Assembly of 2N entangled fermions into multipartite composite bosons

Abstract

An even number of fermions can behave in a bosonic way. The simplest scenario involves two fermions which can form a single boson. But four fermions can either behave as two bipartite bosons or further assemble into a single four-partite bosonic molecule. In general, for 2N fermions there are many possible arrangements into composite bosons. The question is: what determines which fermionic arrangement is going to be realized in a given situation and can such arrangement be considered truly bosonic? This work aims to find the answer to the above question. We propose an entanglement-based method to assess bosonic quality of fermionic arrangements and apply it to study how the ground state of the extended one-dimensional Hubbard model changes as the strength of intra-particle interactions increases.

Molecular interferometers: effects of Pauli principle on entangled-enhanced precision measurements

“…The more natural way to produce entangled states in particle number for molecular interferometers is reducing particle fluctuations in a double well potential, as carried out with ultracold bosonic atoms almost 10 years ago [42]. Finally, given the general character of our theory, the proposed interferometric process for entanglement enhanced metrology can be extended to interacting fermions in optical lattices [32,[43][44][45]. In fact, our proposed interference dynamics could be implemented experimentally by tunning differently the tunneling rate between sites along the x and y directions of a two-dimensional optical lattice [32,44].…”

Composite Fermions as Deformed Oscillators: Wavefunctions and Entanglement

“…The respective wavefunctions of CFs realized by usual fermions satisfy Eqs. (13) which will be solved below. Let us choose a matrix Φ α = Φ α1 with maximal rank and perform the singular value (SVD-or Schmidt-) decomposition:…”

“…The dimensions of unit matrices E m k and square ma-tricesΦ α,k are equal to the multiplicities of singular values λ α1 κ k . Now, the first equation in (13) reduces to the set of r independent systems, k = 1, 2, .., r: From (16)- (17), we infer that the matricesΦ γ,k , γ = = α 1 , constitute the set of commuting normal matrices (commuting with their Hermitian conjugate ones) at fixed k = 1, 2, .., r−1 and possibly at fixed k = r, if λ α1 κr = 0. Under such premises, as known [24], there is a fixed unitary matrixŨ k such thatΦ γ,k =Ũ kDγ,kŨ † k with diagonal oneD γ,k , γ = α 1 .…”

“…Conversely: all the matrices (19) with Tr(D β D α ) = = δ αβ satisfy system (13) and thus give its general solution. The diagonal elements of D α are components of the orthonormal vectors λ α in the complex space:…”

“…An important concept in quantum information theory, quantum communication, and teleportation [9,10] is the notion of entanglement or quantum correlation between the constituents of a composite particle or composite system. Recently, this concept was actively studied just in the context of composite bosons [7,[11][12][13]. Among the measures characterizing the degree of entanglement, best known are the entanglement entropy and purity (= inverse of the Schmidt number) [9,10].…”