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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 $\{\hat{x},\hat{p}\}$ to the dynamical evolution matrix yields quadrature nonreciprocal transmission between the $\hat{x}$ and $\hat{p}$ 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. In QBS, squeezing interactions without dissipation cause the dynamical evolution of the system to display effective non-Hermitian characteristics and induce quantum correlation effects, such as quantum entanglement. Recent studies have shown that the non-Hermitian exceptional points in QBS can alter squeezing dynamics and entanglement dynamics. Therefore, such systems not only offer a natural platform for realizing quantum non-Hermitian dynamics but also constitute an important basis for investigating the relationship between non-Hermitian dynamics and quantum effects, as well as for achieving quantum control based on non-Hermitian properties. Future research may further focus on elucidating the connections between non-Hermitian dynamics and quantum effects in QBS, which is expected to serve as a bridge linking non-Hermitian dynamics and quantum effects.
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Keywords:
- non-Hermitian dynamics /
- quadratic bosonic systems /
- nonreciprocity /
- nonHermitian skin effect /
- quantum correlations
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