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Physical Review A

Dynamical squeezing of photon-added coherent states

V. V. Dodonov, Marcelo A. Marchiolli, Ya. A. Korennoy, Vladimir I. Man’ko, Y A Moukhin

Published Nov 1, 1998• 78 citations
Publisher

Abstract

We study the dynamical squeezing of the photon-added coherent state (PACS) due to a time dependence of the frequency of the electromagnetic field oscillator in a cavity or a vibrational frequency of an ion inside an electromagnetic trap. Explicit expressions for the time dependence of various functions characterizing the quantum state, such as the photon distribution, the Wigner function, the mean values and variances of the quadrature components and of the photon number, show that the dynamically squeezed PACS possesses a larger squeezing coefficient than the usual squeezed states. The dynamical squeezing is accompanied by a change of the sub-Poissonian photon statistics to the super-Poissonian one.

DOI
10.1103/physreva.58.4087

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We study the dynamical squeezing of the photon-added coherent state (PACS) due to a time dependence of the frequency of the electromagnetic field oscillator in a cavity or a vibrational frequency of an ion inside an electromagnetic trap. Explicit expressions for the time dependence of various functions characterizing the quantum state, such as the photon distribution, the Wigner function, the mean values and variances of the quadrature components and of the photon number, show that the dynamically squeezed PACS possesses a larger squeezing coefficient than the usual squeezed states. The dynamical squeezing is accompanied by a change of the sub-Poissonian photon statistics to the super-Poissonian one.
We study the evolution of the photon-added coherent state | α, m ⟩ (introduced by Agarwal and Tara [Phys. Rev. A43, 492 (1991)]) due to a time dependence of the frequency of the electromagnetic field oscillator in a cavity or a vibrational frequency of an ion inside an electromagnetic trap. We give explicit expressions for the photon distribution function, mean values and variances of the quadrature components and of the photon number, the Wigner and Q -functions, etc. We show that the parametric excitation leads to strong oscillations of the photon (phonon) distribution function and changes the subpoissonian photon statistics to the superpoissonian one. Besides, it enables to achieve a larger squeezing coefficient than in the usual squeezed states.
Photon distribution function, means and dispersions are found explicitly for the nonclassical state of light which is created from the photon--added coherent state ∣α,m⟩\vert α,m \rangle∣α,m⟩ due to a time--dependence of the frequency of the electromagnetic field oscillator. Generating function for factorial momenta is obtained. The Wigner function and Q--function are constructed explicitly for the excited photon--added coherent state of light. Influence of added photons on known oscillations of photon distribution function for squeezed light is demonstrated. oscillator are considered.
The investigation of photon statistics and quadrature squeezing in superpositions of two coherent states under the influence of a continuous measurement of photon number shows that the photon statistics of the cavity mode oscillates between sub-Poissonian and super-Poissonian distributions and that the quadrature fluctuation oscillates between squeezing and nonsqueezing at each time when one photon of a cavity mode is registered by a counter. These oscillatory behaviors are caused by the influence of the continuous measurement of photon number and the quantum interference between the two coherent states in the superposition.
We study the statistical properties of squeezed Kerr states generated by squeezing, with a two-photon parametric process, the output of a Kerr medium whose input is coherent light. The squeezing has the effect of allowing the photon statistics to depend on the Kerr nonlinearity. Without the squeezing the statistics are Poissonian, but after squeezing they may be either sub-Poissonian or super-Poissonian. We also study the Q-function quasiprobability distribution for these states and related distributions associated with the quantum-mechanical phase. Finally, we show that quadrature squeezing can be enhanced and that squeezing and sub-Poissonian statistics can coexist.
We construct the photon-added coherent states of a noncommutative harmonic oscillator associated to a qqq-deformed oscillator algebra. Various nonclassical properties of the corresponding system are explored, first, by studying two different types of higher-order quadrature squeezing, namely, the Hillery type and the Hong-Mandel type, and second, by testing the sub-Poissonian nature of photon statistics in higher order with the help of the correlation function and the Mandel parameter. Also, we compare the behavior of different types of quadrature and photon number squeezing of our system with those of the ordinary harmonic oscillator by considering the same set of parameters.
By introducing a generalization of the (p, q)-deformed boson oscillator algebra, we establish a two-parameter deformed oscillator algebra in an infinite-dimensional subspace of the Hilbert space of a harmonic oscillator without first finite Fock states. We construct the associated coherent states, which can be interpreted as photon-added deformed states. In addition to the mathematical characteristics, the quantum statistical properties of these states are discussed in detail analytically and numerically in the context of conventional as well as deformed quantum optics. Particularly, we find that for conventional (nondeformed) photons the states may be quadrature squeezed in both cases Q = pq < 1, Q = pq > 1 and their photon number statistics exhibits a transition from sub-Poissonian to super-Poissonian for Q < 1 whereas for Q > 1 they are always sub-Poissonian. On the other hand, for deformed photons, the states are sub-Poissonian for Q > 1 and no quadrature squeezing occurs while for Q < 1 they show super-Poissonian behavior and there is a simultaneous squeezing in both field quadratures.PACS Nos.: 42.50.Ar, 03.65.–w