Comment on "Properties and dynamics of generalized squeezed states"

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.

Figures (2)

• Figure 1: Behaviour of the average photon number $\langle \hat{a}^{\dagger} \hat{a} \rangle_n$ as a function of the squeezing parameter $r$. Panels (a) and (b) corresponds to the tri-squeezed, $\left|{r_3}\right\rangle = \hat{U}_3(r) \left|{0}\right\rangle$, and quadri-squeezed, $\left|{r_4}\right\rangle = \hat{U}_4(r) \left|{0}\right\rangle$, respectively. Different curves have been obtained under different truncation $N$ of the Fock basis, as indicated in the labels. Note the significant change of $\langle \hat{a}^{\dagger} \hat{a}\rangle_n$ for similar $N$ that suggests lack of convergence.
• Figure 2: (a) First $M=20$ and $M=10$ coefficients $c_m^{(3)}$ (orange dots) and $c_m^{(4)}$ (green dots) for $n = 3$ and $n = 4$, respectively, as a function of $m$. Note that, by symmetry, the odd coefficients are zero $c_{2m+1}^{(n)}=0$. An exponential fit for the last five points for each case have been plotted as straight lines. (b) Average photon number for the tri-squeezed state as a function of the squeezing parameter for different approximations. Orange and green lines correspond to a numerical computation using $N=60000$ and $N=60001$ Fock basis, respectively. The dashed black line represents the Taylor series considering the first $M=20$ terms. The dashed red line denotes the estimated radius of convergence $R_3$ for the Taylor series.

Theorems & Definitions (2)

• Theorem 1
• proof