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Analytical investigation on the Autler–Townes splittings and the two-photon effects in a Doppler free signal lineshape of a double-\(\varvec{\lambda }\) type four-level system

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Abstract

By exploiting the pump–probe (signal) spectroscopy, the analytical expressions for the signal lineshapes of a four-level double-\(\lambda \) type system is obtained by solving the steady-state optical Bloch equations. By varying the pump frequencies (positions), the signal lineshapes are investigated as the function of signal detuning. The Autler–Townes effects and hence the ac-Stark splitting of the energy levels are exhibited when the pump is in on-resonance position. On the other hand, the off-resonance pump leads to the two-photon absorption and the shifts of the signal resonance peak positions. The analytical expressions for the imaginary part of the signal polarisation and hence the absorption lineshapes are certainly useful for investigating various situations involving the pump intensity, decay time of energy levels and the spacing between the closely spaced levels. A few symbolic calculations involving the analytical expressions of the signal polarisation are provided to have the physical realisation. The data used for these calculations are partly theoretical in nature and are compatible with the real experiment. We neglect the Doppler effects and a semiclassical formalism of atom–field interaction is adopted throughout the investigation.

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Acknowledgements

One of the authors (MK) thanks the University Grants Commission (UGC), Government of India for financial support through the National Fellowship for Higher Education (F1-17.1/2016-17/NFST-2015-17-ST-WES-878/(SA-III/Website).

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Authors and Affiliations

  1. Department of Physics, Visva-Bharati, Santiniketan, 731 235, India

    Monojit Kora & Swapan Mandal

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  1. Monojit Kora
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  2. Swapan Mandal
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Correspondence to Swapan Mandal.

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Kora, M., Mandal, S. Analytical investigation on the Autler–Townes splittings and the two-photon effects in a Doppler free signal lineshape of a double-\(\varvec{\lambda }\) type four-level system. Pramana - J Phys 97, 4 (2023). https://doi.org/10.1007/s12043-022-02481-1

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  • DOI: https://doi.org/10.1007/s12043-022-02481-1

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