Reply to Comment on ‘Properties and dynamics of generalized squeezed states’

Abstract In our paper (Ashhab and Ayyash 2025 New J. Phys. 27 054104), 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 (Gordillo and Puebla 2026 arXiv:2507.12250). 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 Ashhab and Ayyash (2025 New J. Phys. 27 054104). 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 Ashhab et al (2026 Phys. Rev. A 113 013703). Further analysis was reported in Fischer et al (2025 arXiv:2508.09044). 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 Fischer et al (2025 arXiv:2508.09044). Furthermore, we show that the oscillatory behaviour persists in two closely related, well-behaved models.