Constructing squeezed states of light with associated Hermite polynomials
Centre de Recherches Mathématiques, Université de Montréal, H3C 3J7, Montréal, QC, Canada
2 Département de Mathématiques et de Statistique, Université de Montréal, H3C 3J7, Montréal, QC, Canada
3 Physics Department, Cinvestav, AP 14-740, 07000, México City, México
Accepted: 5 May 2021
Published online: 14 May 2021
A new class of states of light is introduced that is complementary to the well-known squeezed states. The construction is based on the general solution of the three-term recurrence relation that arises from the saturation of the Schrödinger inequality for the quadratures of a single-mode quantized electromagnetic field. The new squeezed states are found to be linear superpositions of the photon-number states whose coefficients are determined by the associated Hermite polynomials. These results do not seem to have been noticed before in the literature. As an example, the new class of squeezed states includes superpositions characterized by odd-photon number states only, so they represent the counterpart of the prototypical squeezed-vacuum state which consists entirely of even-photon number states.
© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2021