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Classical and quantum description of a periodically driven multi-photon anharmonic oscillator

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Abstract

The Hamiltonian and hence the relevant equations of motion involving the dynamics of a driven classical anharmonic oscillator of 2m-th anaharmonicity are constructed. In order to derive the model of a driven multi-photon quantum anharmonic oscillator, we neglect the non-conserving energy terms. Assuming the periodical nature of the driven/forcing term, the dynamical nature of the field operators are expressed in terms of the coupling constant, excitation/photon number and the driven parameters. The solutions are found useful for investigating the squeezing effects and the antibunching of photons of the radiation field prepared in the initial thermal/Fock states. The squeezing effects of the radiation field is found impossible. However, a clear signature of the antibunching of photons is exhibited. It corroborates the fact that the presence of one nonclassical phenomenon does not warrant the presence of the second one. The solutions presented here are exact analytical in nature. Nevertheless, a detailed investigation on the driven quantum anharmonic oscillator is not done before. The present investigation will be of fundamental importance.

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Acknowledgements

One of the authors (DKB) is thankful to the CSIR for awarding him a Senior Research Fellowship (09/202(0062)/2017-EMR-I). SM is thankful to the University Grants Commission (F.No.42-852/2013(SR)) and the Council of Scientific and Industrial Research (CSIR) (03(1283)/13/EMR-II), New Delhi for financial support.

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  1. Department of Physics, Visva-Bharati, Santiniketan, 731235, India

    Dolan Krishna Bayen & Swapan Mandal

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  1. Dolan Krishna Bayen
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  2. Swapan Mandal
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Correspondence to Swapan Mandal.

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Bayen, D.K., Mandal, S. Classical and quantum description of a periodically driven multi-photon anharmonic oscillator. Opt Quant Electron 51, 388 (2019). https://doi.org/10.1007/s11082-019-2096-1

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