Quantum metrology with nonclassical states of atomic ensembles

Pezzé, Luca; Smerzi, Augusto; Oberthaler, Markus K.; Schmied, Roman; Treutlein, Philipp

doi:10.1103/revmodphys.90.035005

Cited by 1,374 publications

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References 597 publications

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“…If ξ 2 S < 1, a state is spin squeezed, and, importantly, also exhibits quantum entanglement no matter whether the system is in a pure or mixed state [27].…”

Section: Is Obtained By Averaging the Expectation Values Of The Indivmentioning

confidence: 99%

“…4b shows, ξ s presents a behaviour qualitatively very similar to S(t). Related to common spin-squeezing scenarios [27], the spin squeezing is most effective when the mean spin vector on the Bloch sphere is perpendicular to the direction of the spin-spin interaction. Importantly, this occurs when M x = 0, which we found above to be inherently tied to DQPTs.…”

Section: Qptmentioning

confidence: 99%

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Direct Observation of Dynamical Quantum Phase Transitions in an Interacting Many-Body System

et al. 2017

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Dynamical quantum phase transitions (DQPTs) extend the concept of phase transitions and thus universality to the non-equilibrium regime. In this letter, we investigate DQPTs in a string of ions simulating interacting transverse-field Ising models. We observe non-equilibrium dynamics induced by a quantum quench and show for strings of up to 10 ions the direct detection of DQPTs by measuring a quantity that becomes non-analytic in time in the thermodynamic limit. Moreover, we provide a link between DQPTs and the dynamics of other relevant quantities such as the magnetization, and we establish a connection between DQPTs and entanglement production.Today, the equilibrium properties of quantum matter are theoretically described with remarkable success. Yet, in recent years pioneering experiments have created novel quantum states beyond this equilibrium paradigm [1,2]. Thanks to this progress, it is now possible to experimentally study exotic phenomena such as many-body localization [3,4], prethermalization [5, 6], particle-antiparticle production in the lattice Schwinger model [7], and light-induced superconductivity [8]. Understanding general properties of such nonequilibrium quantum states provides a significant challenge, calling for new concepts that extend important principles such as universality to the non-equilibrium realm. A general approach towards this major goal is the theory of dynamical quantum phase transitions (DQPTs) [9], which extends the concept of phase transitions and thus universality to the nonequilibrium regime. In this letter, we directly observe the defining real-time non-analyticities at DQPTs in a trappedion quantum simulator for interacting transverse-field Ising models. Moreover, we provide a link between DQPTs and the dynamics of other relevant quantities such as the magnetization, and we establish a connection between DQPTs and entanglement production. Our work advances towards experimentally characterizing nonequilibrium quantum states and their dynamics, by offering general experimental tools that can be applied also to other inherently dynamical phenomena.Statistical mechanics and thermodynamics provide us with an excellent understanding of equilibrium quantum manybody systems. A key concept in this framework is the canonical partition function Z(T ) = Tr(e −H/k B T ), with T the temperature, k B the Boltzmann constant, and H the system Hamiltonian. The partition function encodes thermodynamics via the free-energy density f = −(k B T/N) log [Z(T )], where N de- * Present address:ARC Centre of Excellence for Engineered Quantum Systems, School of Physics, University of Sydney, NSW, 2006, Australia notes the number of degrees of freedom. A phase transition, i.e., a sudden change of macroscopic behaviour, is associated with a non-analytical behaviour of f as a function of temperature or another control parameter g such as an external magnetic field. Quantum phase transitions (QPTs) [10] occur when T is kept at absolute zero, where the system's groundstate properties undergo a non-analyt...

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“…If ξ 2 S < 1, a state is spin squeezed, and, importantly, also exhibits quantum entanglement no matter whether the system is in a pure or mixed state [27].…”

Section: Is Obtained By Averaging the Expectation Values Of The Indivmentioning

confidence: 99%

Section: Qptmentioning

confidence: 99%

Direct Observation of Dynamical Quantum Phase Transitions in an Interacting Many-Body System

et al. 2017

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“…4(b) shows, ξ s presents a behavior qualitatively very similar to SðtÞ. Related to common spin-squeezing scenarios [34], the spin squeezing is most effective when the mean spin vector on the Bloch sphere is perpendicular to the direction of the spin-spin interaction. Importantly, this occurs when M x ¼ 0, which we found above to be inherently tied to DQPTs.…”

