Quantum nondemolition measurement based generation of entangled states in two Bose–Einstein condensates

Abstract

We theoretically study a scheme for generating entanglement between two Bose–Einstein condensates (BECs). The scheme involves placing two BECs in the path of a Mach–Zehnder interferometer, where the coherent light interacts with the atoms due to a quantum nondemolition Hamiltonian. In contrast to standard approaches where a Holstein–Primakoff approximation is used, we use an exact wavefunction approach where the atoms can be initialized in an arbitrary state and the light–atom interaction times can be arbitrary. In the short time regime, it is possible to construct a very simple approximate theory for the overall effect of the scheme: amplitudes in the superposition between the two BECs with unequal spin eigenvalues are damped. We analyze the types of correlations, entanglement, Einstein–Podolsky–Rosen (EPR) steering, and Bell correlations that are produced and show that the state is similar to a spin-EPR state. Using a two-pulse sequence the correlations can be dramatically improved, where the state further approaches a spin-EPR state.

Decoherence effects in quantum nondemolition measurement induced entanglement between Bose-Einstein condensates

“…Here we only give the final results, for further details we refer the reader to Ref. [79]. Initially, the state of the BECs are polarized in the S x -direction…”

“…To see how this results in an entangled state, consider the particular outcome n d = 0, which can then be approximated according to Ref. [79] as…”

“…The derivation of the state (14) produced by the sequence shown in Fig. 1 does not require the HP approximation meaning that this state is not constrained to the short time regime (τ < 1 √ N ) [79]. Under the HP approximation, the same procedure produces a two-mode squeezed state such that the EPR variables Var(S x 1 −S x 2 ), Var(S y 1 + S y…”

“…Many BEC entangling schemes have been theoretically proposed using a variety of approaches such as cavity QED [64][65][66][67][68], state-dependent forces [69], Rydberg excitations [70], and splitting a single squeezed BEC [71,72]. In particular QND measurement based schemes are promising from the point of view that they have already been achieved in atomic ensembles [73][74][75][76][77][78][79]. These are fundamental to performing various quantum information tasks based on atomic ensembles, such as quantum teleportation [80,81], remote state preparation and clock synchronization [82,83], and quantum computing [84,85].…”

“…In this paper, we calculate the effects of decoherence on entangled BEC states produced by the QND entangling scheme of Ref. [79]. This protocol involves two spatially separated BECs placed in the two arms of a Mach-Zehnder interferometer in the path of coherent light (Fig.…”