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arXiv · 2206.14149

Entanglement between uncoupled modes with time-dependent complex frequencies

D. Cius·G. M. Uhdre·A. S. M. de Castro·F. M. Andrade
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Abstract

In this work we present the general unified description for the unitary time-evolution generated by time-dependent non-Hermitian Hamiltonians embedding the bosonic representations of $\mathfrak{su}(1,1)$ and $\mathfrak{su}(2)$ Lie algebras. We take into account a time-dependent Hermitian Dyson maps written in terms of the elements of those algebras with the relation between non-Hermitian and its Hermitian counterpart being independent of the algebra realization. As a direct consequence, we verify that a time-evolved state of uncoupled modes modulated by a time-dependent complex frequency may exhibits a non-zero entanglement even when the cross-operators, typical of the interaction between modes, are absent. This is due the non-local nature of the non-trivial dynamical Hilbert space metric encoded in the time-dependent parameters of the general Hermitian Dyson map, which depend on the imaginary part of the complex frequency.

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D. Cius, G. M. Uhdre, A. S. M. de Castro, F. M. Andrade. 2022-06-28. Entanglement between uncoupled modes with time-dependent complex frequencies. https://doi.org/10.1103/physreva.107.022403

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