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Chinese Journal of Lasers

Squeezing Property of Coherent Light Coupled to a Nonlinear Medium of Inversion Symmetry

Hong Li

Published Jan 1, 2004• 0 citations
OpenAlex

Abstract

An analytical approach is adopted for the calculation of squeezed property of coherent light interacting with a nonlinear medium of inversion symmetry. A medium is called inversion symmetric if the potential energy remains invariant under parity transformation. Thus the even order susceptibilities would vanish for the medium and the leading contribution to the nolinear polarization due to the medium is the third order susceptibility. Therefore interaction Hamitonian of the single mode light field with the medium is proportional to the fourth power of the annihilation operator plus creation operator. This means is to take care all the non conserving energy terms for the calculation of the squeezing property of coherent light passing through the nonlinear medium of inversion symmetry. For a single mode light, two dimensionless quadrature operators are defined which are proportional to the usual position and momentum operators respectively. Using the Heisenberg operator equation of motion, the differential equation of the quadrature operators and the approximate solutions to the equations are got. Then the quantum fluctuations of the two quadratures are calculated. The result shows that the squeezing property of the two quadrature operators is controllable through changing the following parameters: coupling constant, mean photon number, light field frequency, and interaction time.

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An analytical approach is adopted for the calculation of squeezed property of coherent light interacting with a nonlinear medium of inversion symmetry. A medium is called inversion symmetric if the potential energy remains invariant under parity transformation. Thus the even order susceptibilities would vanish for the medium and the leading contribution to the nolinear polarization due to the medium is the third order susceptibility. Therefore interaction Hamitonian of the single mode light field with the medium is proportional to the fourth power of the annihilation operator plus creation operator. This means is to take care all the non conserving energy terms for the calculation of the squeezing property of coherent light passing through the nonlinear medium of inversion symmetry. For a single mode light, two dimensionless quadrature operators are defined which are proportional to the usual position and momentum operators respectively. Using the Heisenberg operator equation of motion, the differential equation of the quadrature operators and the approximate solutions to the equations are got. Then the quantum fluctuations of the two quadratures are calculated. The result shows that the squeezing property of the two quadrature operators is controllable through changing the following parameters: coupling constant, mean photon number, light field frequency, and interaction time.
The interaction of coherent light with a nonlinear medium is modeled here by a general quantum anharmonic oscillator. The model is not exactly solvable in a closed analytical form. But we need operator solutions of the equations of motion corresponding to these models in order to study the quantum fluctuations of coherent light in nonlinear media. In the present work we derive approximate operator solutions. From these solutions we observe that there exists an apparent discrepancy between the solutions obtained by different techniques. We compare different solutions and conclude that all correct solutions are equivalent and the apparent discrepancy is due to the use of different ordering of the operators. We use these solutions to investigate the possibilities of observing different optical phenomena in a nonlinear dielectric medium. To be precise, we have studied quantum phase fluctuations of coherent light in a third order inversion symmetric nonlinear medium. Fluctuations in phase space quadrature for the same system are studied and the possibility of generating squeezed state is reported. Fluctuations in photon number are studied and the nonclassical phenomenon of antibunching is predicted. We have generalized the results obtained for third order nonlinear medium and have studied the interaction of an intense laser beam with a general (m-1)-th order nonlinear medium. Aharanov Anandan nonadiabatic geometric phase is also discussed in the context of (m-1)-th order nonlinear medium.
With the help of second-order nonlinear interactions and hence Hamiltonian, we construct the equations of motion corresponding to pump and signal (second harmonic) fields in a second harmonic generation. The corresponding coupled differential equations involving the non-commuting field operators are not solvable in closed analytical forms. With the help of a perturbation method, we obtain analytical solutions of these field operators up to cubic orders in the interaction constant. In an appropriate limit (truncating the solution up to the second order in the interaction constant), these solutions lead to the existing solutions under the short-time approximation. The present analytical solutions are exploited to investigate the squeezing and the antibunching of photons of the input coherent light coupled to the said second-order nonlinear medium. We report the squeezing and antibunching effects of the pump field even for solutions up to the second order and hence the present results are consistent with earlier results. However, for the second harmonic mode, we report the squeezing involving the leading cubic term in the interaction constant.
The roles of the asymmetry of coherent light and of an active medium in squeezed-state generation in a weakly noncentrosymmetric semiconductor are discussed. It is suggested that origin of medium asymmetry lies in the parity indefiniteness of the transition states, whereas field asymmetry is due to the polarization property of light. Third-order nonlinear optical susceptibility is obtained from the semiclassical density matrix approach, whereas the light-squeezing process is studied by use of Heisenberg’s equation of motion. The analysis is applied to GaAs that has been duly irradiated by a tunable nanosecond pulsed Co:MgF2 laser with its photon energy off resonant below the semiconductor’s band edge. It has been found that the effect of asymmetry on squeezed-state generation and photon number is finite only when both of the asymmetries are present simultaneously. One may also notice that the asymmetry improves the squeezing level and reduces the time span of squeezed-light generation.
Coherent light interacting with a nonlinear nonabsorbing medium of inversion symmetry is modelled as a quartic anharmonic oscillator if the lowest (i.e. third) order of nonlinearity is considered. The equation of motion of the quadrature operators of such an oscillator is solved approximately in a closed analytical form. The corresponding solution is used to investigate the possibility of finding the continuous squeezed states. It is found that the amount of squeezing is increased with the increase of intensity of the applied field. An improvement of the squeezing is also possible if the coupling strength is increased. We report the squeezing effect of the input vacuum field. The possibility of generating continuous squeezing in an absolute sense (i.e. 100%) of the input radiation field is also discussed.
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.
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.