Dynamical phase transitions as a resource for quantum enhanced metrology

Macieszczak, Katarzyna; Guţǎ, Mădălin; Lesanovsky, Igor; Garrahan, Juan P.

doi:10.1103/physreva.93.022103

Cited by 95 publications

(111 citation statements)

References 42 publications

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“…Therefore, a question naturally arises: what sensitivity can be achieved using interacting systems close to a quantum-critical point? In the last few years, this question has attracted growing interest and it has been addressed by different methods [3][4][5][6][7][8][9]. These studies may be roughly divided in two classes.The first approach, which we will call the "dynamical" paradigm [5,7], focus on the time evolution induced by a Hamiltonian close to a critical point.…”

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confidence: 99%

“…In the last few years, this question has attracted growing interest and it has been addressed by different methods [3][4][5][6][7][8][9]. These studies may be roughly divided in two classes.The first approach, which we will call the "dynamical" paradigm [5,7], focus on the time evolution induced by a Hamiltonian close to a critical point. In this approach, one prepares a probe system in a suitably chosen state, lets it evolve according to the critical Hamiltonian, and finally measures it.…”

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confidence: 99%

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Critical Quantum Metrology with a Finite-Component Quantum Phase Transition

et al. 2020

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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 make use of 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 systems can lead to a quantum-enhanced time-scaling of the quantum Fisher information, and so of the measurement sensitivity.In a system close to a critical point, small variations of physical parameters may lead to dramatic changes in the equilibrium state properties. The possibility of exploiting this sensitivity for metrological purposes is well known, and it has already been applied in classical devices, e.g. in superconducting transition-edge sensor [1]. Besides, the development of quantum metrology has extensively shown that quantum states can outperform their classical counterparts for sensing tasks [2]. Therefore, a question naturally arises: what sensitivity can be achieved using interacting systems close to a quantum-critical point? In the last few years, this question has attracted growing interest and it has been addressed by different methods [3][4][5][6][7][8][9]. These studies may be roughly divided in two classes.The first approach, which we will call the "dynamical" paradigm [5,7], focus on the time evolution induced by a Hamiltonian close to a critical point. In this approach, one prepares a probe system in a suitably chosen state, lets it evolve according to the critical Hamiltonian, and finally measures it. This bear close similarity to the standard interferometric paradigm of quantum metrology [2]. On the other hand, the "static" approach [3, 6] is based on the equilibrium properties of the system. It consists in preparing and measuring the system ground state in the unitary case, or the system steady-state when open quantum systems are considered. In proximity of the phase transition the susceptibility of the equilibrium state diverges, and so it does the achievable measurement precision. Unfortunately, the time required to prepare the equilibrium state diverges as well, both in the unitary [10] and in the driven-dissipative case [11,12], a behavior called critical slowing down. Only very re-cently, it has been demonstrated that for a large class of spin models these two approaches are formally equivalent [9], and that they both make it possible to achieve the optimal scaling limit of precision with respect to system size and to measurement time. These results were obtained considering spin systems that undergo quantum phase transitions in the thermodynamic limit, where the numb...

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Critical Quantum Metrology with a Finite-Component Quantum Phase Transition

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“…This behaviour, which is observed during a single run of the experiment, is conveniently described using the formalism of quantum jumps in which the system is characterized in terms of a pure wavefunction that undergoes stochastic evolution [37][38][39].The timescale τ of this intermittency is given by the inverse of the Liouvillian gap or asymptotic decay rate (ADR), i.e. the eigenvalue λ 2 of the Liouvillian operator L with the second largest real part [23,40,41]. Since a DPT is defined by a vanishing Liouvillian gap [13,14], it will necessarily imply that τ diverges.…”

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confidence: 99%

“…Understanding this phenomena is important for the dynamical characterization of dissipative systems with a closed Liouvillian gap. This limit has been proven relevant in quantum metrology, since it yields a Heisenberg scaling (quadratic in time) of the quantum Fisher information [23].To discuss the effect of dissipative freezing, we analyse a model that can be solved numerically, yet displays a rich variety of non-ergodic dynamics. This model consists of a coherently-driven spin ensemble with squeezed, collective arXiv:1908.11862v1 [quant-ph]…”

