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International Journal of Theoretical Physics

, Volume 58, Issue 1, pp 294–307 | Cite as

Accurate Number Densities of Ideal Photons in a One-Dimensional Barrel Cavity

  • Ze Cheng
  • Jiang Hong Man
Article

Abstract

Our experimental scheme is based on a barrel optical microcavity filled with a dye solution. It is found that the number of non-condensed photons is characterized by an analytical function, which involves a q-digamma function in mathematics. We employ the q-digamma function to calculate the spatial and momentum distributions of ideal photons in a one-dimensional barrel cavity. The first main finding in this paper is that the spatial and momentum distributions possess a similar profile. The second main finding is that when photons are in the normal state, the density profile exhibits Friedel oscillations. The third main finding is that when photons are in the BEC state, the density profile exhibits a sharp peak with extremely narrow width. The fourth main finding is that the central peak of the density distribution is a monotonically increasing function of the photon number N but is a monotonically decreasing function of the temperature T.

Keywords

Bose-Einstein condensation One-dimensional photons Optical microcavity Number densities of photons 

Notes

Acknowledgments

This work was supported by the National Natural Science Foundation of China under Grants No. 10174024 and No. 10474025.

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of PhysicsHuazhong University of Science and TechnologyWuhanPeople’s Republic of China

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