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arXiv:2005.02820 · Physical Review Research

Discrimination of thermal baths by single-qubit probes

Ilaria Gianani, Donato Farina, Marco Barbieri, Valeria Cimini, Vasco Cavina, Vittorio Giovannetti

Published Sep 25, 2020• 14 citations
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Abstract

Nonequilibrium states of quantum systems in contact with thermal baths help distinguishing between environments with different temperatures or different statistics.We extend these studies to a more generic problem that consists in discriminating between two baths with disparate constituents at unequal temperatures.Notably there exist temperature regimes in which the presence of coherence in the initial state preparation is beneficial for the discrimination capability.We also find that nonequilibrium states are not universally optimal and detail the conditions in which it becomes advantageous to wait for complete thermalization of the probe.These concepts are illustrated in a linear-optical simulation.

DOI
10.1103/physrevresearch.2.033497

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Nonequilibrium states of quantum systems in contact with thermal baths help distinguishing between environments with different temperatures or different statistics.We extend these studies to a more generic problem that consists in discriminating between two baths with disparate constituents at unequal temperatures.Notably there exist temperature regimes in which the presence of coherence in the initial state preparation is beneficial for the discrimination capability.We also find that nonequilibrium states are not universally optimal and detail the conditions in which it becomes advantageous to wait for complete thermalization of the probe.These concepts are illustrated in a linear-optical simulation.
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.
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We address a particular instance where open quantum systems may be used as quantum probes for an emergent property of a complex system, as the temperature of a thermal bath. The inherent fragility of the quantum probes against decoherence is the key feature making the overall scheme very sensitive. The specific setting examined here is that of quantum thermometry, which aims to exploit decoherence as a resource to estimate the temperature of a sample. We focus on temperature estimation for a bosonic bath at equilibrium in the Ohmic regime (ranging from sub-Ohmic to super-Ohmic), by using pairs of qubits in different initial states and interacting with different environments, consisting either of a single thermal bath or of two independent ones at the same temperature. Our scheme involves pure dephasing of the probes, thus avoiding energy exchange with the sample and the consequent perturbation of temperature itself. We discuss the role of correlations among the probes and the presence of a local versus a global bath. We show that entanglement improves thermometry at short times if the two qubits are embedded in a common bath, whereas if the interaction time is not constrained, then coherence rather than entanglement is the key resource in quantum thermometry.
Distinguishing hot from cold is the most primitive form of thermometry. Here we consider how well this task can be performed using a single qubit to distinguish between two different temperatures of a bosonic bath. In this simple setting, we find that letting the qubit equilibrate with the bath is not optimal, and depending on the interaction time it may be advantageous for the qubit to start in a state with some quantum coherence. We also briefly consider the case that the qubit is initially entangled with a second qubit that is not put into contact with the bath and show that entanglement allows for even better thermometry.
The possibility of discriminating the statistics of a thermal bath using indirect measurements performed on quantum probes is presented. The scheme relies on the fact that, when weakly coupled with the environment of interest, the transient evolution of the probe toward its final thermal configuration is strongly affected by the fermionic or bosonic nature of the bath excitations. Using figures of merit taken from quantum metrology such as the Holevo-Helstrom probability of error and the quantum Chernoff bound, we discuss how to achieve the greatest precision in this statistics tagging procedure, analyzing different models of probes and different initial preparations and by optimizing over the time of exposure of the probe.
Accurate temperature estimation in the quantum and cryogenic regimes remains a fundamental challenge. Here, we investigate nonequilibrium quantum thermometry using a single-qubit probe coupled to a bosonic bath through noncommuting interaction operators, which unify pure dephasing and dissipative dynamics within a spin-boson model. We show that the interference between these two coupling channels induces strong non-Markovian feedback between populations and coherences, leading to coherence trapping and enhanced thermal sensitivity. Remarkably, by tuning the coupling structure, the probe's temperature sensitivity exhibits a quadratic low-temperature scaling, even under weak coupling. Moreover, while coherence-based measurements are formally suboptimal, they become the most informative in the early nonequilibrium regime, where memory effects dominate. Our findings identify noncommutative system-bath couplings as a practical and tunable resource for achieving high-precision quantum thermometry in realistic open-system architectures.