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Communications in Theoretical Physics

Production of the Superposition of Nonlinear Coherent States and Entangled Nonlinear Coherent States

Amir Karimi, Mohammad Kazem Tavassoly

Published Sep 1, 2015• 16 citations
Publisher

Abstract

Abstract In this paper, by using the parity operator as well as the nonlinear displacement-type operator, we define new operators which by the action of them on the vacuum state of the radiation field, superposition of two nonlinear coherent states and two-mode entangled nonlinear coherent states are generated. Also, we show that via the generalization of the presented method, the superposition of more than two nonlinear coherent states and n-mode entangled nonlinear coherent states can be generated.

DOI
10.1088/0253-6102/64/3/341

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Abstract In this paper, by using the parity operator as well as the nonlinear displacement-type operator, we define new operators which by the action of them on the vacuum state of the radiation field, superposition of two nonlinear coherent states and two-mode entangled nonlinear coherent states are generated. Also, we show that via the generalization of the presented method, the superposition of more than two nonlinear coherent states and n-mode entangled nonlinear coherent states can be generated.
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.
A new kind of k-quantum nonlinear coherent states, i.e., the k eigenstates of the k-th power of the generalized annihilation operator of f-oscillators, are obtained and their properties are discussed. The completeness of the k states is investigated. An alternative method to construct them is proposed. It is shown that these states may form a complete Hilbert space, and all of them can be generated by a linear superposition of k Roy-type nonlinear coherent states. Physically, they can be generated by a linear superposition of the time-dependent Roy-type nonlinear coherent states at different instants.
We propose a scheme for generating the superposition and the entanglement of squeezed vacuum states of electromagnetical fields. The scheme involves single-photon source, single photon detector, and cross Kerr nonlinearity. The Kerr nonlinearity required for generating the superposition of squeezed vacuum states is 1/2 of that required for generating the superposition of coherent states. The proposal can also be extended to generate the entanglement states between two coherent states and that between one coherent state and one squeezed vacuum state.
We demonstrate several results for the nonlinear interferometer, that emerge from a formalism which elegantly describes the output field of the nonlinear interferometer as two-mode entangled coherent states. We clarify the relationship between squeezing and entangled coherent states, since a weak nonlinear evolution produces a squeezed output, while a strong nonlinear evolution produces a two-mode, two-state entangled coherent state. In between these two extremes exist superpositions of two-mode coherent states manifesting varying degrees of entanglement for arbitrary values of the nonlinearity. The cardinality of the basis set of the entangled coherent states is finite when the ratio \ensuremath{\chi}/\ensuremath{\pi} is rational, where \ensuremath{\chi} is the nonlinear strength. We also show that entangled coherent states can be produced from product coherent states via a nonlinear medium without the need for the interferometric configuration. This provides an important experimental simplification in the process of creating entangled coherent states.