Quantum critical systems are extremely sensitive to parameter variation near the critical point. Moreover, the derivatives with respect to the order parameter may exhibit divergence. This quantum criticality is widely utilized to enhance the performance of quantum metrology. In this study, we take the dissipative quantum Rabi model (QRM) as an example and use the bath-engineering technique to simulate the dissipative QRM to explore the impact of the quantum criticality on the quantum metrology under dissipation. We numerically calculate the dynamics of the inverse variance of the dissipative QRM around the critical point by using the quantum-simulation method and compare our results with those obtained by the numerically exact hierarchical equations of motion (HEOM). Our simulations show that in the case of the strong dissipation or the high temperature, the precision does not exhibit divergence when approaching the point of the quantum phase transition, and the enhancement of quantum metrology by quantum criticality is relatively limited. More importantly, the quantum-simulation method based on the bath-engineering technique can accurately simulate the dynamical evolution of the critical system and consumes significantly fewer resources as compared with the HEOM. Thus, it can be an alternative solution for investigating the dynamical evolution of larger critical systems for quantum metrology.
Quantum critical systems are extremely sensitive to parameter variation near the critical point. Moreover, the derivatives with respect to the order parameter may exhibit divergence. This quantum criticality is widely utilized to enhance the performance of quantum metrology. In this study, we take the dissipative quantum Rabi model (QRM) as an example and use the bath-engineering technique to simulate the dissipative QRM to explore the impact of the quantum criticality on the quantum metrology under dissipation. We numerically calculate the dynamics of the inverse variance of the dissipative QRM around the critical point by using the quantum-simulation method and compare our results with those obtained by the numerically exact hierarchical equations of motion (HEOM). Our simulations show that in the case of the strong dissipation or the high temperature, the precision does not exhibit divergence when approaching the point of the quantum phase transition, and the enhancement of quantum metrology by quantum criticality is relatively limited. More importantly, the quantum-simulation method based on the bath-engineering technique can accurately simulate the dynamical evolution of the critical system and consumes significantly fewer resources as compared with the HEOM. Thus, it can be an alternative solution for investigating the dynamical evolution of larger critical systems for quantum metrology.
Because quantum critical systems are very sensitive to the variation of parameters around the quantum phase transition (QPT), quantum criticality has been presented as an efficient resource for metrology. In this paper, we address the issue whether the divergent feature of the inverted variance is realizable in the presence of noise when approaching the QPT. Taking the quantum Rabi model (QRM) as an example, we obtain the analytical result for the inverted variance with single-photon relaxation. We show that the inverted variance may be convergent in time due to the noise. Since the precision of the metrology is very sensitive to the noise, as a remedy, we propose squeezing the initial state to improve the precision under decoherence. In addition, we also investigate the criticality-based metrology under the influence of the two-photon relaxation. Strikingly, although the maximum inverted variance still manifests a power-law dependence on the energy gap, the exponent is positive and depends on the dimensionless coupling strength. This observation implies that the criticality may not enhance but weaken the precision in the presence of two-photon relaxation, due to the non-linearity introduced by the two-photon relaxation.
Quantum Rabi model (QRM) is a fundamental model for light-matter interactions, the finite-component quantum phase transition (QPT) in the QRM has established a paradigmatic application for critical quantum metrology (CQM). However, such a paradigmatic application is restricted to a local regime of the QPT which has only a single critical point. In this work we propose a globalized CQM in the QRM by introducing an auxiliary nonlinear term which is realizable and can extend the critical point to a continuous critical regime. As a consequence, a high measurement precision is globally available over the entire coupling regime from the original critical point of the QRM down to the weak-coupling limit, as demonstrated by the globally accessible diverging quantum Fisher information in dynamics. We illustrate a measurement scheme by quadrature dynamics, with globally criticality-enhanced inverted variance as well as the scaling relation with respect to finite frequencies. In particular, we find that the globally high measurement precisions still survive in the presence of decoherence. Our proposal paves a way to break the local limitation of QPT of the QRM in CQM and enables a broader application, with implications of applicability in realistic situation.
Critical quantum metrology exploits the dramatic growth of the quantum Fisher information near quantum phase transitions to enhance the precision of parameter estimation. This enhancement is commonly associated with a closing energy gap, which causes the characteristic timescales for adiabatic preparation or relaxation to diverge with increasing system size. As a consequence, the apparent growth of the quantum Fisher information largely reflects the increasing evolution time induced by critical slowing down rather than a genuine improvement in metrological performance, thereby limiting the practical usefulness of such protocols. Here we show that the relationship between energy gaps, quantum correlations, and achievable precision in interacting quantum systems can be far more subtle. In particular, quantum-enhanced sensitivity can also emerge when the energy gap increases, eliminating critical slowing down and enabling substantially faster relaxation dynamics. Although the corresponding quantum Fisher information may decrease due to the shorter evolution time, the resulting precision can nevertheless remain quantum-enhanced. Building on this insight, we introduce an anti-critical quantum metrology scheme in which quantum-enhanced precision arises while the energy gap grows. We illustrate this mechanism using the quantum Rabi model, thereby identifying a route to metrological advantage that avoids the slow dynamics associated with conventional criticality.
The quantum Rabi model (QRM) with linear coupling between light mode and qubit exhibits the analog of a second-order phase transition for vanishing mode frequency which allows for criticality-enhanced quantum metrology in a few-body system. We show that the QRM including a nonlinear coupling term exhibits much higher measurement precisions due to its first-order-like phase transition at finite frequency, avoiding the detrimental slowing-down effect close to the critical point of the linear QRM. When a bias term is added to the Hamiltonian, the system can be used as a fluxmeter or magnetometer if implemented in circuit QED platforms.
Quantum metrology fundamentally relies upon the efficient management of quantum uncertainties. We show that under equilibrium conditions the management of quantum noise becomes extremely flexible around the quantum critical point of a quantum many-body system: this is due to the critical divergence of quantum fluctuations of the order parameter, which, via Heisenberg's inequalities, may lead to the critical suppression of the fluctuations in conjugate observables. Taking the quantum Ising model as the paradigmatic incarnation of quantum phase transitions, we show that it exhibits quantum critical squeezing of one spin component, providing a scaling for the precision of interferometric parameter estimation which, in dimensions d>2, lies in between the standard quantum limit and the Heisenberg limit. Quantum critical squeezing saturates the maximum metrological gain allowed by the quantum Fisher information in d=∞ (or with infinite-range interactions) at all temperatures, and it approaches closely the bound in a broad range of temperatures in d=2 and 3. This demonstrates the immediate metrological potential of equilibrium many-body states close to quantum criticality, which are accessible, e.g., to atomic quantum simulators via elementary adiabatic protocols.
Critical systems near quantum phase transitions were predicted to be useful for improvement of metrological precision, thanks to their ultrasensitive response to tiny variations of the control Hamiltonian. However, realizing criticality enhanced quantum metrology is experimentally challenging, mainly owing to decoherence and critical slowing down associated with the corresponding quantum state preparation. We circumvent these problems by making use of the critical behaviors in the Jaynes-Cummings model, to which the signal field is coupled. The information is encoded in the qubit's excitation number, which displays a divergent changing rate at the critical point, and is extremely robust against decoherence and nonadiabatic effects. We demonstrate such a metrological protocol in a superconducting circuit, where an Xmon qubit, interacting with a resonator, is used as a probe for estimating the amplitude of a microwave field. The measured quantum Fisher information exhibits a critical quantum enhancement, confirming the potential for quantum metrology.