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Journal of Modern Optics

Two-mode superposition coherent states with spatial vortex structure for the quantized radiation field

Kaicheng Zhu, Shaoxin Li, Xiaojuan Zheng, Yiping Zhou

Published Apr 5, 2012• 8 citations
Publisher

Abstract

Through superposing M two-mode coherent state a two-mode superposition coherent state with a spatial vortex structure in configuration space is constructed. Such quantum vortex state is an eigenstate of sum of squared two-mode annihilation operators and is always entangled. In the limiting condition of large M the quantum vortex state has a modified Bessel–Gaussian vortex structure with topological charge index n. Experimentally, such two-mode vortex states may be prepared by virtue of a multimode coherent state with currently available technology.

DOI
10.1080/09500340.2012.676095

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Through superposing M two-mode coherent state a two-mode superposition coherent state with a spatial vortex structure in configuration space is constructed. Such quantum vortex state is an eigenstate of sum of squared two-mode annihilation operators and is always entangled. In the limiting condition of large M the quantum vortex state has a modified Bessel–Gaussian vortex structure with topological charge index n. Experimentally, such two-mode vortex states may be prepared by virtue of a multimode coherent state with currently available technology.
A new kind of quantum non-Gaussian state with vortex structure termed as a modified Bessel–Gaussian vortex state is constructed, and it is an eigenstate of sum of squared annihilation operator a2+b2. The quantum vortex state exhibits a rich variety of nonclassical signatures and is always entangled. The dependence of its statistical properties on state parameters is analyzed, and the non-Gaussianity is investigated in detail. It is found that, for sufficient small values of α, the properties clearly depend on the topological charge index n. Moreover, a scheme for generating such quantized vortex states is proposed.
The pair coherent state evolution during a parametric frequency conversion is analyzed. And the wavefunction of the evolving pair coherent state in configuration space is obtained. It is found that the state may become a modified Bessel-Gaussian vortex state with topological charge index q which is a new non-Gaussian state. In coherent state representation such a modified Bessel-Gaussian vortex state is an eigenstate of sum of squared two-mode annihilation operators a2 + b2. The result obtained in this paper provides a new scheme for generating quantized vortex states in experiment with currently available technology.
We study the properties of wave-packet states with vortex structure. In particular we present the characteristics of a two-mode radiation field characterized by a configuration-space wave function ${\ensuremath{\psi}}_{v}=(x\ensuremath{-}{iy)}^{m}{e}^{\ensuremath{-}{(x}^{2}{+y}^{2})/2{\ensuremath{\sigma}}^{2}}.$ We show the generation of such states by the interaction of \ensuremath{\Lambda} systems with squeezed radiation in a two-mode cavity. The two modes are correlated due to entanglement, which also produces the mixed state of each mode even though the state of the two-mode field is a pure state.
The evolution of a system state is derived based on the nonresonant interaction of a three-level “Λ" type atom with two cavity modes at a pair coherent state and two classic fields, and a cavity field state is analyzed in detail under conditional detecting. It is found that the quantized modified Bessel—Gaussian states as well as the superposition states consisting of the quantized vortex states with different weighted coefficients may be prepared through carefully preparing an initial atomic state and appropriately adjusting the interaction time. The scheme provides an additional choice to realize the two-mode quantized vortex state within the context of cavity quantum electrodynamics (QED).