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Modern Physics Letters B

Multi-mode coherent states and multi-mode nonlinear coherent states

Won Sang Chung

Published May 26, 2014• 0 citations
Publisher

Abstract

In this paper, three-mode nonlinear coherent states are introduced by using the complex solution of the equation q3 = 1. The photon-added or photon-subtracted three-mode nonlinear coherent states are shown to be three-mode nonlinear coherent states with different nonlinear functions. The Z3-graded parity coherent states are introduced as examples of three-mode nonlinear coherent states. Finally, multi-mode coherent states and multi-mode nonlinear coherent states are also constructed in a similar way.

DOI
10.1142/s0217984914501152

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In this paper, three-mode nonlinear coherent states are introduced by using the complex solution of the equation q3 = 1. The photon-added or photon-subtracted three-mode nonlinear coherent states are shown to be three-mode nonlinear coherent states with different nonlinear functions. The Z3-graded parity coherent states are introduced as examples of three-mode nonlinear coherent states. Finally, multi-mode coherent states and multi-mode nonlinear coherent states are also constructed in a similar way.
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.
In this paper, after a brief review on the nonlinear coherent states and parity operator by using this operator and nonlinear displacement-type operator, we construct new operators which by the action of them on the vacuum state of the field, we generate a superposition of two nonlinear coherent states and two-modes entangled nonlinear coherent states. Also, we show that by the generalization of the presented method in this paper, the superposition of more than two nonlinear coherent states with the vacuum state of the field and n-mode entangled nonlinear coherent states can be generated.
One of the most promising nonclassical states in the context of quantum optics are hybrid coherent states, which include a combination of coherent states and single-photon-added coherent states. Although hybrid coherent states have been proposed and experimentally generated in various forms, the realization of two-mode hybrid coherent states is still lacking. Here, two-mode hybrid coherent states are introduced by employing two nonlinear optical Kerr media. The two-mode hybrid coherent states can be applied in quantum information and communication applications. In this paper, we investigate the key nonclassical properties of hybrid coherent states, such as photon statistics, the Mandel factor, and Wigner function negativity.