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Quantum Optics Journal of the European Optical Society Part B

Interaction of squeezed light with a Kerr medium

Arup Banerjee

Published Feb 1, 1993• 5 citations
Publisher

Abstract

The author considers interaction of squeezed light with a non-linear Kerr medium modelled as an anharmonic oscillator. Evolution of quantum fluctuations in the field amplitude and the first-order coherence function have been studied for both the sub-Poissonian and super-Poissonian statistics. Further, the author has also investigated the effect of the squeezing parameter of the initial state. The results for the first-order coherence function are obtained analytically.

DOI
10.1088/0954-8998/5/1/003

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The author considers interaction of squeezed light with a non-linear Kerr medium modelled as an anharmonic oscillator. Evolution of quantum fluctuations in the field amplitude and the first-order coherence function have been studied for both the sub-Poissonian and super-Poissonian statistics. Further, the author has also investigated the effect of the squeezing parameter of the initial state. The results for the first-order coherence function are obtained analytically.
A systematic study of squeezing obtained from k-photon anharmonic oscillator (with interaction hamiltonian of the form (a†)kak, k ≥ 2) interacting with light whose statistics can be varied from sub-Poissonian to poissonian via binomial state of field and super-Poissonian to poissonian via negative binomial state of field is presented. We predict that for all values of k there is a tendency increase in squeezing with increased sub-Poissonian character of the field while the reverse is true with super-Poissonian field. We also present non-classical behavior of the first order coherence function explicitly for k = 2 case (i.e., for two-photon anharmonic oscillator model used for a Kerr-like medium) with variation in the statistics of the input light.
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 study amplitude-squared squeezing in interaction of coherent light with a nonlinear Kerr medium modelled as an anharmonic oscillator with interaction Hamiltonian H = ½ λ a +2 a 2, where λ is proportional to χ(3) of the nonlinear medium and a is annihilation operator for the interacting field. We find the squeezing parameter S ( τ, r ) in terms of a dimensionless interaction time τ = λ t and Kerr parameter r , which is product of, τ and the average number of photons and obtain almost complete amplitude-squared squeezing (i.e., S ≈ 0) for very small interaction time and very large intensity of the interacting light. We optimize squeezing parameter S ( τ, r ) by an analytic estimation assuming high intensity of the interacting light and realistic values of Kerr nonlinearity following J.Bajer et al. [Czech. J. Phy. 52, 1313 (2002)] and obtain a scaling law for optimal amplitude-squared squeezing with minimum value S min , at r = r min for a given τ. The validity of the scaling law is checked numerically and analytically in the region of realistic values of Kerr nonlinearity and intensity of the interacting light.
In this framework, the effect of a Kerr-like medium and the coupling function dependent on the number of photons operator on the interaction between a two-level atom and a non-linear field is studied. A relation between the Kerr-like medium parameter and the field-atom coupling parameter is used to obtain a simplified formula for Rabi frequency. The wave function of the proposed model is obtained, followed by the derivation of the phase distribution and from which the wehrl entropy formula is calculated. The effect of the initial state and the non-linear func?tion dependent on the number of photons operator and the Kerr-like medium on entanglement is calculated through the Wehrl entropy formula, wehrl distribution and the behaviour of photons by studying the correlation function. The entangle?ment decreases when the function dependent on the number of photons operator is taken into account, while the entanglement gradually improves when the squeezed state is considered, and the entanglement decreases significantly when considering the Kerr medium. An oscillatory distribution is formed between the classical and non-classical in the coherent state. The non-classical distribution disappears when considering the squeezed state and the Kerr-like medium.
In the present communication, we consider the problem of two quantum systems with the Kerr-like medium nonlinearity. The system is cast form of an interaction between two operators of the form su(1,1) Lie algebra and su(2) Lie algebra. We obtain the wave function via the evolution operator where we use the Heisenberg equations of motion to derive the constants of motion. We discuss the atomic inversion. It is found that the Kerr-like medium decreases the amplitude and increases the fluctuations. Also we consider different types of squeezing, it is shown that the entropy squeezing is pronounced in the second quadrature, but it shows a small amount in the first quadrature. For the variance squeezing, a small amount occurs in the presence of the Kerr-like medium. However, the normal squeezing occurs in the first quadrature where the squeezing is sensitive to both the Kerr-like medium parameter and the initial state. Furthermore, the degree of entanglement is examined through the linear entropy. It is shown that the function decreases besides rapid fluctuations. The correlation function displays nonclassical behavior in addition to an increase in the amplitude of the fluctuations.