Squeezing of coherent light coupled to a periodically driven two-photon anharmonic oscillator
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Squeezing of coherent light coupled to a periodically driven two-photon anharmonic oscillator Dolan Krishna Bayen, Swapan Mandala Department of Physics, Visva-Bharati, Santiniketan 731235, India Received: 4 February 2020 / Accepted: 25 April 2020 © Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract The electromagnetic field coupled to a (2l − 1) order of nonlinear medium leads to the model of a 2lth anharmonic oscillator, l ≥ 2 being an integer. The oscillator with l = 2 corresponds to the model of a quartic anharmonic oscillator. In spite of the huge advancement of mathematical physics, we are still in search of exact analytical solution to the lowest order (i.e., l = 2) of anharmonic oscillator. There are few interesting reports where the approximate solutions to the classical and quantum quartic oscillator problems are explored. In the present investigation, the exact analytical solutions of the quartic anharmonic oscillator under rotating wave approximation and hence the two-photon anharmonic oscillator with periodic forcing are exhibited. The solutions corresponding to the quantized two-photon anharmonic oscillator with periodic forcing is used to calculate the second-order variances of the canonically conjugate quadrature in terms of the initial coherent state. The effects of the forcing parameters on the second-order variances and hence on the squeezing effects are examined for various photon numbers and the dimensionless interaction constants. In these studies, we assume that the oscillator is in on-resonance with those of the external forcing term. The off-resonant contribution is found to be small and is neglected.
1 Introduction The electromagnetic field coupled to a material medium induces the polarization proportional to the electric field amplitude. The basic physics behind the induced linear polarization and hence the linear susceptibility is easily understood in terms of a forced damped harmonic oscillator where the electrons execute harmonic motion under the restoring force exerted by the nucleus [1]. The linear nature of the induced polarization does not hold good for intense electric field and hence the appearance of nonlinear polarization and the nonlinear susceptibility is inevitable. On the other hand, the ultra-intense electromagnetic field amplitude is attainable through the high-power laser sources. For this reason, with the availability of high-power laser sources, the investigation on the matter-field interaction has received considerable interests. The high-power lasers and hence the intense electromagnetic field is responsible for the invocation of nonlinear polarization and hence the subject of nonlinear optics. We find that the appearance of nonlinear polarization is easily explained in terms of the forced damped anharmonic oscillator. The model is named after the celebrated nonlinear
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Eur. Phys. J. Plus
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