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Chinese Physics B

Effect of system–reservoir correlations on temperature estimation*

Zhu Wen-li, Wei Wu, Hong‐Gang Luo

Published Dec 8, 2019• 5 citations
Publisher

Abstract

In many previous temperature estimation schemes, the temperature of a sample is directly read out from the final steady state of a quantum probe, which is coupled to the sample. However, in these studies, information of correlations between system (the probe) and reservoir (the sample) is usually eliminated, leading the steady state of the probe is a canonical equilibrium state with respect solely to system’s Hamiltonian. To explore the influence of system–reservoir correlations on the estimation precision, we investigate the equilibration dynamics of a spin interacting with a finite temperature bosonic reservoir. By incorporating an intermediate harmonic oscillator or a collective coordinate into the spin, the system–reservoir correlations can be correspondingly encoded in a Gibbs state of an effective Hamilton, which is size consistent with the original bare spin. Extracting information of temperature from this corrected steady state, we find the effect of the system-reservoir correlations on the estimation precision is highly sensitive to the details of the spectral density function of the measured reservoir.

DOI
10.1088/1674-1056/ab5fc0

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In many previous temperature estimation schemes, the temperature of a sample is directly read out from the final steady state of a quantum probe, which is coupled to the sample. However, in these studies, information of correlations between system (the probe) and reservoir (the sample) is usually eliminated, leading the steady state of the probe is a canonical equilibrium state with respect solely to system’s Hamiltonian. To explore the influence of system–reservoir correlations on the estimation precision, we investigate the equilibration dynamics of a spin interacting with a finite temperature bosonic reservoir. By incorporating an intermediate harmonic oscillator or a collective coordinate into the spin, the system–reservoir correlations can be correspondingly encoded in a Gibbs state of an effective Hamilton, which is size consistent with the original bare spin. Extracting information of temperature from this corrected steady state, we find the effect of the system-reservoir correlations on the estimation precision is highly sensitive to the details of the spectral density function of the measured reservoir.
Abstract We study the impact of quantum correlations existing within the system-environment thermal equilibrium state while estimating the parameters of the spin reservoir. By employing various physical situations of interest, we present results for the reservoir temperature and its coupling strength with the central two-level system. The central system (probe) interacts with the bunch of randomly oriented spin systems and attains a thermal equilibrium state. We consider a projective measurement which prepares the probe’s initial state, and then the global system (probe and reservoir) evolves unitarily. The reduced density operator encapsulates the information about the spin reservoir which can be extracted by doing measurements on the probe. The precision of such measurement is quantified by quantum Fisher information. We repeat this process if the probe-reservoir initial state is not correlated (product state). We compare the estimation results for both with and without the outturn of initial correlations. In the temperature estimation case, our results are promising as one can significantly improve the accuracy of the estimates by including the effect of initial correlations. A similar trend prevails in the case of coupling strength estimation especially at low temperatures.
We study the role of bath-induced correlations in temperature estimation of cold Bosonic baths. Our protocol includes multiple probes, that are not interacting, nor are they initially correlated to each other. They interact with a Bosonic sample and reach a non-equilibrium steady state, which is measured to estimate the temperature of the sample. It is well-known that in the steady state such non-interacting probes may get correlated to each other and even entangled. Nonetheless, the impact of these correlations in metrology has not been deeply investigated yet. Here, we examine their role for thermometry of cold Bosonic gases and show that, although being classical, bath-induced correlations can indeed lead to sub-shot-noise precision for thermometry at low temperatures; e.g., for a probe of 303030 non-interacting impurities they can enhance the quantum Fisher information by two orders of magnitude. The proposed thermometry scheme here does not require precise dynamical control of the probes and tuning the parameters, as it is build upon the non-equilibrium steady state of a non-interacting system. Our results put forward new possibilities in thermometry at low temperatures, of relevance for instance in cold gases and Bose--Einstein condensates.
