Comment on "Properties and dynamics of generalized squeezed states"

TL;DR

This paper clarifies that the oscillatory dynamics observed in high-order generalized squeezed states are numerical artifacts caused by basis truncation, not genuine physical effects, emphasizing the need for careful analysis in such quantum states.

Contribution

The authors demonstrate that reported oscillations in high-order generalized squeezed states are due to numerical artifacts and provide theoretical proof that these states cannot exhibit intrinsic oscillatory photon number dynamics.

Findings

Oscillations are caused by basis truncation artifacts.

The average photon number is a non-decreasing function.

High-order states contain infinite energy after finite squeezing.

Abstract

A recent article [S. Ashhab and M. Ayyash, New J. Phys. 27, 054104 (2025)] 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.