The comprehension of quantum phase transitions (QPTs) is considered as a critical foothold in the field of many-body physics. Developing protocols to effectively identify and understand QPTs thus represents a key but challenging task for present quantum simulation experiments. Here, we establish a dynamical quench-interferometric framework to probe a zero-temperature QPT, which utilizes the evolved state by quenching the QPT Hamiltonian as input of a unitary interferometer. The metrological capability quantified by the quantum Fisher information captivatingly shows an unique peak in the vicinity of the quantum critical point, allowing us to probe the QPT without cooling the system to its ground state. We show that the probing can be implemented by extracting quantum fluctuations of the interferometric generator as well as parameter estimation uncertainty of the interferometric phase, and subsequently allows identifying the boundary of the phase diagram. Our results establish an important link between QPTs and quantum metrology, and enrich the toolbox of studying non-equilibrium many-body physics in current quantum simulators.
The comprehension of quantum phase transitions (QPTs) is considered as a critical foothold in the field of many-body physics. Developing protocols to effectively identify and understand QPTs thus represents a key but challenging task for present quantum simulation experiments. Here, we establish a dynamical quench-interferometric framework to probe a zero-temperature QPT, which utilizes the evolved state by quenching the QPT Hamiltonian as input of a unitary interferometer. The metrological capability quantified by the quantum Fisher information captivatingly shows an unique peak in the vicinity of the quantum critical point, allowing us to probe the QPT without cooling the system to its ground state. We show that the probing can be implemented by extracting quantum fluctuations of the interferometric generator as well as parameter estimation uncertainty of the interferometric phase, and subsequently allows identifying the boundary of the phase diagram. Our results establish an important link between QPTs and quantum metrology, and enrich the toolbox of studying non-equilibrium many-body physics in current quantum simulators.
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.
Quantum phase transitions are highly remarkable phenomena manifesting in quantum many-body systems. However, their precise identifications in equilibrium systems pose significant theoretical and experimental challenges. Thus far, dynamical detection protocols employing global quantum quenches have been proposed, wherein transitions are discerned via global nonequilibrium excitations. In this work, we demonstrate that quantum phase transitions can be detected through localized out-of-equilibrium excitations induced by local quantum quenches. While the resulting dynamics after the quench is influenced by both the local quench operation and the intrinsic dynamics of the quantum system, the effects of the former are exclusively extracted using the cutting-edge framework called quantum reservoir probing (QRP). Through the QRP, we find that the impacts of the local quenches vary across different quantum phases and are significantly suppressed by quantum fluctuations amplified near quantum critical points; consequently, phase boundaries are precisely delineated. We demonstrate that the QRP can detect quantum phase transitions in the paradigmatic integrable and nonintegrable quantum spin systems, and even topological quantum phase transitions, all within the identical framework employing local quantum quenches and single-site observables. Quantum phase transitions, traditionally examined for divergent fluctuations in space and time at equilibrium, are now revealing local, nonequilibrium signatures. Kobayashi and Motome explore nonequilibrium quantum dynamics triggered by local quantum quenches utilizing a new approach of quantum reservoir probing.
Quantum phase transitions (QPTs) involve transformations between different states of matter that are driven by quantum fluctuations. These fluctuations play a dominant role in the quantum critical region surrounding the transition point, where the dynamics are governed by the universal properties associated with the QPT. The resulting quantum criticality has been explored by probing linear response for systems near thermal equilibrium. While time dependent phenomena associated with classical phase transitions have been studied in various scientific fields, understanding critical real-time dynamics in isolated, non-equilibrium quantum systems is of fundamental importance both for exploring novel approaches to quantum information processing and realizing exotic new phases of matter. Here, we use a Rydberg atom quantum simulator with programmable interactions to study the quantum critical dynamics associated with several distinct QPTs. By studying the growth of spatial correlations while crossing the QPT at variable speeds, we experimentally verify the quantum Kibble-Zurek mechanism (QKZM) for an Ising-type QPT, explore scaling universality, and observe corrections beyond simple QKZM predictions. This approach is subsequently used to investigate novel QPTs associated with chiral clock model providing new insights into exotic systems, and opening the door for precision studies of critical phenomena and applications to quantum optimization.
The study of quantum phase transitions requires the preparation of a many-body system near its ground state, a challenging task for many experimental systems. The measurement of quench dynamics, on the other hand, is now a routine practice in most cold atom platforms. Here we show that quintessential ingredients of quantum phase transitions can be probed directly with quench dynamics in integrable and nearly integrable systems. As a paradigmatic example, we study global quench dynamics in a transverse-field Ising model with either short-range or long-range interactions. When the model is integrable, we discover a new dynamical critical point with a nonanalytic signature in the short-range correlators. The location of the dynamical critical point matches that of the quantum critical point and can be identified using a finite-time scaling method. We extend this scaling picture to systems near integrability and demonstrate the continued existence of a dynamical critical point detectable at prethermal timescales. We quantify the difference in the locations of the dynamical and quantum critical points away from (but near) integrability. Thus, we demonstrate that this method can be used to approximately locate the quantum critical point near integrability. The scaling method is also relevant to experiments with finite time and system size, and our predictions are testable in near-term experiments with trapped ions and Rydberg atoms.
Abstract Critical quantum metrology, which exploits quantum critical systems as probes to estimate a physical parameter, has gained increasing attention recently. However, the critical quantum metrology with a continuous quantum phase transition (QPT) is experimentally challenging since a continuous QPT only occurs at the thermodynamic limit. Here, we propose an adiabatic scheme on a perturbed Ising spin model with a first-order QPT. By introducing a small transverse magnetic field, we can not only encode an unknown parameter in the ground state but also tune the energy gap to control the evolution time of the adiabatic passage. Moreover, we experimentally implement the critical quantum metrology scheme using nuclear magnetic resonance techniques and show that at the critical point the precision achieves the Heisenberg scaling as 1/ T . As a theoretical proposal and experimental implementation of the adiabatic scheme of critical quantum metrology and its advantages of easy implementation, inherent robustness against decays and tunable energy gap, our adiabatic scheme is promising for exploring potential applications of critical quantum metrology on various physical systems.
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.