Entanglement and spin squeezing in the two-atom Dicke model

Abstract

We analyze the relation between the entanglement and spin-squeezing parameter in the two-atom Dicke model and identify the source of the discrepancy recently reported by Banerjee and Zhou et al that one can observe entanglement without spin squeezing. Our calculations demonstrate that there are two criteria for entanglement, one associated with the two-photon coherences that create two-photon entangled states, and the other associated with populations of the collective states. We find that the spin-squeezing parameter correctly predicts entanglement in the twoatom Dicke system only if it is associated with two-photon entangled states, but fails to predict entanglement when it is associated with the entangled symmetric state. This explicitly identifies the source of the discrepancy and explains why the system can be entangled without spin-squeezing. We illustrate these findings in three examples of the interaction of the system with thermal, classical squeezed vacuum and quantum squeezed vacuum fields.

Quantum spin squeezing

“…[13,216,15,217,218], the relationships between negative pairwise correlation, concurrence, and ξ 2 S for symmetric states and even (odd)-parity states were found. References [219,220] showed that for a two-qubit Dicke system, parameter ξ 2 S is better than ξ 2 R to measure entanglement. A multipartite entanglement criterion for spin-squeezing parameter was given in Ref.…”

Stationary two-atom entanglement induced by nonclassical two-photon correlations

“…The collective parameters Γ 12 and Ω 12 , which arise from the mutual interaction between the atoms, significantly modify the master equation of a two-atom system. The parameter Γ 12 introduces a coupling between the atoms through the vacuum field that the spontaneous emission from one of the atoms influences the spontaneous emission from the other.…”

“…It has been shown that entangled states in a two-atom system can be created by a continuous driving of the atoms with a coherent or chaotic thermal field [5,9,10,11,12], or by a pulse excitation followed by a continuous observation of radiative decay [13,14,15]. Moreover, the effect of spontaneous emission on initially prepared entangled state has also been discussed [16,17,18,19].…”

Perspectives for a mixed two-qubit system with binomial quantum states

“…This periodicity follows a consequence of the fact that the generalized Rabi frequency in the two-photon transition is proportional to n rather than to √ n which is the case in the single-photon process. In the presence of the Stark shifts namely r = β (i) 2 /β (i) 1 , we note that the Rabi frequency as well as the temporal width of the oscillations packets decrease (see figure 3b). The most obvious difference, is that the population inversion collapses to a nonzero value with the inclusion of Stark shifts but to a zero value without it.…”