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arXiv:2103.13418 · Physical Review Research

Identifying and harnessing dynamical phase transitions for quantum-enhanced sensing

Qingze Guan, Robert J. Lewis-Swan

Published Aug 30, 2021• 23 citations
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Abstract

We use the quantum Fisher information (QFI) to diagnose a dynamical phase transition (DPT) in a closed quantum system, which is usually defined in terms of nonanalytic behavior of a time-averaged order parameter. Employing the Lipkin-Meshkov-Glick model as an illustrative example, we find that the DPT correlates with a peak in the QFI that can be explained by a generic connection to an underlying excited-state quantum phase transition that also enables us to relate the scaling of the QFI with the behavior of the order parameter. Motivated by the QFI as a quantifier of metrologically useful correlations and entanglement, we also present a robust interferometric protocol that can enable DPTs as a platform for quantum-enhanced sensing.

DOI
10.1103/physrevresearch.3.033199

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We use the quantum Fisher information (QFI) to diagnose a dynamical phase transition (DPT) in a closed quantum system, which is usually defined in terms of nonanalytic behavior of a time-averaged order parameter. Employing the Lipkin-Meshkov-Glick model as an illustrative example, we find that the DPT correlates with a peak in the QFI that can be explained by a generic connection to an underlying excited-state quantum phase transition that also enables us to relate the scaling of the QFI with the behavior of the order parameter. Motivated by the QFI as a quantifier of metrologically useful correlations and entanglement, we also present a robust interferometric protocol that can enable DPTs as a platform for quantum-enhanced sensing.
We investigate dynamical quantum phase transitions (DQPTs) in quantum systems that possess well-defined classical limits, focusing on the spinor Bose-Einstein condensate and the Lipkin-Meshkov-Glick model. We diagnose the DQPTs with the long-time average of the quantum Fisher information (QFI) showing that it abruptly changes at the transition point. Using mean-field and semiclassical approximations, we demonstrate that the long-time average of the QFI reveals universal behavior that persists across different systems.
Quantum phase transitions have been shown to be highly beneficial for quantum sensing, owing to diverging quantum Fisher information close to criticality. In this work we consider a periodically modulated Lipkin-Meshkov-Glick model to show that discrete time crystal (DTC) phase transition in this setup can enable us to achieve quantum-enhanced high-precision sensing of field strength. We employ a detailed finite-size scaling analysis, a time-averaged Inverse Participation Ratio analysis, and mean-field analysis in the thermodynamic limit, to determine the critical properties of this second-order phase transition. Our studies provide a comprehensive understanding of how quantum criticality in DTCs involving long-range interactions can be harnessed for advanced quantum sensing applications.
We consider the general problem of estimating an unknown control parameter of an open quantum system. We establish a direct relation between the evolution of both system and environment and the precision with which the parameter can be estimated. We show that when the open quantum system undergoes a first-order dynamical phase transition the quantum Fisher information (QFI), which gives the upper bound on the achievable precision of any measurement of the system and environment, becomes quadratic in observation time (cf. ``Heisenberg scaling''). In fact, the QFI is identical to the variance of the dynamical observable that characterizes the phases that coexist at the transition, and enhanced scaling is a consequence of the divergence of the variance of this observable at the transition point. This identification makes it possible to establish the finite time scaling of the QFI. Near the transition the QFI is quadratic in time for times shorter than the correlation time of the dynamics. In the regime of enhanced scaling the optimal measurement whose precision is given by the QFI involves measuring both system and output. As a particular realization of these ideas, we describe a theoretical scheme for quantum enhanced estimation of an optical phase shift using the photons being emitted from a quantum system near the coexistence of dynamical phases with distinct photon emission rates.
Quantum phase transitions universally exist in the ground and excited states of quantum many-body systems, and they have a close relationship with the nonequilibrium dynamical phase transitions, which however are challenging to identify. In the system of spin-1 Bose-Einstein condensates, though dynamical phase transitions with correspondence to equilibrium phase transitions in the ground state and uppermost excited state have been probed, those taking place in intermediate excited states remain untouched in experiments thus far. Here we unravel that both the ground- and excited-state quantum phase transitions in spinor condensates can be diagnosed with dynamical phase transitions. A connection between equilibrium phase transitions and nonequilibrium behaviors of the system is disclosed in terms of the quantum Fisher information. We also demonstrate that near the critical points parameter estimation beyond the standard quantum limit can be implemented. This work not only advances the exploration of excited-state quantum phase transitions via a scheme that can immediately be applied to a broad class of few-mode quantum systems, but also provides a new perspective on the relationship between quantum criticality and quantum enhanced sensing.
The characterization of entanglement is a central problem for the study of quantum many-body dynamics. Here, we propose the quantum Fisher information (QFI) as a useful tool for the study of multipartite-entanglement dynamics in many-body systems. We illustrate this by considering the regular-to-ergodic transition in the Dicke model---a fully connected spin model showing quantum thermalization above a critical interaction strength. We show that the QFI has a rich dynamical behavior which drastically changes across the transition. In particular, the asymptotic value of the QFI as well as its characteristic timescales witness the transition both through their dependence on the interaction strength and through the scaling with the system size. Since the QFI also sets the ultimate bound for the precision of parameter estimation, it provides a metrological perspective on the characterization of entanglement dynamics in many-body systems. Here, we show that quantum ergodic dynamics allows for a much faster production of metrologically useful states.
Critical metrology relies on the precise preparation of a system in its ground state near a quantum phase transition point where quantum correlations get very strong. Typically, this increases the quantum Fisher information with respect to changes in system parameters and thus improves the optimally possible measurement precision limited by the Cramér-Rao bound. Hence critical metrology involves encoding information about the unknown parameter in changes of the system's ground state. Conversely, in conventional metrology methods like Ramsey interferometry, the eigenstates of the system remain unchanged, and information about the unknown parameter is encoded in the relative phases that excited system states accumulate during their time evolution. Here we introduce an approach combining these two methodologies into a unified protocol applicable to closed and driven-dissipative systems. We show that the quantum Fisher information in this case exhibits an additional interference term originating from the interplay between eigenstate and relative phase changes. We provide analytical expressions for the quantum and classical Fisher information in such a setup, elucidating as well a straightforward measurement approach that nearly attains the maximum precision permissible under the Cramér-Rao bound. We showcase these results by focusing on the squeezing Hamiltonian, which characterizes the thermodynamic limit of Dicke and Lipkin-Meshkov-Glick Hamiltonians.