Nonlinear Quantum Metrology of Many-Body Open Systems

Beau, Mathieu; Campo, Adolfo del

doi:10.1103/physrevlett.119.010403

Cited by 82 publications

(59 citation statements)

References 47 publications

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“…Such democratic couplings are, however, difficult to create in nature. Recently, those results were extended to describe both open and noisy systems [18][19][20][21][22].…”

Section: Introductionmentioning

confidence: 99%

At the Limits of Criticality-Based Quantum Metrology: Apparent Super-Heisenberg Scaling Revisited

et al. 2018

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We address the question of whether the super-Heisenberg scaling for quantum estimation is indeed realizable. We unify the results of two approaches. In the first one, the original system is compared with its copy rotated by the parameter-dependent dynamics. If the parameter is coupled to the one-body part of the Hamiltonian, the precision of its estimation is known to scale at most as N −1 (Heisenberg scaling) in terms of the number of elementary subsystems used N. The second approach compares the overlap between the ground states of the parameter-dependent Hamiltonian in critical systems, often leading to an apparent super-Heisenberg scaling. However, we point out that if one takes into account the scaling of time needed to perform the necessary operations, i.e., ensuring adiabaticity of the evolution, the Heisenberg limit given by the rotation scenario is recovered. We illustrate the general theory on a ferromagnetic Heisenberg spin chain example and show that it exhibits such super-Heisenberg scaling of ground-state fidelity around the critical value of the parameter (magnetic field) governing the one-body part of the Hamiltonian. Even an elementary estimator represented by a single-site magnetization already outperforms the Heisenberg behavior providing the N −1.5 scaling. In this case, Fisher information sets the ultimate scaling as N −1.75 , which can be saturated by measuring magnetization on all sites simultaneously. We discuss universal scaling predictions of the estimation precision offered by such observables, both at zero and finite temperatures, and support them with numerical simulations in the model. We provide an experimental proposal of realization of the considered model via mapping the system to ultracold bosons in a periodically shaken optical lattice. We explicitly derive that the Heisenberg limit is recovered when the time needed for preparation of quantum states involved is taken into account.

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“…Such democratic couplings are, however, difficult to create in nature. Recently, those results were extended to describe both open and noisy systems [18][19][20][21][22].…”

Section: Introductionmentioning

confidence: 99%

At the Limits of Criticality-Based Quantum Metrology: Apparent Super-Heisenberg Scaling Revisited

et al. 2018

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“…Indeed, as has been experimentally observed [37,38] and theoretically investigated [46], the DTC order in an open system is usually destroyed by decoherence. On the other hand, it is known that dissipation and decoherence can also serve as resources for quantum tasks such as quantum computation [47] and metrology [48]. From this perspective, it is natural to ask whether the DTC order exists and can even be stabilized in open systems [49].…”

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confidence: 99%

Discrete Time-Crystalline Order in Cavity and Circuit QED Systems

2018

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Discrete time crystals are a recently proposed and experimentally observed out-of-equilibrium dynamical phase of Floquet systems, where the stroboscopic evolution of a local observable repeats itself at an integer multiple of the driving period. We address this issue in a driven-dissipative setup, focusing on the modulated open Dicke model, which can be implemented by cavity or circuit QED systems. In the thermodynamic limit, we employ semiclassical approaches and find rich dynamical phases on top of the discrete time-crystalline order. In a deep quantum regime with few qubits, we find clear signatures of a transient discrete time-crystalline behavior, which is absent in the isolated counterpart. We establish a phenomenology of dissipative discrete time crystals by generalizing the Landau theory of phase transitions to Floquet open systems.Introduction.-Phases and phase transitions of matter are key concepts for understanding complex many-body physics [1,2]. Recent experimental developments in various quantum simulators, such as ultracold atoms [3,4], trapped ions [5,6] and superconducting qubits [7,8], motivate us to seek for quantum many-body systems out of equilibrium [9][10][11], such as many-body localized phases [12][13][14][15][16][17] and Floquet topological phases [18][19][20][21][22][23][24][25].In recent years, much effort has been devoted to periodically driven (Floquet) quantum many-body systems that break the discrete time-translation symmetry (TTS) [26]. In contrast to the continuous TTS breaking [27][28][29] that has turned out to be impossible at thermal equilibrium [30,31], the discrete TTS breaking has been theoretically proposed [32][33][34][35][36] and experimentally demonstrated [37,38]. Phases with broken discrete TTS feature discrete time-crystalline (DTC) order characterized by periodic oscillations of physical observables with period nT , where T is the Floquet period and n = 2, 3, · · · . The DTC order is expected to be stabilized by many-body interactions against variations of driving parameters. Note that the system is assumed to be in a localized phase [33,34,36,37] or to have long-range interactions [38][39][40]. Otherwise, the DTC order only exists in a prethermalized regime [41,42] since the system will eventually be heated to a featureless infinite-temperature state due to persistent driving [43][44][45].While remarkable progresses are being made concerning the DTC phase, most studies focus on isolated systems. Indeed, as has been experimentally observed [37,38] and theoretically investigated [46], the DTC order in an open system is usually destroyed by decoherence. On the other hand, it is known that dissipation and decoherence can also serve as resources for quantum tasks such as quantum computation [47] and metrology [48]. From this perspective, it is natural to ask whether the DTC order exists and can even be stabilized in open systems [49]. Such a possibility has actually been pointed out in Ref. [41], but neither a detailed theoretical model nor a concrete experimental imp...

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“…For an observer with no access to the measurement outcomes, the evolution is described by an open quantum dynamics, resulting from the coupling of the system to an inaccessible environment. In this scenario, the observer would expect the standard QSL to hold, with the time for a quantum state to sweep a given Bures angle  t ( ) being given by equations (4) and (5). Said differently, the description by the observer is consistent with the standard QSL as    QSL .…”

Section: Resultsmentioning

confidence: 99%

“…Building on the seminal work by Mandelstam and Tamm [3], Quantum Speed Limits (QSL) have been formulated to provide a lower bound on the passage time, or more generally, on the minimum time required for a state to evolve into a distinguishable state under a given dynamics. It is by now understood that QSL impose constraints on parameter estimation in quantum metrology [4,5] and on quantum control protocols [6][7][8][9][10][11]. In addition, they can be used to ascertain the ultimate computational power of physical systems [12][13][14][15] and the performance of thermodynamic devices such as quantum engines and batteries [16,17].…”

Section: Introductionmentioning

confidence: 99%

Quantum speed limits under continuous quantum measurements

García-Pintos

Campo

2019

New J. Phys.

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The pace of evolution of physical systems is fundamentally constrained by quantum speed limits (QSL), which have found broad applications in quantum science and technology. We consider the speed of evolution for quantum systems undergoing stochastic dynamics due to continuous measurements. It is shown that that there are trajectories for which standard QSL are violated, and we provide estimates for the range of velocities in an ensemble of realizations of continuous measurement records. We determine the dispersion of the speed of evolution and characterize the full statistics of single trajectories. By characterizing the dispersion of the Bures angle, we further show that continuous quantum measurements induce Brownian dynamics in Hilbert space.

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Nonlinear Quantum Metrology of Many-Body Open Systems

Cited by 82 publications

References 47 publications

At the Limits of Criticality-Based Quantum Metrology: Apparent Super-Heisenberg Scaling Revisited

At the Limits of Criticality-Based Quantum Metrology: Apparent Super-Heisenberg Scaling Revisited

Discrete Time-Crystalline Order in Cavity and Circuit QED Systems

Quantum speed limits under continuous quantum measurements

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