Conventional criticality-based quantum metrological schemes work only at zero or very low temperature because the quantum uncertainty around the quantum phase-transition point is generally erased by thermal fluctuations with the increase of temperature. Such an ultralow-temperature requirement severely restricts the development of quantum critical metrology. In this paper, we propose a thermodynamic-criticality-enhanced quantum sensing scenario at finite temperature. In our scheme, a qubit is employed as a quantum sensor to estimate parameters of interest in the Dicke model which experiences a thermodynamic phase transition. It is revealed that the thermodynamic criticality of the Dicke model can significantly improve the sensing precision. Enriching the scope of quantum critical metrology, our finding provides a possibility to realize highly sensitive quantum sensing without cooling.
Conventional criticality-based quantum metrological schemes work only at zero or very low temperature because the quantum uncertainty around the quantum phase-transition point is generally erased by thermal fluctuations with the increase of temperature. Such an ultralow-temperature requirement severely restricts the development of quantum critical metrology. In this paper, we propose a thermodynamic-criticality-enhanced quantum sensing scenario at finite temperature. In our scheme, a qubit is employed as a quantum sensor to estimate parameters of interest in the Dicke model which experiences a thermodynamic phase transition. It is revealed that the thermodynamic criticality of the Dicke model can significantly improve the sensing precision. Enriching the scope of quantum critical metrology, our finding provides a possibility to realize highly sensitive quantum sensing without cooling.
Abstract Criticality is widely regarded as a potential resource to boost the performance of quantum sensing. In existing protocols of criticality-enhanced quantum sensing, the criticality typically originates either from the probe or from the detected system itself. We here propose a scheme for sensing a dissipative reservoir based on the thermal criticality induced by the probe-reservoir interaction at finite temperature. It is revealed that the strong-coupling characteristics of the probe are able to create an additional thermal criticality, which significantly enhances the sensing performance. Our proposed scheme does not require precise dynamical control and is universal to different initial states, as it is built upon the equilibrium state generated by the natural dissipative dynamics of the probe. Expanding the scope of critical metrology, our findings pave a possible route toward high-precision quantum sensing.
Quantum metrology, a cornerstone of quantum technologies, exploits entanglement and superposition to achieve higher precision than classical protocols in parameter-estimation tasks. When combined with critical phenomena such as phase transitions, the divergence of quantum fluctuations is predicted to enhance the performance of quantum sensors. Here, we implement a critical quantum sensor using a superconducting parametric (i.e., two-photon driven) Kerr resonator. The sensor, a linear resonator terminated by a superconducting quantum interference device, operates near the critical point of a finite-component second-order dissipative phase transition obtained by scaling the system parameters. We analyze the performance of a frequency-estimation protocol and show that quadratic precision scaling with respect to the system size can be achieved with finite values of the Kerr nonlinearity. Since each photon emitted from the cavity carries more information about the parameter to be estimated compared to its classical counterpart, our protocol opens up perspectives for faster or more precise metrological protocols. Our results demonstrate that quantum advantage in a sensing protocol can be achieved by exploiting a phase transition.
Abstract Quantum systems can be used as probes in the context of metrology for enhanced parameter estimation. In particular, the delicacy of critical systems to perturbations can make them ideal sensors. Arguably the simplest realistic probe system is a spin- 1 2 impurity, which can be manipulated and measured in-situ when embedded in a fermionic environment. Although entanglement between a single impurity probe and its environment produces nontrivial many-body effects, criticality cannot be leveraged for sensing. Here we introduce instead the two-impurity Kondo model as a novel paradigm for critical quantum metrology, and examine the multiparameter estimation scenario at finite temperature. We explore the full metrological phase diagram numerically and obtain exact analytic results near criticality. Enhanced sensitivity to the inter-impurity coupling driving a second-order phase transition is evidenced by diverging quantum Fisher information (QFI) and quantum signal-to-noise ratio (QSNR). However, with uncertainty in both coupling strength and temperature, the multiparameter QFI matrix becomes singular—even though the parameters to be estimated are independent—resulting in vanishing QSNRs. We demonstrate that by applying a known control field, the singularity can be removed and measurement sensitivity restored. For general systems, we show that the degradation in the QSNR due to uncertainties in another parameter is controlled by the degree of correlation between the unknown parameters.
Critical quantum metrology exploits the hypersensitivity of quantum systems near phase transitions to achieve enhanced precision in parameter estimation. While single-parameter estimation near critical points is well established, the simultaneous estimation of multiple parameters, which is essential for practical sensing applications, remains challenging. This difficulty arises from sloppiness, a phenomenon that typically renders the quantum Fisher information matrix (QFIM) singular or nearly singular. In this work, we demonstrate that multiparameter critical metrology is not only feasible but can also retain divergent precision scaling, provided one accepts a trade-off in the scaling exponent. Using the ground state of the single-cavity Dicke model (DM), we show that two Hamiltonian parameters can be simultaneously estimated with a scalar variance bound scaling as the square root of the critical parameter. This overcomes the inherent sloppiness by leveraging higher-order contributions to the QFIM. To recover the optimal quadratic scaling, we introduce the Dicke dimer (DD) with photon hopping. In this extended model, a triple point in the phase diagram enables the simultaneous closure of two excitation gaps, which effectively increases the rank of the QFIM and restores the ideal single-parameter scaling for specific parameter pairs. Furthermore, we extend our analysis to dissipative settings subject to photon loss. Finally, we establish a connection between the derived critical scalings and the fundamental state preparation time, providing a unified framework to operationally compare different sensing strategies. Our results demonstrate that critical quantum metrology can be made robust against dissipation and scalable to multiparameter scenarios, paving the way for practical quantum sensors operating near phase transitions.
Temperature estimation of interacting quantum many-body systems is both a challenging task and topic of interest in quantum metrology, given that critical behavior at phase transitions can boost the metrological sensitivity. Here we study noninvasive quantum thermometry of a finite, two-dimensional Ising spin lattice based on measuring the dephasing dynamics of a spin probe coupled to the lattice. We demonstrate a strong critical enhancement of the achievable precision in terms of the quantum Fisher information, which depends on the coupling range and the interrogation time. Our numerical simulations are compared to instructive analytic results for the critical scaling of the sensitivity in the Curie-Weiss model of a fully connected lattice and to the mean-field description in the thermodynamic limit, both of which fail to describe the critical spin fluctuations on the lattice the spin probe is sensitive to. Phase metrology could thus help to investigate the critical behavior of finite many-body systems beyond the validity of mean-field models. Published by the American Physical Society 2024
Critical quantum metrology relies on the extreme sensitivity of a system's eigenstates near the critical point of a quantum phase transition to Hamiltonian perturbations. This means that these eigenstates are extremely sensitive to all the parameters of the Hamiltonian. In realistic settings, there is always some degree of uncertainty in the control parameters used to tune the system to criticality. These uncertainties, while not the target of estimation, can significantly affect the attainable precision, effectively acting as nuisance parameters in the estimation process. Despite being a practically relevant source of noise, their impact on critical metrology has been largely overlooked. In this work we present a general framework that interpolates between single- and multiparameter estimation settings, enabling a systematic analysis of how such uncertainties influence sensitivity. We apply this framework to the paradigmatic transverse field Ising and Lipkin-Meshkov-Glick models, explicitly demonstrating how uncertainty in control parameters affects the metrological performance of critical sensors. For finite-size systems, we identify a fundamental trade-off between robustness to uncertainty and the ability to retain a quantum advantage at the critical point. Our results contribute to a deeper understanding of the practical limitations of critical quantum metrology and provide a route toward its more resilient implementation.