Dicke coupling by feasible local measurements at the superradiant quantum phase transition

Optimality and Noise Resilience of Critical Quantum Sensing

We compare critical quantum sensing to passive quantum strategies to perform frequency estimation, in the case of single-mode quadratic Hamiltonians. We show that, while in the unitary case both strategies achieve precision scaling quadratic with the number of photons, in the presence of dissipation this is true only for critical strategies. We also establish that working at the exceptional point or beyond threshold provides suboptimal performance. This critical enhancement is due to the emergence of a transient regime in the open critical dynamics, and is invariant to temperature changes. When considering both time and system size as resources, for both strategies the precision scales linearly with the product of the total time and the number of photons, in accordance with fundamental bounds. However, we show that critical protocols outperform optimal passive strategies if preparation and measurement times are not negligible. Our results are applicable to a broad variety of critical sensors whose phenomenology can be reduced to that of a single-mode quadratic Hamiltonian, including systems described by finite-component and fully connected models.

Critical Quantum Metrology Assisted by Real-Time Feedback Control

We investigate critical quantum metrology, that is, the estimation of parameters in many-body systems close to a quantum critical point, through the lens of Bayesian inference theory. We first derive a no-go result stating that any nonadaptive strategy will fail to exploit quantum critical enhancement (i.e., precision beyond the shot-noise limit) for a sufficiently large number of particles N whenever our prior knowledge is limited. We then consider different adaptive strategies that can overcome this no-go result and illustrate their performance in the estimation of (i) a magnetic field using a probe of 1D spin Ising chain and (ii) the coupling strength in a Bose-Hubbard square lattice. Our results show that adaptive strategies with real-time feedback control can achieve sub-shot-noise scaling even with few measurements and substantial prior uncertainty.

Integrable quantum many-body sensors for AC field sensing

Quantum sensing is inevitably an elegant example of the supremacy of quantum technologies over their classical counterparts. One of the desired endeavors of quantum metrology is AC field sensing. Here, by means of analytical and numerical analysis, we show that integrable many-body systems can be exploited efficiently for detecting the amplitude of an AC field. Unlike the conventional strategies in using the ground states in critical many-body probes for parameter estimation, we only consider partial access to a subsystem. Due to the periodicity of the dynamics, any local block of the system saturates to a steady state which allows achieving sensing precision well beyond the classical limit, almost reaching the Heisenberg bound. We associate the enhanced quantum precision to closing of the Floquet gap, resembling the features of quantum sensing in the ground state of critical systems. We show that the proposed protocol can also be realized in near-term quantum simulators, e.g. ion-traps, with a limited number of qubits. We show that in such systems a simple block magnetization measurement and a Bayesian inference estimator can achieve very high precision AC field sensing.

Critical Quantum Metrology in the Non-Linear Quantum Rabi Model

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.

Many-Body Nonlocality as a Resource for Quantum-Enhanced Metrology

We demonstrate that the many-body nonlocality witnessed by a broad family of Bell inequalities is a resource for ultraprecise metrology. We formulate a general scheme which allows one to track how the sensitivity grows with the nonlocality extending over an increasing number of particles. We illustrate our findings with some prominent examples-a collection of spins forming an Ising chain and a gas of ultracold atoms in any two-mode configuration. We show that in the vicinity of a quantum critical point the rapid increase of the sensitivity is accompanied by the emergence of the many-body Bell nonlocality. The method described in this work allows for a systematic study of highly quantum phenomena in complex systems, and also extends the understanding of the beneficial role played by fundamental nonclassical effects in implementations of quantum-enhanced protocols.

Global Sensing and Its Impact for Quantum Many-Body Probes with Criticality

Quantum sensing is one of the key areas that exemplify the superiority of quantum technologies. Nonetheless, most quantum sensing protocols operate efficiently only when the unknown parameters vary within a very narrow region, i.e., local sensing. Here, we provide a systematic formulation for quantifying the precision of a probe for multiparameter global sensing when there is no prior information about the parameters. In many-body probes, in which extra tunable parameters exist, our protocol can tune the performance for harnessing the quantum criticality over arbitrarily large sensing intervals. For the single-parameter sensing, our protocol optimizes a control field such that an Ising probe is tuned to always operate around its criticality. This significantly enhances the performance of the probe even when the interval of interest is so large that the precision is bounded by the standard limit. For the multiparameter case, our protocol optimizes the control fields such that the probe operates at the most efficient point along its critical line. Finally, it is shown that even a simple magnetization measurement significantly benefits from our global sensing protocol.

