Abstract
We describe a family of quantum states of the Schrödinger cat type as superpositions of the harmonic oscillator coherent states with coefficients defined by the quadratic Gauss sums. These states emerge as eigenfunctions of the lowering operators obtained after canonical transformations of the Heisenberg–Weyl algebra associated with the ordinary and fractional Fourier transformations. The first member of this family is given by the well known Yurke–Stoler coherent state.
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Acknowledgments
The author is indebted to P. K. Panigrahi for an inspiring invitation to lecture at the QIQT-2021 School (Kolkata, July 2021) and to A. S. Zhedanov for a useful discussion on the Gauss sums.
Funding
This study has been partially funded within the framework of the HSE University Basic Research Program.
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Translated from Teoreticheskaya i Matematicheskaya Fizika, 2022, Vol. 212, pp. 403–413 https://doi.org/10.4213/tmf10276.
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Spiridonov, V.P. Superpositions of coherent states determined by Gauss sums. Theor Math Phys 212, 1237–1245 (2022). https://doi.org/10.1134/S0040577922090069
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DOI: https://doi.org/10.1134/S0040577922090069