Entanglement and fermionization of two distinguishable fermions in a strict and non strict one-dimensional space

Abstract

The fermionization regime and entanglement correlations of two distinguishable harmonically confined fermions interacting via a zero-range potential is addressed. We present two alternative representations of the ground state that we associate with two different types of one-dimensional spaces. These spaces, in turn, induce different correlations between particles and thus require a suitable definition of entanglement. We find that the entanglement of the ground state is strongly conditioned by those one-dimensional space features. We also find that in the strongly attractive regime the relative ground state is a highly localized state leading to maximum entanglement. Our analysis shows that in the strongly repulsive regime the ground state changes smoothly from a superposition of Slater-like states to a finite superposition of Slaters, this lack of accessible states yields to Pauli blocking as a strong signature of fermionization. Our results indicate that entangled states could be obtained in current experiments by reaching the non-interacting regime from the interacting regime. Entangled states could also be obtained when a state is brought from the interacting regime into the strongly repulsive regime by changing the scattering length near the confinement-induced resonance. Finally, we show that the first excited state obtained in the absence of interactions and the third excited fermionized state are maximally entangled.

Composite-boson formalism applied to strongly bound fermion pairs in a one-dimensional trap

“…( 12) vanishes, and thus the coboson ansatz is not defined for γ = 0. Nevertheless, using perturbation theory together with analytical results for the Schmidt coefficients [46] one can calculate the limit value of the fidelity between the true ground state and the coboson ansatz, and find that as the attractive interaction strength approaches zero, F approaches a value of approximately 0.37. Indeed, for γ ∼ 0 we obtain χ 2 ∼ 0.342 θ 2 and F ∼ θ 2 /8χ 2 with θ ∼ γ/ 2πħ hωx ω .…”

Indistinguishable entangled fermions: basics and future challenges

“…Since we are dealing with two distinguishable fermions, the symmetry of the eigenfunctions of Hfalse^ is due to the symmetry of the potential rather than to an ad hoc imposition related to the nature of the particles. However, in [46], it is argued that the solutions in terms of u< and u> account for a lack of information about the location of the individual particles: one of them is on the left and the other one on the right, but we cannot distinguish which one (1 or 2) lies at each side of the boundary x1=x2. In this case, it seems reasonable to resort to the formalism employed when dealing with systems of indistinguishable fermions to extract information about the correlations between the particles with variables u<,>.…”

Two trapped particles interacting by a finite-ranged two-body potential in two spatial dimensions

“…The theoretical prediction of Bose-Einstein condensation goes back to a century ago when Bose worked out the quantum statistics of photons [1] which lead Einstein to make theoretical background for the non-interacting massive bosons that at below a certain finite but small temperature a finite fraction of the total number of particles will occupy the single particle ground state [2]. Following this, F. London drew an analogy between the superfludity of liquid 4 He and Bose-Einstein condensation [3] that led to the further extension of the theoretical development.…”

“…The study of Exact solution of harmonically trapped two ultra cold spin-0 bosons in 2D interacting via finite range two body potential modelled by a Gaussian potential, has been shown to put vast interest in the last few decades in the field of optical lattices, quantum information and entanglement has been discuss for the two identical particles [4][5][6]. Manybody physics is rather complex when atom-atom interaction is considered.…”