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arXiv:2412.01028 · Physical Review A

Low-temperature quantum metrology enhanced by strong coupling

Ze-Zhou Zhang, Hong‐Gang Luo, Wei Wu

Published May 23, 2025• 4 citations
arXivHTMLPDF

Abstract

Equilibrium probes have been widely used in various noisy quantum metrology schemes. However, such an equilibrium-probe-based metrology scenario severely suffers from the low-temperature-error-divergence problem in the weak-coupling regime. To circumvent this limit, we propose a strategy to eliminate the error-divergence problem by utilizing the strong-coupling effects, which can be captured by the reaction-coordinate mapping. The strong couplings induce a noncanonical equilibrium state which greatly enhances the metrology performance. It is found that our metrology precision behaves as a polynomial-type scaling relation, which suggests the reduction of temperature can be used as a resource to improve the metrology performance. Our result is sharply contrary to that of the weak-coupling case, in which the metrology precision exponentially decays as the temperature decreases. Paving a way to realize a high-precision noisy quantum metrology at low temperatures, our result reveals the importance of the non-Markovianity in quantum technologies.

DOI
10.1103/physreva.111.052623

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Equilibrium probes have been widely used in various noisy quantum metrology schemes. However, such an equilibrium-probe-based metrology scenario severely suffers from the low-temperature-error-divergence problem in the weak-coupling regime. To circumvent this limit, we propose a strategy to eliminate the error-divergence problem by utilizing the strong-coupling effects, which can be captured by the reaction-coordinate mapping. The strong couplings induce a noncanonical equilibrium state which greatly enhances the metrology performance. It is found that our metrology precision behaves as a polynomial-type scaling relation, which suggests the reduction of temperature can be used as a resource to improve the metrology performance. Our result is sharply contrary to that of the weak-coupling case, in which the metrology precision exponentially decays as the temperature decreases. Paving a way to realize a high-precision noisy quantum metrology at low temperatures, our result reveals the importance of the non-Markovianity in quantum technologies.
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.
We consider the problem of estimating the temperature TTT of a very cold equilibrium sample. The temperature estimates are drawn from measurements performed on a quantum Brownian probe strongly coupled to it. We model this scenario by resorting to the canonical Caldeira-Leggett Hamiltonian and find analytically the exact stationary state of the probe for arbitrary coupling strength. In general, the probe does not reach thermal equilibrium with the sample, due to their nonperturbative interaction. We argue that this is advantageous for low-temperature thermometry, as we show in our model that (i) the thermometric precision at low TTT can be significantly enhanced by strengthening the probe-sampling coupling, (ii) the variance of a suitable quadrature of our Brownian thermometer can yield temperature estimates with nearly minimal statistical uncertainty, and (iii) the spectral density of the probe-sample coupling may be engineered to further improve thermometric performance. These observations may find applications in practical nanoscale thermometry at low temperatures---a regime which is particularly relevant to quantum technologies.
We investigate quantum thermometry using a single-qubit probe embedded in a non-Markovian environment, employing the numerically exact hierarchical equations of motion (HEOM) to overcome the limitations of Born-Markov approximations. Through a systematic analysis of the dynamical and steady-state behavior of the quantum signal-to-noise ratio (QSNR) for temperature estimation, we identify several key findings that challenge the conventional expectation that strong coupling necessarily enhances thermometric performance. In nonequilibrium dynamical thermometry, weak system-environment coupling generally yields the optimal QSNR, whereas in the steady-state regime, strong coupling enhances sensitivity only in the ultralow-temperature limit, while weak coupling significantly improves precision at moderately low temperatures. To optimize performance across coupling regimes, we develop a hybrid computational framework that integrates HEOM with quantum-enhanced particle swarm optimization, enabling precise quantum dynamical control under varying coupling strengths. Our results reveal fundamental constraints and opportunities in quantum thermometry, offering practical strategies for the design of high-performance quantum thermometers operating in realistic open quantum systems.
Equilibrium quantum thermometry seeks to enhance temperature estimation for reservoirs at thermal equilibrium using quantum resources, yet achieving the Heisenberg scaling in a physical protocol remains a significant challenge. Moreover, quantum measurements face an intrinsic limitation arising from an exponential suppression of thermometric sensitivity as the temperature approaches zero. This limitation severely hinders access to high precision in the low-temperature regime. Here, we demonstrate a simple but powerful quantum engineering protocol to overcome these limitations and reach high precision for temperature estimation. By engineering a small subset of central probes and their linear coupling to a larger array of adjacent probes, we show that the composite partition function can be tailored to yield Heisenberg-limited precision for temperature estimation. Critically, we show that this protocol can simultaneously saturate the Landau bound at low temperatures, an inverse quadratic scaling with the temperature, thereby fully exploiting the potential of equilibrium thermometry and circumventing the exponential suppression of thermometric sensitivity in the low-temperature regime. This scheme relies solely on linear interactions, avoiding complicated many-body couplings and ensuring scalability with the number of probes. Moreover, we find that the comparable precision can be achieved using only local measurements on the central probes, substantially reducing the implementation complexity compared to global measurement schemes and offering a promising approach toward high-precision equilibrium thermometry in physical systems.
We study low-temperature non-equilibrium quantum thermometry with a bosonic probe: a quantum harmonic oscillator strongly coupled to a bosonic bath at temperature TTT through a Drude--Ohmic spectral density. We treat the probe--bath dynamics both exactly, using the quadratic solution of Boyanovsky and Jasnow, and within a renormalized Gorini--Kossakowski--Lindblad--Sudarshan (GKLS) master equation. From the time-dependent covariance matrix we extract the quantum Fisher information (QFI) for general single-mode Gaussian probe states, including squeezed ones. In the strong-coupling, non-Markovian regime the QFI is non-monotonic in time, displaying bath-memory revivals that make a finite interrogation time t∗>0t^*>0t∗>0 strictly optimal. By contrast, we prove that the Markovian QFI rises monotonically to its stationary value and develops no interior optimum, so that its optimum is always pinned to the boundary t∗→∞t^*\to\inftyt∗→∞; this complements existing Markovian precision-rate bounds, which concern (F(t)/t)(\mathcal F(t)/t)(F(t)/t) rather than the single-shot QFI (F(t))(\mathcal F(t))(F(t)). Squeezed initial states yield a large transient advantage that thermalisation eventually erases, establishing squeezing and interrogation time as complementary thermometric resources. At equilibrium, strong coupling replaces the exponential Boltzmann suppression of the low-temperature relative error by a far milder polynomial divergence. As the model maps directly onto circuit quantum electrodynamics, these protocols appear within current experimental reach.
The rapidly developing quantum technologies and thermodynamics have put forward a requirement to precisely control and measure the temperature of microscopic matter at the quantum level. Many quantum thermometry schemes have been proposed. However, precisely measuring low temperature is still challenging because the obtained sensing errors generally tend to diverge with decreasing temperature. Using a continuous-variable system as a thermometer, we propose non-Markovian quantum thermometry to measure the temperature of a quantum reservoir. A mechanism to make the sensing error $\ensuremath{\delta}T$ scale with the temperature TTT as the Landau bound $\ensuremath{\delta}T\ensuremath{\simeq}T$ in the full-temperature regime is discovered. Our analysis reveals that it is the quantum criticality of the total thermometer-reservoir system that causes this enhanced sensitivity. Efficiently avoiding the error-divergence problem, our result gives an efficient way to precisely measure the low temperature of quantum systems.