Reply to Comment on "Properties and dynamics of generalized squeezed states"

TL;DR

This paper defends the physical validity of generalized squeezing states, arguing that their oscillatory dynamics are genuine features rather than simulation artifacts, and clarifies the conditions under which these states are well-defined.

Contribution

The authors demonstrate that generalized squeezing operators can be physically meaningful with additional system information, countering claims that their dynamics must be monotonic.

Findings

Oscillatory dynamics are intrinsic to generalized squeezing states.

The physical validity depends on the inclusion of additional system details.

Oscillations persist in well-behaved models, challenging previous assertions.

Abstract

In our paper [1], our numerical simulations showed that, unlike displacement and conventional squeezing, higher-order squeezing exhibits oscillatory dynamics. Subsequently, Gordillo and Puebla pointed out that simulation results depend on whether the size of the state space in the simulations is even or odd [2]. Using additional derivations, they argued that the oscillatory dynamics is unphysical and that the photon number must increase monotonically as a function of the squeezing parameter $r$. We agree with the observation of an even-odd parity dependence in the simulations. We independently noticed the same feature in our simulations after the publication of Ref. [1]. This observation led us to perform a more detailed investigation of the numerical simulation and mathematical aspects of the generalized squeezing problem. Our new findings were reported in Ref. [3]. Further analysis was reported in Ref. [4]. Our conclusion is that the generalized squeezing operator is physically not well defined but can be made well defined when combined with additional information about the physical system under study. We demonstrated this point in the case where we include an additional nonlinear interaction term in the Hamiltonian. We disagree with the claim that the photon number must be a monotonically increasing function of $r$. This claim contradicts the mathematically rigorous results of Ref. [4]. Furthermore, we show that the oscillatory behaviour persists in two closely related, well-behaved models.