Full counting statistics of time-of-flight images

Abstract

Inspired by recent advances in cold atomic systems and non-equilibrium physics, we introduce a novel 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 quasi-condensate. 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.

Quench action and large deviations: Work statistics in the one-dimensional Bose gas

“…An analogous result holds for the case of odd N [82]. As we will see further below, our analytic study ultimately hinges on the existence of the exact formula (21).…”

“…As a first ingredient for the computation of p(w), we consider the zero-density limit of the overlap in Eq. (21), which has been already studied in the literature [82,101,102]. In particular one finds…”

Gumbel statistics for entanglement spectra of many-body localized eigenstates

“…For these statistics, the rate of convergence depends nontrivially on the structure of F [35]. When comparing the statistics of a collection of extreme values with Gumbel statistics, it is convenient [25][26][27][28][30][31][32][33][34] to take a n and b n such that the distribution has mean 0 and standard deviation 1. The distribution function of the same type as G given in Eq.…”

“…We report the surprising observation of Gumbel statistics [24,29]. These statistics, being observed in studies on various physical phenomena [30][31][32][33][34], apply to the extreme value of n → ∞ independent samples drawn from a distribution with a faster than powerlaw asymptotic decay. Our result provides an analytical, * w.buijsman@uva.nl parameter-free characterization of the many-body localized eigenstates.…”

Relaxation of the order-parameter statistics in the Ising quantum chain

“…However, in spite of a generous literature regarding PDFs of various observables (mainly conserved quantities, transverse magnetisation in the Ising spin chain, particle number in the Bose(Fermi)-Hubbard model, etc.) in different quantum models, both non-interacting and interacting, either at the equilibrium [34][35][36][37][38][39][40][41][42][43][44][45] or out-of-equilibrium [46][47][48][49][50][51], the results on the order-parameter statistics are very few [33,52,53]. In particular analytical finding on the PDF of the longitudinal magnetisation in the Ising quantum chain are only limited to some universal scaling behaviour in the ground state at the critical point [54].…”