Many-particle entanglement in two-component Bose-Einstein condensates

Abstract

We investigate schemes to dynamically create many particle entangled states of a two component Bose-Einstein condensate in a very short time proportional to 1/N where N is the number of condensate particles. For small N we compare exact numerical calculations with analytical semiclassical estimates and find very good agreement for N ≥ 50. We also estimate the effect of decoherence on our scheme, study possible scenarios for measuring the entangled states, and investigate experimental imperfections.

Entanglement of two-mode Bose-Einstein condensates

“…Since entanglement in bipartite systems is well understood, the entanglement between the modes of the system can be simply calculated. We demonstrate that while the states created in reference [16] are indeed entangled, the entanglement has a different character.…”

“…In [16], to determine the structure of the canonical entangled states, the system described by the Hamiltonian (1) was decomposed into N subsystems consisting of the individual bosons, each with an internal degree of freedom described by a two dimensional Hilbert space spanned by the two states |A and |B . In this description, the system is viewed as a collection of N singlequbit subsystems.…”

“…By this measure certain states of the condensate were shown to be entangled. We argue here that the decomposition of the system in reference [16] into subsystems made up of individual bosons is not physically realizable, due to the indistinguishibility of the bosons within the condensates [17,18]. We argue that a more physically relevant interpretation is to decompose the system into a bipartite system of the two modes.…”

“…In the simplest model system, bosons are restricted to occupy one of two modes, each of which is a BEC. A dynamical scheme for engineering many-particle entanglement between the particles in such a system has been proposed by Micheli et al [16]. However, since there is presently no definitive measure for entanglement between three or more subsystems, the amount of entanglement in the output state is not analyzed quantitatively.…”

“…In the case of a bimodal Bose-Einstein condensate investigated in [15,16], the entangled subsystems were identified as the individual atoms in the condensate, and a mathematical measure of the multipartite entanglement proposed. By this measure certain states of the condensate were shown to be entangled.…”