Experimental characterization of a quantum many-body system via higher-order correlations

Schweigler, Thomas; Kasper, Valentin; Erne, Sebastian; Mazets, I. E.; Rauer, Bernhard; Cataldini, Federica; Langen, Tim; Gasenzer, Thomas; Berges, Jürgen; Schmiedmayer, Jörg

doi:10.1038/nature22310

Cited by 235 publications

(338 citation statements)

References 38 publications

(54 reference statements)

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“…In fact measurements of CCFs precise enough to reveal nonGaussian features are also feasible in the same experimental setup and have been performed in the ground state of the system for a wide range of parameter values [78]. This suggests that an experimental realization of a quantum quench of J from an intermediate value to zero would make the observation of such deviations possible.…”

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confidence: 95%

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Memory-preserving equilibration after a quantum quench in a one-dimensional critical model

Sotiriadis

2016

Phys. Rev. A

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One of the fundamental principles of statistical physics is that only partial information about a system's state is required for its macroscopic description. This is not only true for thermal ensembles, but also for the unconventional ensemble, known as Generalized Gibbs Ensemble (GGE), that is expected to describe the relaxation of integrable systems after a quantum quench. By analytically studying the quench dynamics in a prototypical one-dimensional critical model, the massless free bosonic field theory, we find evidence of a novel type of equilibration characterized by the preservation of an enormous amount of memory of the initial state that is accessible by local measurements. In particular, we show that the equilibration retains memory of non-Gaussian initial correlations, in contrast to the case of massive free evolution which erases all such memory. The GGE in its standard form, being a Gaussian ensemble, fails to predict correctly the equilibrium values of local observables, unless the initial state is Gaussian itself. Our findings show that the equilibration of a broad class of quenches whose evolution is described by Luttinger liquid theory with an initial state that is non-Gaussian in terms of the bosonic field, is not correctly captured by the corresponding bosonic GGE, raising doubts about the validity of the latter in general onedimensional gapless integrable systems such as the Lieb-Liniger model. We also propose that the same experiment by which the GGE was recently observed [Langen et al., Science 348 (2015) 207-211] can also be used to observe its failure, simply by starting from a non-Gaussian initial state.Introduction -Understanding the physics of quantum many-body systems out of equilibrium is one of the most challenging open problems today [1,2]. Of central interest is the problem of quantum quenches i.e. abrupt changes of the Hamiltonian parameters of a closed quantum system [3], especially in one-dimensional (1d) integrable systems where the study of quantum dynamics has led to intriguing discoveries, like the experimental observation of lack of thermalization [4] and the theoretical prediction of the Generalized Gibbs Ensemble (GGE) [5] which has recently been observed experimentally [6]. The GGE is expected to describe the equilibration of local observables after a quantum quench in an integrable system by taking into account all constraints associated to its conserved charges [3,5,. While in its standard form it was constructed exclusively out of local conserved charges [28,29], it has been recently shown that quasi-local charges must also be included [46][47][48][49][50][51][52][53][54][55][56][57][58][59][60]. This gives an answer to the fundamental question of how much information about the initial state survives in the final values of local observables. Other aspects of interest are the asymptotic behavior towards equilibrium [13,30,34,41,61] or the restoration of symmetries of the post-quench Hamiltonian that are absent in the initial state [62,63].

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confidence: 95%

“…the ground state of a genuinely interacting Hamiltonian. We will show that this is feasible using present technology in the same experimental setup [78].…”

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confidence: 99%

Memory-preserving equilibration after a quantum quench in a one-dimensional critical model

Sotiriadis

2016

Phys. Rev. A

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“…This universal relation between the long time decay of C xv and other exponents that are easier to measure can be used to infer C xv for systems where it cannot be measured directly. The position-velocity correlations are obtained using a new direct method to measure the phase-space density distribution that can be used to access different types of phenomena such as deviations from equipartition theorem [22,23] for the nonequilibrium steady-state scenario of the discussed system with the addition of an underlying harmonic potential, and to probe phase-space correlations in systems of a quantum nature, described by a single wavefunction [30,43]. The short-time dynamics in anomalous diffusion is model-dependent and non-trivially experimentally accessible [44].…”

