From many-particle interference to correlation spectroscopy

Abstract

We show how robust statistical features of a many-particle quantum state's two-point correlations after transmission through a multi-mode random scatterer can be used as a sensitive probe of the injected particles' mutual indistinguishability. This generalizes Hong-Ou-Mandel interference as a diagnostic tool for many-particle transmission signals across multi-mode random scatterers. Furthermore, we show how, from such statistical features of the many-particle interference pattern, information can be deduced on the temporal structure of the many-particle input state, by inspection of the many-particle interference with an additional probe particle of tuneable distinguishability.

Signatures of Indistinguishability in Bosonic Many-Body Dynamics

“…This fundamental question is, however, key to a variety of complex quantum phenomena, such as dynamical equilibration after a quench [34][35][36], correlation formation [37,38], or transport in interacting many-body systems [39,40]. Furthermore, certification of the bosonic, fermionic, as well as (in)distinguishable character of particles [12,14,[41][42][43][44] could also be achieved by identifying the corresponding interference fingerprints in the (interacting) dynamics.Hence, it is the purpose of this work to systematically explore the impact of particles' indistinguishability on the time evolution of interacting many-body systems. We consider bosons which occupy a discrete set of coupled modes and whose mutual (in)distinguishability is controlled by an additional internal degree of freedom.…”

“…According to our arXiv:1710.08876v4 [quant-ph] 20 Apr 2018 measure, the DOI does not solely depend on the repartition of particles among species, but also on how the species are distributed over the external modes [49]. This interplay between external and internal degrees of freedom, although discussed for the indistinguishability of two photons [50, 51], has not been clearly resolved in previously introduced DOI measures [42,[45][46][47][48].…”

Spectral Structure and Many-Body Dynamics of Ultracold Bosons in a Double-Well

“…While it is, therefore, clear that the only promising route for an efficient characterization of large and complex quantum systems can be through effective descriptions—such as offered, e.g., by the theory of open quantum systems [ 19 , 20 , 21 , 22 ], modern semiclassics [ 23 ], or random matrix theory [ 24 , 25 ]—there is an intermediate range of system sizes where efficient numerical methods can (a) be gauged against each other, to benchmark their quantitative reliability, without any a priori restriction on the explored portion of Hilbert space, and (b) contribute to gauge effective theories against (numerically) exact solutions [ 26 , 27 , 28 ], at spectral densities where quantum granular effects induce possibly sizeable deviations [ 29 ] from effective theory predictions (which always rely on some level of coarse graining). In our view, it is this intermediate system sizes where efficient methods of numerical simulation develop their full potential, since they can inspire and ease the development, e.g., of powerful statistical methods and paradigms (such as scaling properties [ 18 , 26 , 30 ])—which then enable robust predictions in the realm of fully unfolding complexity.…”

Benchmarking of Gaussian boson sampling using two-point correlators

“…These expressions can then be averaged over the Haar measure by using techniques from random matrix theory to obtain the relevant statistical signatures, established in Refs. [53,57]. In Sec.…”