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High precision multi-temperature quantum thermometry via dynamical control

Victor Mukherjee, Analía Zwick, Arnab Ghosh, Gershon Kurizki

Published Nov 27, 2017• 4 citations
OpenAlex

Abstract

We consider a thermometer modelled by a dynamically-controlled multilevel quantum system in contact with a bath. Periodic modulation of the energy level spacings of our quantum thermometer enables us to dramatically increase the accuracy of temperature estimation. As opposed to the diverging relative error near the absolute zero obtained in conventional thermometers, our control scheme enables high precision temperature estimation arbitrarily close to the absolute zero, by maximizing its quantum Fisher information. Alternatively, dynamical control may allow for high-precision measurement of multiple temperatures.

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We consider a thermometer modelled by a dynamically-controlled multilevel quantum system in contact with a bath. Periodic modulation of the energy level spacings of our quantum thermometer enables us to dramatically increase the accuracy of temperature estimation. As opposed to the diverging relative error near the absolute zero obtained in conventional thermometers, our control scheme enables high precision temperature estimation arbitrarily close to the absolute zero, by maximizing its quantum Fisher information. Alternatively, dynamical control may allow for high-precision measurement of multiple temperatures.
Abstract High-precision low-temperature thermometry is a challenge for experimental quantum physics and quantum sensing. Here we consider a thermometer modeled by a dynamically-controlled multilevel quantum probe in contact with a bath. Dynamical control in the form of periodic modulation of the energy-level spacings of the quantum probe can dramatically increase the maximum accuracy bound of low-temperatures estimation, by maximizing the relevant quantum Fisher information. As opposed to the diverging relative error bound at low temperatures in conventional quantum thermometry, periodic modulation of the probe allows for low-temperature thermometry with temperature-independent relative error bound. The proposed approach may find diverse applications related to precise probing of the temperature of many-body quantum systems in condensed matter and ultracold gases, as well as in different branches of quantum metrology beyond thermometry, for example in precise probing of different Hamiltonian parameters in many-body quantum critical systems.
The metrological limits of thermometry operated in nonequilibrium dynamical regimes are analyzed. We consider a finite-dimensional quantum system, employed as a quantum thermometer, in contact with a thermal bath inducing Markovian thermalization dynamics. The quantum thermometer is initialized in a generic quantum state, possibly including quantum coherence with respect to the Hamiltonian basis. We prove that the precision of the thermometer, quantified by the Quantum Fisher Information, is enhanced by the quantum coherence in its initial state. We analytically show this in the specific case of qubit thermometers for which the maximization of the Quantum Fisher Information occurs at a finite time during the transient thermalization dynamics. Such a finite-time precision enhancement can be better than the precision that is achieved asymptotically.
Abstract Quantum thermometry refers to the study of measuring ultra-low temperatures in quantum systems. The precision of such a quantum thermometer is limited by the degree to which temperature can be estimated by quantum measurements. More precisely, the maximal precision is given by the inverse of the quantum Fisher information. In the present analysis, we show that quantum thermometers that are described by nonlinear Schrödinger equations allow for a significantly enhanced precision, that means larger quantum Fisher information. This is demonstrated for a variety of pedagogical scenarios consisting of single and two-qubits systems. The enhancement in precision is indicated by non-vanishing quantum speed limits, which originate in the fact that the thermal, Gibbs state is typically not invariant under the nonlinear equations of motion.
Quantum thermometry aims to measure temperature in nanoscale quantum systems, paralleling classical thermometry. However, temperature is not a quantum observable, and most theoretical studies have therefore concentrated on analyzing fundamental precision limits set by the quantum Fisher information through the quantum Cramer-Rao bound. In contrast, whether a direct temperature readout can be achieved in quantum thermometry remains largely unexplored, particularly under the nonequilibrium conditions prevalent in real-world applications. To address this, we develop a direct temperature readout scheme based on a thermodynamic inference strategy. The scheme integrates two conceptual developments: (i) By applying the maximum entropy principle with the thermometer's mean energy as a constraint, we assign a reference temperature to the nonequilibrium thermometer. We demonstrate that this reference temperature outperforms a commonly used effective temperature defined through equilibrium analogy. (ii) We obtain positive semi-definite error functions that lower-bound the deviation of the reference temperature from the true temperature-in analogy to the quantum Cramer-Rao bound for the mean squared error-and vanish upon thermalization with the sample. Combining the reference temperature with these error functions, we introduce a notion of corrected dynamical temperature which furnishes a postprocessed temperature readout under nonequilibrium conditions. This corrected dynamical temperature can be evaluated adaptively without prior knowledge of the actual temperature. We validate the corrected dynamical temperature in a qubit-based thermometer under a range of nonequilibrium initial states, confirming its capability to estimate the true temperature. Importantly, we find that increasing quantum coherence can enhance the precision of this readout.
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.
In quantum theory, the inescapable interaction between a system and its surroundings would lead to a loss of coherence and leakage of information into the environment. An effective approach to retain the quantum characteristics of the system is to decouple it from the environment. However, things get complicated in quantum parameter estimation tasks, especially when the unknown parameter originates from the environment. Here, we propose a general dynamical modulation scheme that enables the enhancement of estimation precision irrespective of the origin of the parameters to be estimated. Notably, beyond the capability of dynamically decoupling the system from the environment, our proposal can select the effective frequency of the system and in turn manipulate the dynamics of the system, such as the steady-state probability and the decay rate, which are sensitive to the bath parameter. Therefore, the quantum Fisher information is dramatically increased, leading to superior estimation precision. Specifically, we elucidate the effectiveness of our proposal with prototypical examples of the Ramsey spectroscopy and quantum thermometer. Our findings offer an alternative route to enhance the precision of quantum estimation processes and may have potential applications in diverse branches of quantum metrology.