Creating Multimode Squeezes States And Greenberger-Horne-Zeilinger Entangled States Using Atomic Coherent Effects

The reduction of quantum noise is one of the important issues in quantum op-tics, nonlinear optics and laser physics since Caves first noted the possibilities of ma-nipulating quantum fluctuations with the aim of precision measurement。 Squeezing is defined, for an optical field, when the fluctuations in a certain quadrature are reduced below the vacuum level at the expense of increasing them in its canonically conjugate variable。 Since then great effort has been paid to it。 Either the theoret-ical proposals have been presented or the experimental implementations have been performed。 With the development of quantum teleportation network, one requires to generate multimode quantum teleportation network. Recently, an effective and tunable field squeeze operator for a single-mode field or for a two-mode field has been proposed。 The squeeze operator acts on a cavity with an atomic ensemble and is decoupled from the atomic degrees of freedom。The squeeze parameter is scaled up with the number of atoms present in the interaction region。So far, we have known that squeezing can happen either for a single-mode quadrature or for a two-mode quadrature。Of extreme importance is the close cor-relation of the two-and multimode squeezing to the continuous variable (CV) en-tanglement, which is the important resources for the quantum information and quantum computation。However, to our knowledge, beyond the two-mode case, the multimode squeeze operator has not yet been proposed or realized for atomic sys-tems。Here we propose a mechanism for it。The multimode squeezing is of the par-ticular importance since it is closely correlated to the fully inseparable multipartite states. Such multipartite inseparability is called the genuine multipartite entangle-ment。 One of important types of genuine multipartite entanglement is Greenberger-Horne-Zcilinger (GHZ) entanglement。We propose a scalable scheme for a unitary multimode operator using an optical cavity with an atomic ensemble。We exem-plify three-mode and four-mode cases and engineer the squeeze operators that are decoupled from the atomic degrees of freedom。 The squeeze parameter can be largesince they axe proportional to the number of atoms。 Using the input-output theorywc show that ideal squeezed states and perfect squeezing could be approached atthe output. At the same time, wc show that tripartite and quadripartite GHZ en?tangled states for continuous variables arc obtainable。 The responsible mechanismis based on the atomic coherence controlled parametric interactions。 The scalabilityof the scheme is simply obtained by including more transitions in the atomic system。...