An approximate effective beamsplitter interaction between light and atomic ensembles

Entanglement concentration for two atomic ensembles using an effective atom-light beamsplitter

“…Further, it is assumed that any displacement of the joint atomic quadrature distributions Entanglement concentration for two atomic ensembles using an effective atom-light beamsplitter7 from the centre in phase space caused by the entanglement process itself are small so that the constraints on the beamsplitter-like interaction still hold [19]. For ease of calculation, the atomic state is represented in the number basis as in Equation (1) where λ = tanh(r) is the squeezing parameter, dependent on the interaction strength κ between a light mode and atomic ensemble during the initial entanglement process via the relation (13).…”

“…The first is of the formĤ 1 = φP LXA and the outgoing light modes are redirected back into the atomic ensembles to interact via a second interaction,Ĥ 2 = −φX LPA . We use the reasonable approximations on the quadratures that x l ≈ 1 − φ 2 x l and (1 − φ 2 ) x a ≈ 1 − φ 2 x a for small φ with similar conditions on p l and p a [19]. This double-pass scheme then performs the role of a beamsplitter transformation and is treated accordingly in what follows.…”

“…Depending on the geometry of the setup, either of the two underlying dynamics can be selected. In this paper, we exploit the fact that the double-pass Hamiltonian can approximate, with high fidelity, an actual beamsplitter transformation, the quality of the approximation being dependent not only on the interaction strength, but also on the particular quantum states of the interacting modes [19]. Tuning the interaction parameter, a highly asymmetric atom-light beamsplitter can be realized.…”

Entanglement Concentration for two atomic ensembles using an effective atom-light beamsplitter

“…Entanglement concentration for two atomic ensembles using an effective atom-light beamsplitter7 from the centre in phase space caused by the entanglement process itself are small so that the constraints on the beamsplitter-like interaction still hold [19]. For ease of calculation, the atomic state is represented in the number basis as in Equation ( 1) where λ = tanh(r) is the squeezing parameter, dependent on the interaction strength κ between a light mode and atomic ensemble during the initial entanglement process via the relation (13).…”

“…The first is of the form Ĥ1 = φ PL XA and the outgoing light modes are redirected back into the atomic ensembles to interact via a second interaction, Ĥ2 = −φ XL PA . We use the reasonable approximations on the quadratures that x l ≈ 1 − φ 2 x l and (1 − φ 2 ) x a ≈ 1 − φ 2 x a for small φ with similar conditions on p l and p a [19]. This double-pass scheme then performs the role of a beamsplitter transformation and is treated accordingly in what follows.…”