Two Distinguishable Fermions Entanglement Generation And Fermionization

We propose a procedure for entanglement generation which could be implemented in current experiments performed with two distinguishable interacting fermions confined in a 1D harmonic trap [Phys. Rev. Lett. 108, 075303 (2012)]. Our results indicate that entangled states could be obtained by preparing a non-interacting non-entangled product state of the trap and then properly controlling the scattering length by means of the magnetic field. Entanglement could be generated when the prepared non-entangled initial state undergoes a turn on and off interaction procedure in which the state is brought into the interacting regime and then back to the absence of interaction point. Entanglement could also be generated when reaching the strongly repulsive regime by tuning the scattering length near the confinement-induced resonance (CIR), i.e. when the two distinguishable fermions are fermionized. We give exact upper bounds for the entanglement and show that maximally entangled states could be produced. Moreover, our results suggest that the maximum entanglement could be reached by repeatedly turning on and off the interaction or by repeatedly crossing the CIR, being the latter the most convenient procedure because it ensures the obtention of maximally entangled states with a higher probability. The turn on and off procedure, the fermionization of the states, and the CIR crossing constitute three basic experimentally realizable main steps upon which several paths for entanglement generation could be diagrammed.