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Physical Review A

Vortex states for the quantized radiation field

G. S. Agarwal, Ravinder Rupchand Puri, Ravindra Pratap Singh

Published Nov 1, 1997• 43 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.56.4207

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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 \ensuremathψv=(x\ensuremath−iy)me\ensuremath−(x2+y2)/2\ensuremathσ2.{\ensuremath{\psi}}_{v}=(x\ensuremath{-}{iy)}^{m}{e}^{\ensuremath{-}{(x}^{2}{+y}^{2})/2{\ensuremath{\sigma}}^{2}}.\ensuremathψv​=(x\ensuremath−iy)me\ensuremath−(x2+y2)/2\ensuremathσ2. 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.
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.
Recently, two-mode entangled squeezed states have been produced using even and odd squeezed states. Based on such entangled states, we introduce two new classes of quantum states, namely single-mode excited (depleted) entangled squeezed states which are obtained via the iterated action of the creation (annihilation) operator on the first mode of the two-mode entangled squeezed states. In continuation, we study the amount of entanglement of the introduced states by calculating the 'concurrence' and 'linear entropy'. In addition, we investigate several nonclassicality features such as the sub-Poissonian statistics, second-order correlation function between the two modes and quadrature squeezing. Finally, in order to establish the physical realization of the introduced states, a theoretical scheme for their generation based on the interaction of a two-level atom with a quantized cavity field is proposed.
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).