We show that the two definitions of spin squeezing extensively used in the literature ͓M. Kitagawa and M. Ueda, Phys. Rev. A 47, 5138 ͑1993͒ and D.J. Wineland et al., Phys. Rev. A 50, 67 ͑1994͔͒ give different predictions of entanglement in the two-atom Dicke system. We analyze differences between the definitions and show that the spin squeezing parameter of Kitagawa and Ueda is a better measure of entanglement than the commonly used spectroscopic spin squeezing parameter. We illustrate this relation by examining different examples of a driven two-atom Dicke system in which spin squeezing and entanglement arise dynamically. We give an explanation of the source of the difference using the negativity criterion for entanglement. DOI: 10.1103/PhysRevA.68.064301 PACS number͑s͒: 03.67.Mn, 42.50.Dv, 42.50.Fx Spin squeezing results from quantum correlations between atomic spins have received a great deal of attention in recent years ͓1-9͔. The interest in spin squeezing arises not only from the fact that it exhibits reduced fluctuations of the collection of atomic spins below the fundamental spin noise limit, but also from the possibility of interesting novel applications in interferometry and high-precision spectroscopy. Recently, So "rensen et al. ͓10͔ have proposed spin squeezing as a measure of entanglement in multiatom systems, which opens further applications in quantum information and quantum computation ͓11͔. The advantage of spin squeezing over the well-known entanglement measures, such as concurrence ͓12͔ and negativity ͓13,14͔ is that spin squeezing can be used as a measure of entanglement in multiatom systems, whereas the former measures can be applied only to two particle ͑two qubit͒ systems. Hald et al. ͓15͔ recently reported preparation of an entangled multiatom state via quantum state transfer from squeezed light to a collection of atomic spins. Kuzmich et al. ͓16͔ have proposed a scheme to produce spin squeezed states via a quantum nondemolution measurement technique and spin noise reduction using this method has been experimentally observed ͓17͔.There are, however, two different definitions of the spin squeezing parameter frequently used in the literature; the spin squeezing parameter of Kitagawa and Ueda defined as ͓1͔and the spectroscopic spin squeezing parameter introduced in the context of Ramsey spectroscopy as ͓2͔where S is the total spin of the system, n ជ 1 ,n ជ 2 and n ជ 3 are the three mutually orthogonal unit vectors oriented such that the mean value of one of the spin components, assumed here , but not vice versa. We note that the spin squeezing parameter proposed by So "rensen et al. ͓10͔ as a measure of entanglement coincides with the parameter ͑2͒. It should also be noted here that in general spin squeezing is sufficient but not necessary conditions for entanglement ͓18 -20͔. In studying the relation between entanglement and spin squeezing, we discovered that the two definitions of spin squeezing give somewhat different predictions of entanglement in the two-atom Dicke system. It is ...

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.

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The robustness of the three-level transitionless quantum driving proposed by Giannelli and Arimondo [L.Giannelli and E. Arimondo, Phys. Rev. A 89, 033419 (2014)] is investigated. In the case when the excited state is barely populated during the evolution, its decay rate has little effect on the adiabatic population transfer. However, the dephasing which is due to collisions or phase fluctuations of the driving fields will produce a significant effect on the evolution. We found that the dephasing reduces the performance of the population transfer and the fidelity can be far below the quantum computation target even for small dephasing rates.