Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1612.02837 · Physical Review A

Full counting statistics of time-of-flight images

Izabella Lovas, Balázs Dóra, Eugene Demler, Gergely Zaránd

Published May 22, 2017• 55 citations
arXivHTMLPDF

Abstract

Inspired by recent advances in cold atomic systems and nonequilibrium physics, we introduce a characterization scheme, the time-of-flight full counting statistics. We benchmark this method on an interacting one-dimensional Bose gas and show that there the time-of-flight image displays several universal regimes. Finite momentum fluctuations are observed at larger distances, where a crossover from exponential to Gamma distribution occurs upon decreasing momentum resolution. Zero-momentum particles, on the other hand, obey a Gumbel distribution in the weakly interacting limit, characterizing the quantum fluctuations of the former quasicondensate. Time-of-flight full counting statistics is demonstrated to capture (pre-)thermalization processes after a quantum quench and can be useful for characterizing exotic quantum states such as many-body localized systems or models of holography.

DOI
10.1103/physreva.95.053621

Related papers

Full counting statistics of charge in quenched quantum gases

Dávid X. Horváth, Colin Rylands

Unless constrained by symmetry, measurement of an observable on an ensemble of identical quantum systems returns a distribution of values which are encoded in the full counting statistics. While the mean value of this distribution is important for determining certain properties of a system, the full distribution can also exhibit universal behavior. In this paper we study the full counting statistics of particle number in one-dimensional interacting Bose and Fermi gases which have been quenched far from equilibrium. In particular, we consider the time evolution of the Lieb-Liniger and Gaudin-Yang models quenched from a Bose-Einstein condensate initial state and calculate the full counting statistics of the particle number within a subsystem. We show that the scaled cumulants of the charge in the initial state and at long times are simply related and, in particular, the latter are independent of the model parameters. Using the quasiparticle picture we obtain the full time evolution of the cumulants and find that although their end points are fixed, the finite-time dynamics depends strongly on the model parameters. We go on to construct the scaled cumulant generating functions and from this determine the limiting charge probability distributions at long time which are shown to exhibit distinct, nontrivial, and non-Gaussian fluctuations and large deviations. Published by the American Physical Society 2024

arXiv:2312.02929•Physical Review A•Apr 1, 2024•16 citations

Full Counting Statistics and Large Deviations in a Thermal 1D Bose Gas

Maksims Arzamasovs, Dimitri M. Gangardt

We obtain the distribution of a number of atoms in an interval (full counting statistics) for interacting bosons in one dimension. Our results are valid in the weakly interacting regime in a parametrically large window of temperatures and interval lengths. The obtained distribution significantly deviates from a Gaussian away from the quasicondensate regime, and, for sufficiently short intervals, the probability of large number fluctuations is strongly enhanced.

arXiv:1807.09381•Physical Review Letters•Mar 27, 2019•37 citations

Full counting statistics of the momentum occupation numbers of the Tonks-Girardeau gas

P. Devillard, Denis Chevallier, Patrizia Vignolo +1 more

We compute the fluctuations of the number of bosons with a given momentum for the Tonks-Girardeau gas at zero temperature. We show that correlations between opposite momentum states, which are an important identifying characteristic of long-range order in weakly interacting Bose systems, are suppressed and that the full distribution of the number of bosons with nonzero momentum is exponential. The distribution of the quasicondensate is however quasi-Gaussian. The experimental relevance of our findings for recent cold-atom experiments is discussed.

arXiv:2003.05868•Physical Review A•Jun 1, 2020•10 citations

Momentum distribution of one-dimensional Bose gases at the quasicondensation crossover: Theoretical and experimental investigation

T. Jacqmin, Bess Fang, Tarik Berrada +2 more

We investigate the momentum distribution of weakly interacting one-dimensional (1D) Bose gases at thermal equilibrium both experimentally and theoretically. Momentum distribution of 1D Bose gases is measured using a focusing technique, whose resolution we improve via a guiding scheme. The momentum distribution compares very well with quantum Monte Carlo calculations for the Lieb-Liniger model at finite temperature, allowing for an accurate thermometry of the gas that agrees with (and improves upon) the thermometry based on in situ density fluctuation measurements. The quasicondensation crossover is investigated via two different experimental parameter sets, corresponding to the two different sides of the crossover. Classical field theory is expected to correctly describe the quasicondensation crossover of weakly interacting gases. We derive the condition of validity of the classical field theory, and find that, in typical experiments, interactions are too strong for this theory to be accurate. This is confirmed by a comparison between the classical field predictions and the numerically exact quantum Monte Carlo calculations.

arXiv:1207.2855•Physical Review A•Oct 25, 2012•58 citations

Time-integrated observables as order parameters for full counting statistics transitions in closed quantum systems

James M. Hickey, Sam Genway, Igor Lesanovsky +1 more

The dynamical behavior of many-body systems is often richer than what can be anticipated from their static properties. Here we show that in closed quantum systems this becomes evident by considering the statistics of time-integrated observables. In particular, the analytic properties of their generating functions, as estimated by full counting statistics (FCS), allow one to identify FCS phases, i.e., phases with specific fluctuation properties of time-integrated observables, and to locate transitions between these phases. We discuss in detail the case of the quantum Ising chain in a transverse field. We show that this model displays a continuum of full counting statistics transitions, of which the static transition is just an end point. These singularities are not a consequence of particular choices of initial conditions or other external nonequilibrium protocols such as quenches in coupling constants. They can be probed generically through quantum jump statistics of an associated open problem, and for the case of the quantum Ising chain we outline a possible experimental realization of this scheme by digital quantum simulation with cold ions.

