Squeezing of light from Planck-scale physics

Abstract

In this article, the possibility of generating non-classical light due to Planck-scale effects is considered. For this purpose, a widely studied model of deformation of the Heisenberg uncertainty relation is applied to single-mode and multi-mode lights. The model leads to a deformed dispersion relation, which manifests in an advancement in the time of arrival of photons. The key finding is that the model also leads to an oscillatory pattern of squeezing of the state of light. Furthermore, while the amplitude of the oscillations is constant for energy eigenstates, it exhibits linear growth over time for coherent states with the annihilation operator eigenvalue $\alpha \ne 0$. This second case leads to the accumulation of squeezing and phase-space displacement, which can be significant for astrophysical photons. In particular, for $\alpha \sim 1$, coherent light in the optical spectrum emitted at megaparsec distances would acquire squeezing with the amplitude of the order unity. This suggests that measurements of the non-classical properties of light originating from distant astrophysical sources may open a window to test these predictions.

arXiv comment11 pages main text, 1 page appendix, 1 figure. Matches published version. Discussion about the dimension of $\beta$ below Eq. (1) extended. Bibliography reordered

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