Creation of massive entanglement with optimized multiple spin squeezing

Duger Ulam-Orgikh

Denis V. Vasilyev, Christine A. Muschik, Klemens Hammerer

Spin squeezing of collective atomic spins can be achieved conditionally via probing with light and subsequent homodyne detection, as is done in a quantum nondemolition measurement. Recently it has been shown that squeezing can also be created unconditionally by a properly designed dissipative dynamics. We compare the two approaches in a Gaussian description and optimize over all Gaussian light-matter interactions. We find that in the optimal unconditional scheme based on dissipation the level of squeezing scales with optical depth as ${d}^{\ensuremath{-}1/2}$. In contrast, the optimal conditional scheme based on measurement of light---which in fact is not a quantum nondemolition measurement---can provide squeezing which scales as ${d}^{\ensuremath{-}1}$. Our results apply directly also to the creation of entanglement in the form of nonlocal spin squeezing of two atomic ensembles.

Bryan J. Dalton, Libby Heaney, John Goold +2 more

The concept of entangled quantum states is considered in the context of systems of identical particles, based on the requirement that in order to represent physical states both for the overall system and the sub-systems which may be entangled, the density operators must satisfy the symmetrisation principle and global and local super-selection rules that prohibit states in which there are coherences between differing particle numbers. These requirements and their justification are fully discussed. In the second quantisation approach used, both the system and the sub-systems are modes (or sets of modes) rather than particles, particles being associated with different occupancies of the modes. The definition of entangled states is based on first defining the non-entangled states - after specifying which modes constitute the sub-systems. This paper mainly focuses on two mode entanglement for massive bosons. Several inequalities involving variances and mean values of operators involving mode annihilation, creation operators have been proposed as tests for two mode entangled states, including the inequalities that define spin squeezing. Spin squeezing criteria in two mode systems are examined, and spin squeezing is best considered for principle spin operator components where the covariance matrix is diagonal. It is shown that the presence of spin squeezing in at least one of the spin components requires entanglement of the relevant pair of modes. Several of the other proposed tests for entanglement, including ones based on the sum of the variances for two spin components are considered. All of the tests are still valid when the present concept of entanglement based on the symmetrisation and super-selection rule criteria is applied, but further tests have been obtained here. Sometimes the new tests are satisfied whilst than those obtained in other papers are not.

Norbert Schuch, Michael M. Wolf, J. I. Cirac

We investigate the creation of squeezing via operations subject to noise and losses and ask for the optimal use of such devices when supplemented by noiseless passive operations. Both single and repeated uses of the device are optimized analytically and it is proven that in the latter case the squeezing converges exponentially fast to its asymptotic optimum, which we determine explicitly. For the case of multiple iterations we show that the optimum can be achieved with fixed intermediate passive operations. Finally, we relate the results to the generation of entanglement and derive the maximal two-mode entanglement achievable within the considered scenario.

이혁재