Two-axis two-spin squeezed states

Abstract

The states generated by the two-spin generalization of the two-axis countertwisting Hamiltonian are examined. We analyze the behavior at both short and long timescales, by calculating various quantities such as squeezing, spin expectation values, probability distributions, entanglement, Wigner functions, and Bell correlations. In the limit of large spin ensembles and short interaction times, the state can be described by a two-mode squeezed vacuum state; for qubits, Bell state entanglement is produced. We find that the Hamiltonian approximately produces two types of spin Einstein-Podolsky-Rosen (EPR) states, and the time evolution produces aperiodic oscillations between them. In a similar way to the basis invariance of Bell states and two-mode squeezed vacuum states, the Fock state correlations of spin EPR states are basis invariant. We find that it is possible to violate a Bell inequality with such states, although the violation diminishes with increasing ensemble size. Effective methods to detect entanglement are also proposed, and formulas for the optimal times to enhance various properties are calculated.

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

“…While the type of state that is examined is somewhat different to the 2A2S state of Ref. [103], similar correlations are present for small times and we expect that this relation to be a good detector of entanglement. In Fig.…”

“…A great majority of the studies regarding entanglement in atomic ensembles and BEC have been for single atomic ensembles. Recently there has been a growing interest in entanglement between two or more atomic ensembles or BECs [49][50][51][52][53][54][55]. The first experiments to demonstrate this in atomic ensembles were performed by the Polzik group, using two separated atomic ensembles interacting with a pulse of light performing a non-local Bell measurement on the collective spins.…”

Stroboscopic quantum nondemolition measurements for enhanced entanglement generation between atomic ensembles

“…In the regime n c τ 2 ≈ |ατ | 2 > 1, the Gaussian factor suppresses terms except for k 1 = k 2 . This takes the form of an entangled state [64,73].…”

“…This state has basis invariant properties analogous to Bell states, and can be written equivalently as [73] |EPR…”

“…This results in obtaining the sequence of k l , k ′ l , from which the overall coefficient A can be found through (66). Multiplying the coefficient by the associated term in the superposition gives (73). This procedure is far more efficient than evaluating 2L + 1 matrix multiplications directly, each with an overhead of (N + 1) 6 .…”