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arXiv:quant-ph/0409103 · Journal of Physics A Mathematical and General

K-dimensional trio coherent states

Hyo Seok Yi, Nguyen Ba An, Jaewan Kim

Published Oct 29, 2004• 9 citations
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Abstract

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.

DOI
10.1088/0305-4470/37/45/019

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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.
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