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Tomography in loop quantum cosmology

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Abstract

We analyze the tomographic representation for the Friedmann–Robertson–Walker (FRW) model within the Loop Quantum Cosmology framework. We focus on the Wigner quasi-probability distributions associated with Gaussian and Schrödinger cat states, and then, by applying a Radon integral transform for those Wigner functions, we are able to obtain the symplectic tomograms which define measurable probability distributions that fully characterize the quantum model of our interest. By appropriately introducing the quantum dispersion for a rotated and squeezed quadrature operator in terms of the position and momentum, we efficiently interpret the properties of such tomograms, being consequent with Heisenberg’s uncertainty principle. We also obtain, by means of the dual tomographic symbols, the expectation value for the volume operator, which coincides with the values reported in the literature. We expect that our findings result interesting as the introduced tomographic representation may be further benefited from the well-developed measure techniques in the areas of Quantum optics and Quantum information theory.

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Acknowledgements

The authors would like to acknowledge financial support from CONACYT-Mexico under the project CB-2017-283838.

Data sharing is not applicable to this article as no datasets were generated or analyzed during the current study.

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  1. Facultad de Ciencias, Universidad Autónoma de San Luis Potosí, Campus Pedregal, Av. Parque Chapultepec 1610, Col. Privadas del Pedregal, 78217, San Luis Potosí, SLP, Mexico

    Jasel Berra–Montiel & Alberto Molgado

  2. Dual CP Institute of High Energy Physics, Colima, Mexico

    Jasel Berra–Montiel & Alberto Molgado

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  1. Jasel Berra–Montiel
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Berra–Montiel, J., Molgado, A. Tomography in loop quantum cosmology. Eur. Phys. J. Plus 137, 283 (2022). https://doi.org/10.1140/epjp/s13360-022-02504-1

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