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Physical Review A

Even and odd two-photon coherent states of the radiation field

Z. Z. Xin, D. B. Wang, Minoru Hirayama, K.-i. Matumoto

Published Oct 1, 1994• 40 citations
Publisher

Abstract

The orthonormal eigenstates of the square of Yuen's operator b=\ensuremath{\mu}a+\ensuremath{\nu}${\mathit{a}}^{\mathrm{\ifmmode^\circ\else\textdegree\fi{}}}$ are constructed. Some mathematical and quantum statistical properties of them are discussed. A new class of minimum uncertainty state is found.

DOI
10.1103/physreva.50.2865

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The orthonormal eigenstates of the square of Yuen's operator b=\ensuremath{\mu}a+\ensuremath{\nu}a\ifmmode∘\else\textdegree\fi{\mathit{a}}^{\mathrm{\ifmmode^\circ\else\textdegree\fi{}}}a\ifmmode∘\else\textdegree\fi are constructed. Some mathematical and quantum statistical properties of them are discussed. A new class of minimum uncertainty state is found.
We construct mathematically two new types of quantum state which we call the generalized excited even and odd coherent states of the radiation field. They are created by repeatedly applying the pseudo-creation operator b † = ν ∗ a + μ ∗ a † to the even and odd coherent states m times, respectively. Analytic expressions for the quantum statistical properties are derived, and through numerical computation it is found that these states can exhibit highly nonclassical behaviour depending on the degree of excitation m and other parameters. These states may have interesting significance if they can be realized experimentally.
The concept of a two-photon coherent state is introduced for applications in quantum optics. It is a simple generalization of the well-known minimum-uncertainty wave packets. The detailed properties of two-photon coherent states are developed and distinguished from ordinary coherent states. These two-photon coherent states are mathematically generated from coherent states through unitary operators associated with quadratic Hamiltonians. Physically they are the radiation states of ideal two-photon lasers operating far above threshold, according to the self-consistent-field approximation. The mean-square quantum noise behavior of these states, which is basically the same as those of minimum-uncertainty states, leads to applications not obtainable from coherent states or one-photon lasers. The essential behavior of two-photon coherent states is unchanged by small losses in the system. The counting rates or distributions these states generate in photocount experiments also reveal their difference from coherent states.
By applying higher powers of the Bogoliubov transformation operator bdagger = v*a + mu*adagger to the two-photon coherent states (or minimum uncertainty squeezed states) we construct a new type of quantum state which we call the generalized excited two-photon coherent states. Analytic expressions for the quantum statistical properties are derived, and through numerical computation the phase space quasi-probability distributions are found. These states can exhibit highly nonclassical behaviour depending on the degree of excitation m and other parameters. For particular values of two parameters lambda and rho, these generalized states reduce to other classes of coherent states formerly reported. Our theory thus presents a much broader approach to these types of quantum states.
The photon-added odd pair coherent states and photon-added even pair coherent states are constructed,and their nonclassical properties are studied with numeric simulation method.The results show that the constructed states are new quantum optical fields that exhibit the nonclassical properties such as the sub-poissonian distribution characters of photon statistics and the antibunching effect.When the photons are added to the two modes of the odd(even) pair coherent states,the sub-poissonian distribution characters of photon statistics can be obviously enhanced.
A non-classical state of the radiation field, which we call the excited two-photon coherent state, is defined by m-times applying the photon creation operator on Yuen's two-photon coherent state . Its squeezing and sub-Poissonian character are demonstrated. Its generalized quasiprobability distribution functions in the representation are obtained and compared with those of the state and the Agarwal - Tara excited coherent state . It is observed that the exhibits remarkable non-classical properties differing from those of and .