Many-body coherence and entanglement from randomized correlation measurements

Abstract

We show that k-point correlation measurements on output of a non-interacting, multimode, random unitary allow to quantify the k-particle coherence of N ≥ k identical (bosonic or fermionic) particles. For separable many-particle input states, we establish an on average strictly monotonic relationship between such k-particle coherences, the interference contrast in the experimentally accessible counting statistics and the degree of the particles' mutual distinguishability, as controlled by their internal degrees of freedom. Non-separability on input can be unveiled by comparison of correlation measurements of different orders.

Full counting statistics of interacting lattice gases after an expansion: The role of the condensate depletion in the many-body coherence

“…Another interesting direction consists in realizing recent proposals to access non-trivial n-body correlations [23,24]. These theoretical works have shown that nondiagonal correlators can be accessed from combining twoparticle unitary transformations -e.g.…”

“…works have shown that applying random unitary transformations before measuring the FCS provides access to non-diagonal correlators [23,24], further motivating the development of experimental approaches to the FCS, in particular in interacting systems. To reveal the many-body coherence properties of the trapped gas of size L, δk is chosen inferior to 1/L, δk × L 1.…”