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Journal of Optics B Quantum and Semiclassical Optics

Trio coherent states

Nguyen Ba An, Truong Minh Duc

Published Jan 18, 2002• 23 citations
Publisher

Abstract

Novel states called trio coherent states are introduced and studied. It is shown that these states possess inherent nonclassical properties such as sub-Poissonian number distributions and violation of Cauchy-Schwarz inequalities. Concerning squeezing, though the usual multimode squeezing is absent, a new type of higher-order multimode squeezing may occur in a trio coherent state. Finally, an experimental scheme is proposed to generate the introduced trio coherent state.

DOI
10.1088/1464-4266/4/1/313

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Novel states called trio coherent states are introduced and studied. It is shown that these states possess inherent nonclassical properties such as sub-Poissonian number distributions and violation of Cauchy-Schwarz inequalities. Concerning squeezing, though the usual multimode squeezing is absent, a new type of higher-order multimode squeezing may occur in a trio coherent state. Finally, an experimental scheme is proposed to generate the introduced trio coherent state.
We introduce a novel class of higher-order, three-mode states called K-dimensional trio coherent states. We study their mathematical properties and prove that they form a complete set in a truncated Fock space. We also study their physical content by explicitly showing that they exhibit nonclassical features such as oscillatory number distribution, sub-poissonian statistics, Cauchy-Schwarz inequality violation and phase-space quantum interferences. Finally, we propose an experimental scheme to realize the state with K=2 in the quantized vibronic motion of a trapped ion.
We study the multimode higher-order nonclassical effects of novel trio coherent states. We show that such states exhibit antibunching to all orders in the single-mode case. However, the two-mode higher-order antibunching may or may not exist depending on the parameters. We also show that in such states squeezing is fully absent in both single-mode and two-mode situations. As for the three-mode case, the so-called sum-squeezing is impossible but another kind of squeezing may arise for the orders K that are a multiple of three. The degree of the lowest allowable K = 3 order squeezing can reach a remarkable amount of 18 % . Of interest is the following property: when the order grows, the degree of antibunching increases but that of squeezing decreases.
Using the nonlinear coherent states approach, a general formalism for the construction of various classes of nonlinear trio coherent states in the context of multi-mode quantum states has been proposed. In particular, taking into account the most popular nonlinearity function associated with f -deformed coherent states, i.e. the nonlinearity function of the centre-of-mass motion of a trapped ion, it is illustrated that the corresponding trio coherent state possesses some interesting nonclassical properties. To establish this observation, sub-Poissonian statistics, three-mode squeezing, the behaviour of Vogel's characteristic function and the existence of entanglement are investigated. Due to the intrinsic non-classicality nature of the considered three-mode states, their physical production may be of high interest in the quantum optics field. Thus, we have finally demonstrated how nonlinear motional trio coherent states can be generated in three-dimensional anisotropic traps, appropriately.
Even and odd trio coherent states: antibunching and violation of CauchyndashndashndashSchwarz inequalities