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Journal of Physics B Atomic Molecular and Optical Physics

On the possibility of continuous generation of squeezed states in a quartic anharmonic oscillator

Swapan Mandal

Published Mar 1, 2000• 16 citations
Publisher

Abstract

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.

DOI
10.1088/0953-4075/33/5/316

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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 Hamiltonian and the corresponding equations of motion involving the field operators of two quartic anharmonic oscillators indirectly coupled via a linear oscillator are constructed. The approximate analytical solutions of the coupled differential equations involving the non-commuting field operators are solved up to the second order in the anharmonic coupling. In the absence of nonlinearity these solutions are used to calculate the second order variances and hence the squeezing in pure and in mixed modes. The higher order quadrature squeezing and the amplitude squared squeezing of various field modes are also investigated where the squeezing in pure and in mixed modes are found to be suppressed. Moreover, the absence of a nonlinearity prohibits the higher order quadrature and higher ordered amplitude squeezing of the input coherent states. It is established that the mere coupling of two oscillators through a third one is unable to produce any squeezing effects of input coherent light, but the presence of a nonlinear interaction may provide squeezed states and other nonclassical phenomena.
Interaction of intense laser beam with an inversion symmetric third order nonlinear medium is modeled as a quartic anharmonic oscillator. A first order operator solution of the model Hamiltonian is used to study the possibilities of generation of higher order nonclassical states. It is found that the higher order squeezed and higher order antibunched states can be produced by this interaction. It is also shown that the higher order nonclassical states may appear separately, i.e. a higher order antibunched state is not essentially higher order squeezed state and vice versa.
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.
We investigate the quantum entanglement dynamics of undriven anharmonic (nonlinear) oscillators with quartic potentials. We first consider the indirect interaction between two such nonlinear oscillators mediated by a third, linear oscillator and show that this leads to a time-varying entanglement of the oscillators, the entanglement being strongly influenced by the nonlinear oscillator dynamics. In the presence of dissipation, the role of nonlinearity is strongly manifested in the steady-state dynamics of the indirectly coupled anharmonic oscillators. We further illustrate the effect of nonlinearities by studying the coupling between an electromagnetic field in a cavity and one movable mirror which is modelled as a nonlinear oscillator. For this case, we present a full analytical treatment, which is valid in a regime where both the nonlinearity and the coupling due to radiation pressure are weak. We show that, without the need of any conditional measurements on the cavity field, the state of the movable mirror is non-classical as a result of the combined effect of the intrinsic nonlinearity and the radiation-pressure coupling. This interaction is also shown to be responsible for squeezing the movable mirror's position quadrature beyond the minimum uncertainty state even when the mirror is initially prepared in its ground state.