Geometric phase gate for entangling two Bose-Einstein condensates

Abstract

We propose a method of entangling two spinor Bose-Einstein condensates using a geometric phase gate. The scheme relies upon only the ac Stark shift and a common controllable optical mode coupled to the spins. Our scheme allows for the creation of an S z S z type interaction where S z is the total spin. The geometric phase gate can be executed in times of the order of 2π /G, where G is the magnitude of the Stark shift. In contrast to related schemes which relied on a fourth order interaction to produce entanglement, this is a second order interaction in the number of atomic transitions. Closed expressions for the entangling phase are derived and the effects of decoherence due to cavity decay, spontaneous emission, and incomplete de-entangling of the light to the BEC are analyzed.

Geometric phase gate based on the ac Stark shift

“…This formulation could be generalized to other systems, such as quantum dots placed in a microcavity [16]. Another application is to atomic BEC systems, where an ac Stark shift is readily realized via coupling of cavities to optical transitions of atoms [36].…”

Two-axis two-spin squeezed states

“…Comparing this to (38), we observe that the difference is that the second BEC's labels must be changed to k → N − k. This can be achieved using the transformation e iS z π/2 |k (x)…”

“…[33,34] where it was found that a complex structure of entanglement is present, with a time dependence showing fractal characteristics. Methods to generate this state have been examined in numerous works [33][34][35][36][37][38][39]. Procedures to generate other types of entangled states have also been studied [40,41].…”

Correlation-based entanglement criterion in bipartite multiboson systems

“…Several proposals for such an interaction exist, including photon mediated cavity based methods [27,28,30] and interactions with state-dependent forces [45]. The type of entanglement that is produced by such an interaction has an exotic structure with fractal properties (the "devil's crevasse") [34,46].…”

“…In particular, the ability of realizing BECs on atom chips allows for the possibility of excellent coherent control [25], and performing tasks such as spin squeezing [26]. This allows for a naturally scalable architecture where multiple BECs could be produced on the same chip, allowing for the possibility of entanglement between BECs [27][28][29][30]. While entanglement between two BEC has not been realized to date, entanglement between a BEC and an atom has been demonstrated [31].…”