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Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields

Non-Gaussian multiphoton squeezed states

Giacomo Mauro D’Ariano, Mario Rasetti

Published Feb 15, 1987• 27 citations
Publisher

Abstract

The centered distribution functions and their moments are constructed for the generalized multiphoton squeezed states recently defined by the authors. It is shown that such states are non-Gaussian, and exhibit higher-order squeezing, depending on the choice of either the squeezing parameter or the generalized boson number.
DOI
10.1103/physrevd.35.1239

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Abstract A recent article (Ashhab and Ayyash 2025 New J. Phys. 27 , 054104) has reported unexpected oscillatory dynamics in generalized squeezed states of order higher than two as their squeezing parameter increases. This behaviour, observed through numerical simulations using truncated bosonic annihilation and creation operators, appeared in several properties of these states, including their average photon number. The authors argued that these oscillations reflect a genuine physical effect. Here, however, we demonstrate that the observed oscillatory behaviour is a consequence of numerical artefacts. A numerical analysis reveals that the oscillations are highly sensitive to the truncation of the Fock basis, indicating a lack of convergence. This is further supported by a theoretical analysis of the Taylor series of the average photon number, suggesting that these generalized squeezed states contain infinite energy after a finite value of the squeezing parameter. Finally, we provide an analytical proof that the average photon number of any generalized squeezed state is a non-decreasing function, thereby ruling out the possibility of intrinsic oscillatory dynamics. We hope these results help clarify the origin of the reported oscillations and highlight the special care required when dealing with high-order squeezing states.
We introduce nonlinear canonical transformations that yield effective, solvable Hamiltonians of multiphoton down-conversion processes, and we define the associated non-Gaussian multiphoton squeezed states as the coherent states of the multiphoton Hamiltonians. We study in detail the four-photon processes and the associated non-Gaussian four-photon squeezed states. The realization of squeezing, the behaviour of the field statistics, and the structure of the phase space distributions show that these states realize a natural four-photon generalization of the two-photon squeezed states.