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Bath-induced correlations lead to sub-shot-noise thermometry precision

Guim Planella Planas, Marina F. B. Cenni, Antonio Acín, Mohammad Mehboudi

Published Jan 31, 2020• 4 citations
OpenAlex

Abstract

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 $30$ 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.

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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 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.
We unveil a fundamental temperature bias in transient quantum thermometry under Markovian dynamics. For qubit probes evolving in a thermal Markovian environment, we prove that transient precision beyond the steady-state benchmark can be achieved if and only if the probe is initially colder than the bath temperature to be estimated. Cold probes are therefore both necessary and sufficient for enhanced transient precision in the Markovian regime. We then investigate the fate of this bias in the presence of environmental memory. In particular, in a non-Markovian scenario generated by an auxiliary-mediated system-bath coupling, we find that the cold-probe requirement for enhanced transient precision persists, indicating that the temperature bias survives certain forms of memory effects. In contrast, for a non-Markovian collisional model with perfect swap interactions between bath ancillas, transient enhancement is entirely absent regardless of the probe's initial temperature. This indicates that strong non-Markovianity can lead to the complete disappearance of the enhancement effect, placing hot and cold probes on equal footing, with neither capable of achieving enhanced precision in this regime.
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.
Quantum probes, such as single- and two-qubit probes, can accurately measure the temperature of a bosonic bath. The current investigation assesses the precision of the temperature estimate by using quantum Fisher information and the accompanying quantum signal-to-noise ratio. Employing an ancilla as a mediator between the probe and the bath improves thermometric sensitivity by transmitting temperature information into the probe qubit's coherences. In addition, we analyze two interacting qubits that were initially entangled or separated as quantum probes for various environmental configurations. Our findings show that increased precision is gained when the probe approaches its steady state, which is determined by the coupling between the two qubits. Furthermore, we can obtain high-efficiency temperature estimation for any low temperature by changing the interaction between the two qubits. Published by the American Physical Society 2024
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.