Advances in non-Hermitian dynamics of quadratic bosonic systems

TL;DR

This work analyzes how intrinsically Hermitian quadratic bosonic systems (QBS) can exhibit non-Hermitian dynamics through their dynamical matrices, enabling phenomena such as quadrature nonreciprocity, exceptional points (EPs), non-Hermitian topology, and the non-Hermitian skin effect. By mapping QBS to Bogoliubov–de Gennes frameworks and employing models like the Bosonic Kitaev chain and bosonic SSH variants, it demonstrates how real-space and momentum-space evolution matrices become non-Hermitian, yielding EPs at $|J|=|\kappa|$ with $\lambda_\pm=\pm\sqrt{J^2-\kappa^2}$ and rich phase structures. The review highlights quadrature nonreciprocity tunable by quadrature phase, NHSE and bilocal edge localization, and point-gap topology, all while connecting these dynamics to quantum effects such as squeezing and entanglement—even in the absence of dissipation. Together, these results establish QBS as a versatile platform for non-Hermitian physics, enabling quantum control, amplification, and topological engineering with potential applications in quantum sensing and information processing.

Abstract

Non-Hermitian physics has emerged as a rapidly advancing field of research, revealing a range of novel phenomena and potential applications. Traditional non-Hermitian Hamiltonians are typically simulated by constructing asymmetric couplings or by introducing dissipation and gain to realize non-Hermitian systems. The quadratic bosonic system (QBS) with squeezing interaction is intrinsically Hermitian; however, its dynamical evolution matrix in both real and momentum spaces is non-Hermitian. Based on this, applying a field-operator transformation xp to the dynamical evolution matrix yields quadrature nonreciprocal transmission between the x and p operators. This nonreciprocal characteristic can be utilized in signal amplifiers. On the other hand, within the Bogoliubov-de Gennes framework in momentum space, one can observe non-Hermitian topological phenomena such as point-gap topology and the non-Hermitian skin effect, both induced by spectra with nonzero winding numbers. Additionally, QBS can be employed to realize non-Hermitian Aharonov-Bohm cages and to extend non-Bloch band theory. Previous studies in non-Hermitian physics have largely concentrated on classical systems. The influence of non-Hermitian properties on quantum effects remains a key issue awaiting exploration and has evolved into a research direction at the interface of non-Hermitian and quantum physics.

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