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The Mth Coherent State

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A Correction to this article was published on 21 June 2019

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Abstract

In this article, we propose a new kind of quantum states based on acting the number operator M times \( {\hat{n}}^M \) on the coherent state. We term this state the Mth coherent state, based on the value of the power M. We find that it is strongly similar to the coherent state as the analysis of the photonic statistical distributions and the overlap with the coherent state illustrate. Also, we find that it asymptotically reaches the minimum uncertainty and has a localized behavior in the Husimi function. However, in contrast to coherent state, the Mth coherent state has strong nonclassical features such as antibunching and squeezing for a relatively long range. Other parameters and measurements are discussed and studied. Finally, we highlight the similarity between the higher orders of the near coherent states and the Mth coherent states in order to potentially generate our proposed state.

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  • 21 June 2019

    The original article has been corrected. The left image of Figure 3 was previously not correct.

Notes

  1. If there are more than one coherent state and the confusion is possible, we can just call it the 2nd CS or M = 2 of the Mth CS, so Mth be the name.

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Acknowledgements

Taibah University is strongly acknowledged for their financial support to this work.

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  1. Department of Physics, Faculty of Science, Taibah University, Al Madinah Al Munawwarah, Saudi Arabia

    Anas Othman

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  1. Anas Othman
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Correspondence to Anas Othman.

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The ​original ​version ​of ​this ​article ​was ​revised: The left image of Figure 3 was previously not correct.

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Othman, A. The Mth Coherent State. Int J Theor Phys 58, 2451–2463 (2019). https://doi.org/10.1007/s10773-019-04136-1

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