We study the role of bath-induced correlations in temperature estimation of cold bosonic baths. Our protocol includes multiple probes, that are not interacting, nor are they initially correlated to each other. They interact with a bosonic sample and reach a nonthermal steady state, which is measured to estimate the temperature of the sample. It is well known that in the steady state such noninteracting probes may get correlated to each other and even entangled. Nonetheless, the impact of these correlations in metrology has not been deeply investigated yet. Here, we examine their role for thermometry of cold bosonic gases and show that, although being classical, bath-induced correlations can lead to significant enhancement of precision for thermometry. The improvement is especially important at low temperatures, where attaining high precision thermometry is particularly demanding. The proposed thermometry scheme does not require any precise dynamical control of the probes and tuning the parameters and is robust to noise in initial preparation, as it is built upon the steady state generated by the natural dissipative dynamics of the system. Therefore, our results put forward new possibilities in thermometry at low temperatures, of relevance, for instance, in cold gases and Bose-Einstein condensates.
We investigate the effect of initial system-environment correlations to improve the estimation of environment parameters. By employing various physical situations of interest, we present results for the environment temperature and system-environment coupling strength. We consider the spin-spin model whereby a probe (a small controllable quantum system) interacts with a bath of quantum spins and attains a thermal equilibrium state. A projective measurement is then performed to prepare the initial state and allow it to evolve unitarily. The properties of the environment are imprinted upon the dynamics of the probe. The reduced density matrix of the probe state contains a modified decoherence factor and dissipation. This additional factor acts in such a way to improve the estimation of the environment parameters, as quantified by the quantum Fisher information (QFI). In the temperature estimation case, our results are promising as one can improve the precision of the estimates by orders of magnitude by incorporating the effect of initial correlations. The precision increases in the strong coupling regime even if the nearest neighbours' interaction is taken into account. In the case of coupling strength, interestingly the accuracy was found to be continuously increasing in both with and without correlations cases. More importantly, one can see the noticeable role of correlations in improving precision, especially at low temperatures.
Equilibrium probes have been widely used in various schemes of sensing to quantum reservoirs. Many previous studies assumed that the probe-reservoir coupling is sufficiently weak such that the equilibrium state of the probe is approximately described by a canonical Gibbs state at the same temperature of the reservoir. Such a weak-coupling approximation severely restricts the range of application for an equilibrium-probe-based quantum sensing scenario. Going beyond the weak-coupling limitation, we here investigate the noncanonical effect, which is naturally induced by strong couplings, on the performance of a quantum sensing scheme. In this scheme, a quantum two-level system is used as the probe to estimate the parameters of a dissipative bosonic reservoir, by employing the polaron transformation approach. It is found that, compared with that of the canonical-equilibrium-state case, the noncanonical effect can effectively boost the sensing precision at both zero and finite temperatures. Paving the way toward realizing high-precision quantum sensing in practice, our result reveals the positive role of noncanonicality in the studies of quantum technologies.
Accurately characterizing the properties of structured reservoirs is a key challenge in quantum systems and is of great importance for advances in quantum metrology and sensing. In this work, we employ a two-level system (qubit) as a probe, which is coupled to a structured reservoir consisting of an ancilla qubit and a Markovian environment modeled as a thermal bath. By exploiting non-Markovian dynamics, we systematically investigate the effectiveness of different interaction types between the probe and ancilla for estimating critical parameters, including temperature, ancilla frequency, and system-bath coupling strength. We quantify the precision of parameter estimation using quantum Fisher information (QFI) and analyze the system dynamics in both transient and steady-state regimes. Our findings demonstrate that non-Markovianity substantially enhances parameter estimation in the transient regime, with specific interactions facilitating sustained information backflow and yielding higher QFI values. However, the performance of these interactions is contingent on the parameter under estimation and the operational regime. For instance, certain interactions become prominent in the transient regime but exhibit diminished utility in the steady state, whereas others maintain their effectiveness even at equilibrium. These results stress the importance of judiciously selecting interactions adapted to specific estimation objectives and operational regimes.