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confidence: 99%

Observing Power-Law Dynamics of Position-Velocity Correlation in Anomalous Diffusion

et al. 2017

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In this letter we present a measurement of the phase-space density distribution (PSDD) of ultracold 87 Rb atoms performing 1D anomalous diffusion. The PSDD is imaged using a direct tomographic method based on Raman velocity selection. It reveals that the position-velocity correlation function Cxv(t) builds up on a timescale related to the initial conditions of the ensemble and then decays asymptotically as a power-law. We show that the decay follows a simple scaling theory involving the power-law asymptotic dynamics of position and velocity. The generality of this scaling theory is confirmed using Monte-Carlo simulations of two distinct models of anomalous diffusion.The phase-space density distribution (PSDD) contains information concerning the degrees of freedom of a system and allows calculation of any observable. An intriguing system to look at in this context is that of anomalous dynamics for which the mean square displacement (MSD) scales as x 2 ∼ t 2α , with α = 1/2. This type of dynamics, found in a wide variety of systems in nature ranging from dynamics of "bubbles" in denaturing DNA molecules [1], through fluctuations in the stockmarket [2] to models describing brief awakenings in the course of a night's sleep [3], is generally non-universal and system-dependent [4][5][6].A uniquely interesting model system for the study of anomalous diffusion is that of cold atoms diffusing in a dissipative 1D lattice, closely related to Lévy walks and motion in logarithmic potentials, displaying such phenomena as the breakdown of ergodicity and of equipartition, memory effects and slow relaxation to equilibrium [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23]. The major advantage of such a system is the high degree of control it enables over the physical parameters governing the dynamics. One of the fundamental insights that can be obtained from the PSDD of such a system is the phase-space cross correlation between position and velocity C xv . C xv can reveal the fingerprint of the underlying model and in particular is essential for understanding concepts and techniques such as adiabatic cooling in lattices [24], stochastic cooling [25], point source atom interferometry [26,27] and enhanced velocity resolution [28,29], alongside elementary notions in quantum mechanics [30]. These correlations have been surprisingly overlooked in both theory and experiment, perhaps due to the lack of a direct method for imaging the phasespace of atomic clouds, which does not require cumbersome mathematical tools or a specific potential [31][32][33][34][35]. No analysis of the dynamics of the correlations has been reported to the best of our knowledge.In this letter we analyze and measure the dynamics of the position-velocity correlation of an ensemble of classical particles, originating from a point-like source and undergoing one-dimensional anomalous super-diffusion. The measurement is done using a new tomographic method for direct phase-space imaging, utilizing a combination of the straightforward tools of absorpt...

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“…(3). Connected correlators up to tenth order have been measured using this approach [17]. However, such a method is infeasible for connected correlators of very high order, as the number of disconnected correlators that must be measured grows exponentially with n. It is therefore an open question whether there exist experimentally accessible observables, e.g.…”

Section: Discussionmentioning

confidence: 99%

“…Such a study is timely, given the recent successful measurement of multipartite connected correlators in atomic superfluids [17].…”

Section: Introductionmentioning

confidence: 99%

Lieb-Robinson bounds on n -partite connected correlation functions

et al. 2017

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Lieb and Robinson provided bounds on how fast bipartite connected correlations can arise in systems with only short-range interactions. We generalize Lieb-Robinson bounds on bipartite connected correlators to multipartite connected correlators. The bounds imply that an n-partite connected correlator can reach unit value in constant time. Remarkably, the bounds also allow for an n-partite connected correlator to reach a value that is exponentially large with system size in constant time, a feature which stands in contrast to bipartite connected correlations. We provide explicit examples of such systems.

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Experimental characterization of a quantum many-body system via higher-order correlations

Cited by 235 publications

References 38 publications

Memory-preserving equilibration after a quantum quench in a one-dimensional critical model

Memory-preserving equilibration after a quantum quench in a one-dimensional critical model

Observing Power-Law Dynamics of Position-Velocity Correlation in Anomalous Diffusion

Lieb-Robinson bounds on n -partite connected correlation functions

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