The unusual physics and math of generalized squeezing.
Sahel Ashhab - Advanced ICT Institute
Abstract:
We analyze the properties and dynamics of generalized squeezed vacuum states, i.e. states obtained by applying a higher-order squeezing operator to the vacuum state. We calculate the squeezing operator
numerically by taking the exponential of a truncated Hamiltonian matrix. The simulations suggest that, in stark contrast to displacement and two-photon squeezing, higher-order squeezing leads to oscillatory dynamics [1]. The state is squeezed in the initial stages of the dynamics but the squeezing reverses at later stages, and the state reverts almost completely back to the initial state. The maximum squeezing diminishes with increasing squeezing order, rendering the squeezing mechanism increasingly ineffective. Further investigation reveals that the simulation results depend strongly on whether the state space in the simulation contains an even or odd number of states [2]. This result indicates that the infinite-size limit is not well defined, and it raises questions regarding whether the simulation results are physically meaningful [3, 4]. We show that the squeezing Hamiltonian must be complemented with additional regulating terms to make the results truncation-size independent and physically meaningful. Furthermore, we generalize the squeezing Hamiltonian such that the squeezing order can be a fractional number [5]. This generalization allows us to investigate the gradual evolution of the squeezing dynamics between different (integer) squeezing orders, and it allows us to infer results for certain integer squeezing orders for which the computational simulation of the dynamics is especially challenging.
References
[1] S. Ashhab and M. Ayyash, Properties and dynamics of generalized squeezed states, New J. Phys. 27, 054104 (2025).
[2] S. Ashhab, F. Fischer, D. Lonigro, D. Braak, and D. Burgarth, Finite-dimensional approximations of generalized squeezing, Phys. Rev. A 113, 013703 (2026).
[3] R. Gordillo-Hachuel and R. Puebla, Comment on “Properties and dynamics of generalized squeezed states”, New J. Phys. 28, 028002 (2026).
[4] S. Ashhab and M. Ayyash, Reply to Comment on “Properties and dynamics of generalized squeezed states”, New J. Phys. 28, 028001 (2026).
[5] S. Ashhab, Fractional squeezing: spectra and dynamics from generalized squeezing Hamiltonian with fractional orders, J. Phys. A: Math. Theor. 59, 255301 (2026).
Location: QNC 1201