Finite-dimensional approximations of generalized squeezing

Ashhab S, Fischer F, Lonigro D, Braak D, Burgarth D (2026)

Publication Language: English

Publication Type: Journal article

Publication year: 2026

Journal

Physical Review A American Physical Society

Book Volume: 113

Article Number: 013703

Issue: 1

DOI: 10.1103/9vwp-f35c

Abstract

We show unexpected behavior in simulations of generalized squeezing performed with finite-dimensional truncations of the Fock space: even for extremely large dimensions of the state space, the results depend on whether the truncation dimension is even or odd. This situation raises the question of whether the simulation results are physically meaningful. We demonstrate that, in fact, the two truncation schemes correspond to two well-defined, distinct unitary evolutions whose generators are defined on different subsets of the infinite-dimensional Fock space. This is a consequence of the fact that the generalized squeezing Hamiltonian is not self-adjoint on states with finite excitations, but possesses multiple self-adjoint extensions. Furthermore, we present results on the spectrum of the squeezing Hamiltonians corresponding to even and odd truncation sizes that elucidate the properties of the two different self-adjoint extensions corresponding to the even and odd truncation schemes. To make the squeezing operator applicable to a physical system, we must regularize it using other terms that depend on the specifics of the experimental implementation. We show that the addition of a Kerr interaction term in the Hamiltonian leads to uniquely converging simulations, with no dependence on the parity of the truncation size, and demonstrate that the Kerr term indeed renders the Hamiltonian self-adjoint and thus physically interpretable.

Authors with CRIS profile

Felix Fischer Professur für Theoretische Physik Davide Lonigro Professur für Theoretische Physik Daniel Burgarth Professur für Theoretische Physik

Involved external institutions

Japan National Institute of Information and Communications Technology (NICT) / 情報通信研究機構 JP Japan (JP) Universität Augsburg DE Germany (DE)

How to cite

APA:

Ashhab, S., Fischer, F., Lonigro, D., Braak, D., & Burgarth, D. (2026). Finite-dimensional approximations of generalized squeezing. Physical Review A, 113. https://doi.org/10.1103/9vwp-f35c

MLA:

Ashhab, Sahel, et al. "Finite-dimensional approximations of generalized squeezing." Physical Review A 113 (2026).

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