Section: Prl 119 080501 (2017) P H Y S I C a L R E V I E W L E T T Ementioning

confidence: 77%

Quantum Phase Transitions Go Dynamical

Gurarie

2017

Physics

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The theory of phase transitions represents a central concept for the characterization of equilibrium matter. In this work we study experimentally an extension of this theory to the nonequilibrium dynamical regime termed dynamical quantum phase transitions (DQPTs). We investigate and measure DQPTs in a string of ions simulating interacting transverse-field Ising models. During the nonequilibrium dynamics induced by a quantum quench we show for strings of up to 10 ions the direct detection of DQPTs by revealing nonanalytic behavior in time. Moreover, we provide a link between DQPTs and the dynamics of other quantities such as the magnetization, and we establish a connection between DQPTs and entanglement production. DOI: 10.1103/PhysRevLett.119.080501 Today, the equilibrium properties of quantum matter are theoretically described with great success. Yet, in recent years pioneering experiments have created quantum states beyond this equilibrium paradigm [1,2]. Thanks to this progress, it is now possible to experimentally study exotic phenomena such as many-body localization [3,4], prethermalization [5,6], particle-antiparticle production in the lattice Schwinger model [7], and light-induced superconductivity [8]. Understanding general properties of such nonequilibrium quantum states provides a significant challenge, calling for concepts that extend important principles such as universality to the nonequilibrium realm. A general approach towards this major goal is the theory of dynamical quantum phase transitions (DQPTs) [9], which extends the concept of phase transitions and thus universality to the nonequilibrium regime. In this Letter, we directly observe the defining real-time nonanalyticities at DQPTs in a trapped-ion quantum simulator for interacting transverse-field Ising models. Moreover, we provide a link between DQPTs and the dynamics of other relevant quantities such as the magnetization, and we establish a connection between DQPTs and entanglement production.Statistical mechanics and thermodynamics provide us with an excellent understanding of equilibrium quantum many-body systems. A key concept in this framework is the canonical partition function ZðTÞ ¼ Trðe −H=k B T Þ, with T being the temperature, k B the Boltzmann constant, and H the system Hamiltonian. The partition function encodes thermodynamics via the free-energy density f ¼ −ðk B T=NÞ log ½ZðTÞ , where N denotes the number of degrees of freedom.A phase transition, i.e., a sudden change of macroscopic behavior, is associated with a nonanalytical behavior of f as a function of temperature or another control parameter g such as an external magnetic field. QPTs [10] occur when T is kept at absolute 0, where the system's ground-state properties undergo a nonanalytic change as a function of g [see Fig. 1(a)]. Scenarios where boundary conditions are essential, such as for the Casimir effect, can be studied by boundary partition functions Z B ¼ hψ 0 je −RH jψ 0 i, where jψ 0 i encodes the spatial boundary conditions on two ends of the system at dis...

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“…Strategies involving probe states characterized by squeezed quadratures [13] or entanglement between particles [14][15][16][17][18][19] are able to overcome the shot noise, the ultimate quantum bound being the so-called Heisenberg limit. Quantum noise reduction in phase estimation has been demonstrated in several proof-of-principle experiments with atoms and photons [20,21].…”

Section: Introductionmentioning

confidence: 99%

Frequentist and Bayesian Quantum Phase Estimation

Pezzé

Gessner

et al. 2018

Entropy

Self Cite

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Frequentist and Bayesian phase estimation strategies lead to conceptually different results on the state of knowledge about the true value of an unknown parameter. We compare the two frameworks and their sensitivity bounds to the estimation of an interferometric phase shift limited by quantum noise, considering both the cases of a fixed and a fluctuating parameter. We point out that frequentist precision bounds, such as the Cramér-Rao bound, for instance, do not apply to Bayesian strategies and vice versa. In particular, we show that the Bayesian variance can overcome the frequentist Cramér-Rao bound, which appears to be a paradoxical result if the conceptual difference between the two approaches are overlooked. Similarly, bounds for fluctuating parameters make no statement about the estimation of a fixed parameter.

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Quantum metrology with nonclassical states of atomic ensembles

Cited by 1,374 publications

References 597 publications

Direct Observation of Dynamical Quantum Phase Transitions in an Interacting Many-Body System

Direct Observation of Dynamical Quantum Phase Transitions in an Interacting Many-Body System

Quantum Phase Transitions Go Dynamical

Frequentist and Bayesian Quantum Phase Estimation

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