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Symmetries and conservation laws in quantum trajectories: Dissipative freezing

et al. 2019

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In driven-dissipative systems, the presence of a strong symmetry guarantees the existence of several steady states belonging to different symmetry sectors. Here we show that, when a system with a strong symmetry is initialized in a quantum superposition involving several of these sectors, each individual stochastic trajectory will randomly select a single one of them and remain there for the rest of the evolution. Since a strong symmetry implies a conservation law for the corresponding symmetry operator on the ensemble level, this selection of a single sector from an initial superposition entails a breakdown of this conservation law at the level of individual realizations. Given that such a superposition is impossible in a classical, stochastic trajectory, this is a a purely quantum effect with no classical analogue. Our results show that a system with a closed Liouvillian gap may exhibit, when monitored over a single run of an experiment, a behaviour completely opposite to the usual notion of dynamical phase coexistence and intermittency, which are typically considered hallmarks of a dissipative phase transition. We discuss our results with a simple, realistic model of squeezed superradiance.Driven dissipative systems are ubiquitous in many body physics and cavity QED [1][2][3][4][5][6][7][8][9][10][11][12]. These systems are typically gapped and feature a unique, non-equilibrium steady state. In the regime of a dissipative phase transition (DPT), however, this gap vanishes and the null-space of the Liouvillian is spanned by several compatible steady-states. [13][14][15][16][17][18][19][20][21][22]. Due to their fundamental interest and practical applications, such as enhanced metrological properties [23,24], DPTs have attracted a significant amount of attention, with much work being devoted to study the associated phenomena of bistability [3-5, 22, 25-28], hysteresis [2,29], intermittency [6,26,[29][30][31][32], multimodality [25,31], metastability [33] and symmetry breaking [34][35][36]. All these effects are understood as different manifestations of the coexistence of several non-equilibrium phases. In particular, many experiments will look for intermittency as the hallmark of such phase coexistence [6,26,[29][30][31][32]. Intermittency is a phenomenon defined by a random switching between periods of high and low dynamical activity (for instance in the rate of photon emission). This behaviour, which is observed during a single run of the experiment, is conveniently described using the formalism of quantum jumps in which the system is characterized in terms of a pure wavefunction that undergoes stochastic evolution [37][38][39].The timescale τ of this intermittency is given by the inverse of the Liouvillian gap or asymptotic decay rate (ADR), i.e. the eigenvalue λ 2 of the Liouvillian operator L with the second largest real part [23,40,41]. Since a DPT is defined by a vanishing Liouvillian gap [13,14], it will necessarily imply that τ diverges. In most typical situations, this closing is reached in the thermod...

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“…In general, obtaining an expression for the state |Ψ SE is a hard task, but there is a method based on a modified master equation to compute the fidelity Ψ SE (ω 1 )|Ψ SE (ω 2 ) without obtaining the state [21,54,55]. This technique is fundamental to obtain the results for frequency estimation with continuous monitoring of observables transversal to the Hamiltonian [29].…”

Section: Ultimate Qfimentioning

confidence: 99%

Quantum frequency estimation with conditional states of continuously monitored independent dephasing channels

Albarelli

Rossi

Genoni

2020

Int. J. Quantum Inform.

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We discuss the problem of estimating a frequency via N -qubit probes undergoing independent dephasing channels that can be continuously monitored via homodyne or photo-detection. We derive the corresponding analytical solutions for the conditional states, for generic initial states and for arbitrary efficiency of the continuous monitoring. For the detection strategies considered, we show that: i) in the case of perfect continuous detection, the quantum Fisher information (QFI) of the conditional states is equal to the one obtained in the noiseless dynamics; ii) for smaller detection efficiencies, the QFI of the conditional state is equal to the QFI of a state undergoing the (unconditional) dephasing dynamics, but with an effectively reduced noise parameter.

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Dynamical phase transitions as a resource for quantum enhanced metrology

Cited by 95 publications

References 42 publications

Critical Quantum Metrology with a Finite-Component Quantum Phase Transition

Critical Quantum Metrology with a Finite-Component Quantum Phase Transition

Symmetries and conservation laws in quantum trajectories: Dissipative freezing

Quantum frequency estimation with conditional states of continuously monitored independent dephasing channels

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