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ISRN Optics

Nonclassical Effects of Light in Fifth Harmonic Generation up to First-Order Hamiltonian Interaction

Rajendra Pratap, Dilip Kumar Giri, Ajay Prasad

Published Mar 9, 2014• 4 citations
Publisher

Abstract

The nonclassical effects of light in the fifth harmonic generation are investigated by quantum mechanically up to the first-order Hamiltonian interaction. The coupled Heisenberg equations of motion involving real and imaginary parts of the quadrature operators are established. The occurrence of amplitude squeezing effects in both quadratures of the radiation field in the fundamental mode is investigated and found to be dependent on the selective phase values of the field amplitude. The photon statistics in the fundamental mode have also been investigated and found to be sub-Poissonian in nature. It is observed that there is no possibility to produce squeezed light in the harmonic mode up to first-order Hamiltonian interaction. Further, we have found that the normal squeezing in the harmonic mode directly depends upon the fifth power of the field amplitude of the initial pump field up to second-order Hamiltonian interaction. This gives a method of converting higher-order squeezing in the fundamental mode into normal squeezing in the harmonic mode and vice versa. The analytic expression of fifth-order squeezing of the fundamental mode in the fifth harmonic generation is established.

DOI
10.1155/2014/580262

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The nonclassical effects of light in the fifth harmonic generation are investigated by quantum mechanically up to the first-order Hamiltonian interaction. The coupled Heisenberg equations of motion involving real and imaginary parts of the quadrature operators are established. The occurrence of amplitude squeezing effects in both quadratures of the radiation field in the fundamental mode is investigated and found to be dependent on the selective phase values of the field amplitude. The photon statistics in the fundamental mode have also been investigated and found to be sub-Poissonian in nature. It is observed that there is no possibility to produce squeezed light in the harmonic mode up to first-order Hamiltonian interaction. Further, we have found that the normal squeezing in the harmonic mode directly depends upon the fifth power of the field amplitude of the initial pump field up to second-order Hamiltonian interaction. This gives a method of converting higher-order squeezing in the fundamental mode into normal squeezing in the harmonic mode and vice versa. The analytic expression of fifth-order squeezing of the fundamental mode in the fifth harmonic generation is established.
The squeezing and sub-Poissonian eects of light in third harmonic generation are investigated based on the fully quantum mechanical approach up to the rst order Hamiltonian interaction in gt, where g is the coupling constant between the modes per second and t is the interaction time between the waves during the process in a nonlinear medium.The coupled Heisenberg equations of motion involving real and imaginary parts of the quadrature operators are established.The occurrence of amplitude squeezing eects in both the quadratures of the radiation eld in the fundamental mode is investigated and found to be dependent on the selective phase values of the eld amplitude.The photon statistics of the pump mode in this process have also been investigated and found to be sub-Poissonian in nature.It is shown that for particular phase values the amplitude squeezing and sub-Poissonian photon statistics of light occur simultaneously.It is observed that there is no possibility to produce squeezed light in the harmonic mode up to rst-order interaction in gt.Further, it is found that the normal squeezing in the harmonic mode directly depends upon the amplitude-cubed squeezing of the initial pump eld to the case of second-order interaction in gt.This gives a method of converting higher-order (amplitude-cubed) squeezing of the fundamental mode into normal squeezing of the harmonic mode and vice versa.
The occurrence of fourth and fifth-order squeezing in the fundamental mode of the electromagnetic field in spontaneous and stimulated Raman processes under the short-time approximation is investigated on the basis of a fully quantum-mechanical approach. In an idealized model, the Raman process is looked upon as a two-photon on a one phonon interaction process. The coupled Heisenberg equations of motion involving real and imaginary parts of the quadrature operators are established. The dependence of fourth- and fifth-order squeezing in terms of the signal-to-noise ratio on the number of photons is investigated. We have also established the amplitude squeezing effects in the Stokes and vibrational modes, which is found to be dependent on higher-order difference squeezing showing a difference squeezing that can be converted to normal squeezing.
Squeezing of the electromagnetic field is a purely quantum mechanical phenomenon and this quantum effect is expected to manifest itself in optical processes in which the nonlinear response of the system to the radiation field plays an important role. It has generated a great deal of interest in view of the possibility of reducing the noise of an optical signal below the vacuum limit i.e. zero-point oscillations. In this paper the concept of nth-order amplitude squeezing is introduced in the fundamental mode in four- and six-wave mixing processes as a generalization of the higher-order squeezing under short-time approximation based on a fully quantum mechanical approach. It established the coupled Heisenberg equations of motion involving real and imaginary parts of the quadrature operators. The condition for occurrence of nth-order squeezing is obtained from which higher-order squeezing upto n=3 are studied. Dependence of squeezing on photon number is also established. The conditions for obtaining maximum and minimum squeezing are obtained. The method of present investigation can be applied to any higher-order non-linear optical processes and the technique can also be extended for studying squeezing in any N-photon process in general. Further, nth-order squeezing of radiation in N-photon process can also be investigated. The results obtained may help in selecting a suitable process to generate optimum squeezing in the radiation field.
Abstract We theoretically investigate the emergence of nonclassical features, two-mode squeezing, sub-Poissonian photon statistics, and bipartite entanglement, in the third harmonic generation (THG) process, employing a first-order interaction Hamiltonian within the short-time approximation. The study reveals that both first- and second-order squeezing exhibit strong dependence on the input field amplitudes, relative phase, and interaction strength. Asymmetric coherent inputs, where the harmonic mode carries greater intensity than the fundamental, enhance the degree of squeezing and lead to deeper nonclassical minima. The squeezing parameters display periodic phase-dependent oscillations, indicating phase-sensitive control of quantum correlations. Sub-Poissonian photon statistics in the fundamental mode further confirm the quantum nature of the generated light. Entanglement is analyzed through the Duan et al. inseparability criterion and the Hillery–Zubairy (HZ) criteria. While the Duan criterion fails to detect entanglement under purely coherent excitation in the short-time regime, both the HZ-1 and HZ-2 criteria confirm entanglement under specific phase conditions, with HZ-2 exhibiting greater sensitivity at elevated field strengths. These results underscore the potential of THG as a viable platform for the controllable generation of nonclassical light, with implications for continuous-variable quantum optics and integrated quantum photonics.
We have examined non classical effect i.e. higher order single mode antibunching and intermodel antibunching and higher order sub-poissonian photon statistics (HOSPS) in fifth harmonic generation non linear optical process using short time interaction technique.We have found that nonclassical effects directly depend on number of photons prior to interaction with non linear medium.The higher the number of photons present prior to an interaction, the higher will be the nonclassicality in the system.It is additionally found that stoke mode doesn't fulfill the condition of single mode antibunching and HOSPS in fifth harmonic generation process.To examine the optical nonlinearity of nanoparticles, there are significant research efforts concerning the estimation of higher order nonlinear susceptibility which can be utilized as a source for the generation of higher order harmonic generation nonlinear optical processes [19].
The concept of nth-order amplitude squeezing is introduced in the fundamental mode in Raman process as a generalization of the higher-order squeezing under short-time approximation based on a fully quantum mechanical approach. The condition for occurrence of nth-order squeezing is obtained from which higher-order squeezing up to n = 5 are studied. The coupled Heisenberg equation of motion involving real and imaginary parts of the quadrature operators is established. Dependence of squeezing on photon number is also established.