstruct the full density matrix simply doing a proper weighted sum of the outputs of the two channels [28]. Specifically, an AD acting on a qubit S can be formally simulated by coupling the system with an ancilla A and doing the following operations :1.…”

Experimental Quantum Thermodynamics with Linear Optics

“…The first one [48] analyzes the use of a single qubit as a thermometer. In standard thermodynamics, the temperature is defined only for systems in equilibrium with its surroundings acting as a thermal bath.…”

“…In order to reduce the scale of the thermometers, Jevtic et al [49] proposed a model where you can use a single qubit to obtain the information about two temperatures of a bosonic bath. Mancino et al [48] presented an experimental investigation of this model using a laser beam, interferometers, and photodiodes. They implemented and measured optical thermal states prepared in the polarization degree of freedom.…”