Dynamic Framework for Criticality-Enhanced Quantum Sensing

Quantum criticality, as a fascinating quantum phenomenon, may provide significant advantages for quantum sensing. Here we propose a dynamic framework for quantum sensing with a family of Hamiltonians that undergo quantum phase transitions (QPTs). By giving the formalism of the quantum Fisher information (QFI) for quantum sensing based on critical quantum dynamics, we demonstrate its divergent feature when approaching the critical point. We illustrate the basic principle and the details of experimental implementation using quantum Rabi model. The framework is applicable to a variety of examples and does not rely on the stringent requirement for particular state preparation or adiabatic evolution. It is expected to provide a route towards the implementation of criticality-enhanced quantum sensing.

In- and out-of-equilibrium quantum metrology with mean-field quantum criticality

We study the influence that collective transition phenomena have on quantum metrological protocols. The single spherical quantum spin (SQS) serves as stereotypical toy model that allows analytical insights on a mean-field level. First, we focus on equilibrium quantum criticality in the SQS and obtain the quantum Fisher information analytically, which is associated with the minimum lower bound for the precision of estimation of the parameter driving the phase transition. We compare it with the Fisher information for a specific experimental scenario where photon-counting-like measurements are employed. We find how quantum criticality and squeezing are useful resources in the metrological scenario. Second, we obtain the quantum Fisher information for the out-of-equilibrium transition in the dissipative nonequilibrium steady state and investigate how the presence of dissipation affects the parameter estimation. In this scenario, it is known that the critical point is shifted by an amount which depends on the dissipation rate. This is used here to design high precision protocols for a whole range of the transition-driving parameter in the ordered phase. In fact, for certain values of the parameter being estimated, dissipation may be used to obtain higher precision when compared to the equilibrium scenario.

Critical Quantum Metrology with a Finite-Component Quantum Phase Transition

Physical systems close to a quantum phase transition exhibit a divergent susceptibility, suggesting that an arbitrarily high precision may be achieved by exploiting quantum critical systems as probes to estimate a physical parameter. However, such an improvement in sensitivity is counterbalanced by the closing of the energy gap, which implies a critical slowing down and an inevitable growth of the protocol duration. Here, we design different metrological protocols that exploit the superradiant phase transition of the quantum Rabi model, a finite-component system composed of a single two-level atom interacting with a single bosonic mode. We show that, in spite of the critical slowing down, critical quantum optical probes can achieve a quantum-enhanced time scaling of the sensitivity in frequency-estimation protocols.

Fidelity susceptibility in Gaussian random ensembles

The fidelity susceptibility measures the sensitivity of eigenstates to a change of an external parameter. It has been fruitfully used to pin down quantum phase transitions when applied to ground states (with extensions to thermal states). Here, we propose to use the fidelity susceptibility as a useful dimensionless measure for complex quantum systems. We find analytically the fidelity susceptibility distributions for Gaussian orthogonal and unitary universality classes for arbitrary system sizes. The results are verified by a comparison with numerical data.

Quantum Probes for Ohmic Environments at Thermal Equilibrium

It is often the case that the environment of a quantum system may be described as a bath of oscillators with an ohmic density of states. In turn, the precise characterization of these classes of environments is a crucial tool to engineer decoherence or to tailor quantum information protocols. Recently, the use of quantum probes in characterizing ohmic environments at zero-temperature has been discussed, showing that a single qubit provides precise estimation of the cutoff frequency. On the other hand, thermal noise often spoil quantum probing schemes, and for this reason we here extend the analysis to a complex system at thermal equilibrium. In particular, we discuss the interplay between thermal fluctuations and time evolution in determining the precision attainable by quantum probes. Our results show that the presence of thermal fluctuations degrades the precision for low values of the cutoff frequency, i.e., values of the order ωc≲T (in natural units). For larger values of ωc, decoherence is mostly due to the structure of environment, rather than thermal fluctuations, such that quantum probing by a single qubit is still an effective estimation procedure.

Magnetic field sensing subject to correlated noise with a ring spin chain

In this paper, we focus on the magnetic field sensing subject to a correlated noise. We use a ring spin chain with only the nearest neighbor interactions as our probe to estimate both the intensity B and the direction θ of the magnetic field when the probe reaches its steady state. We numerically calculate the quantum Fisher information (QFI) to characterize the estimation precision. On the one hand, for estimating B, we find that the coupling between spins in the probe plays an important role in the precision, and the largest value of the QFI can be achieved when θ = π/2 together with an optimal coupling. Moreover, for any direction, the precision scaling can be better than the Heisenberg-limit (HL) with a proper coupling. On the other hand, for estimating θ, we find that our probe can perform a high precision detection for θ ~ π/2, with the QFI much larger than that for any other directions, especially when the coupling is tuned to the optimal value. And we find that the precision scaling for θ ~ π/2 can be better than the HL, but for other directions, the precision scaling is only limited to the standard quantum limit (SQL). Due to the computational complexity we restrict the number of spins in the probe to 60.