arXiv:1211.4773•Physical Review B•May 30, 2013•40 citations

Momentum-Space Correlations of a One-Dimensional Bose Gas

Bess Fang, Aisling Johnson, Tommaso Roscilde +1 more

Analyzing the noise in the momentum profiles of single realizations of one-dimensional Bose gases, we present the experimental measurement of the full momentum-space density correlations ⟨δn_{p}δn_{p^{'}}⟩, which are related to the two-body momentum correlation function. Our data span the weakly interacting region of the phase diagram, going from the ideal Bose gas regime to the quasicondensate regime. We show experimentally that the bunching phenomenon, which manifests itself as super-Poissonian local fluctuations in momentum space, is present in all regimes. The quasicondensate regime is, however, characterized by the presence of negative correlations between different momenta, in contrast to the Bogolyubov theory for Bose condensates, predicting positive correlations between opposite momenta. Our data are in good agreement with ab initio calculations.

arXiv:1505.04675•Physical Review Letters•Feb 2, 2016•52 citations
Inspired by recent advances in cold atomic systems and nonequilibrium physics, we introduce a characterization scheme, the time-of-flight full counting statistics. We benchmark this method on an interacting one-dimensional Bose gas and show that there the time-of-flight image displays several universal regimes. Finite momentum fluctuations are observed at larger distances, where a crossover from exponential to Gamma distribution occurs upon decreasing momentum resolution. Zero-momentum particles, on the other hand, obey a Gumbel distribution in the weakly interacting limit, characterizing the quantum fluctuations of the former quasicondensate. Time-of-flight full counting statistics is demonstrated to capture (pre-)thermalization processes after a quantum quench and can be useful for characterizing exotic quantum states such as many-body localized systems or models of holography.
Unless constrained by symmetry, measurement of an observable on an ensemble of identical quantum systems returns a distribution of values which are encoded in the full counting statistics. While the mean value of this distribution is important for determining certain properties of a system, the full distribution can also exhibit universal behavior. In this paper we study the full counting statistics of particle number in one-dimensional interacting Bose and Fermi gases which have been quenched far from equilibrium. In particular, we consider the time evolution of the Lieb-Liniger and Gaudin-Yang models quenched from a Bose-Einstein condensate initial state and calculate the full counting statistics of the particle number within a subsystem. We show that the scaled cumulants of the charge in the initial state and at long times are simply related and, in particular, the latter are independent of the model parameters. Using the quasiparticle picture we obtain the full time evolution of the cumulants and find that although their end points are fixed, the finite-time dynamics depends strongly on the model parameters. We go on to construct the scaled cumulant generating functions and from this determine the limiting charge probability distributions at long time which are shown to exhibit distinct, nontrivial, and non-Gaussian fluctuations and large deviations. Published by the American Physical Society 2024
We compute the fluctuations of the number of bosons with a given momentum for the Tonks-Girardeau gas at zero temperature. We show that correlations between opposite momentum states, which are an important identifying characteristic of long-range order in weakly interacting Bose systems, are suppressed and that the full distribution of the number of bosons with nonzero momentum is exponential. The distribution of the quasicondensate is however quasi-Gaussian. The experimental relevance of our findings for recent cold-atom experiments is discussed.
We investigate the momentum distribution of weakly interacting one-dimensional (1D) Bose gases at thermal equilibrium both experimentally and theoretically. Momentum distribution of 1D Bose gases is measured using a focusing technique, whose resolution we improve via a guiding scheme. The momentum distribution compares very well with quantum Monte Carlo calculations for the Lieb-Liniger model at finite temperature, allowing for an accurate thermometry of the gas that agrees with (and improves upon) the thermometry based on in situ density fluctuation measurements. The quasicondensation crossover is investigated via two different experimental parameter sets, corresponding to the two different sides of the crossover. Classical field theory is expected to correctly describe the quasicondensation crossover of weakly interacting gases. We derive the condition of validity of the classical field theory, and find that, in typical experiments, interactions are too strong for this theory to be accurate. This is confirmed by a comparison between the classical field predictions and the numerically exact quantum Monte Carlo calculations.
The dynamical behavior of many-body systems is often richer than what can be anticipated from their static properties. Here we show that in closed quantum systems this becomes evident by considering the statistics of time-integrated observables. In particular, the analytic properties of their generating functions, as estimated by full counting statistics (FCS), allow one to identify FCS phases, i.e., phases with specific fluctuation properties of time-integrated observables, and to locate transitions between these phases. We discuss in detail the case of the quantum Ising chain in a transverse field. We show that this model displays a continuum of full counting statistics transitions, of which the static transition is just an end point. These singularities are not a consequence of particular choices of initial conditions or other external nonequilibrium protocols such as quenches in coupling constants. They can be probed generically through quantum jump statistics of an associated open problem, and for the case of the quantum Ising chain we outline a possible experimental realization of this scheme by digital quantum simulation with cold ions.
Analyzing the noise in the momentum profiles of single realizations of one-dimensional Bose gases, we present the experimental measurement of the full momentum-space density correlations ⟨δn_{p}δn_{p^{'}}⟩, which are related to the two-body momentum correlation function. Our data span the weakly interacting region of the phase diagram, going from the ideal Bose gas regime to the quasicondensate regime. We show experimentally that the bunching phenomenon, which manifests itself as super-Poissonian local fluctuations in momentum space, is present in all regimes. The quasicondensate regime is, however, characterized by the presence of negative correlations between different momenta, in contrast to the Bogolyubov theory for Bose condensates, predicting positive correlations between opposite momenta. Our data are in good agreement with ab initio calculations.