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

Multiparameter Estimation Perspective on Non-Hermitian Singularity-Enhanced Sensing

Describing the evolution of quantum systems by means of non-Hermitian generators opens a new avenue to explore the dynamical properties naturally emerging in such a picture, e.g. operation at the so-called exceptional points, preservation of parity-time symmetry, or capitalizing on the singular behavior of the dynamics. In this Letter, we focus on the possibility of achieving unbounded sensitivity when using the system to sense linear perturbations away from a singular point. By combining multiparameter estimation theory of Gaussian quantum systems with the one of singular-matrix perturbations, we introduce the necessary tools to study the ultimate limits on the precision attained by such singularity-tuned sensors. We identify under what conditions and at what rate can the resulting sensitivity indeed diverge, in order to show that nuisance parameters should be generally included in the analysis, as their presence may alter the scaling of the error with the estimated parameter.

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.

From classical to quantum walks with stochastic resetting on networks

Random walks are fundamental models of stochastic processes with applications in various fields, including physics, biology, and computer science. We study classical and quantum random walks under the influence of stochastic resetting on arbitrary networks. Based on the mathematical formalism of quantum stochastic walks, we provide a framework of classical and quantum walks whose evolution is determined by graph Laplacians. We study the influence of quantum effects on the stationary and long-time average probability distribution by interpolating between the classical and quantum regime. We compare our analytical results on stationary and long-time average probability distributions with numerical simulations on different networks, revealing differences in the way resets affect the sampling properties of classical and quantum walks.

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.