Engineering of Non-Hermitian Trajectories and Phase Structure in an Open Bose-Hubbard Model via Rate Operator Transformations

Abstract:Non-Hermitian evolution can be realized through post-selection on stochastic pure-state trajectories arising in continuously monitored open quantum systems. The rate operator formalism provides a versatile and systematic framework for unraveling a master equation into stochastic pure-state evolutions, offering enhanced control over the resulting non-Hermitian dynamics. In the present work, we explore the applicability of the rate operator formalism as a tool for engineering non-Hermitian dynamics. Specifically, we apply this approach to the Bose-Hubbard model subject to environmental dephasing, examining its consequences for controlled state manipulation. Our analysis is framed within the broader contexts of quantum state engineering and measurement-induced phase transitions. We demonstrate that the rate operator formalism enables the construction of effective non-Hermitian Hamiltonians exhibiting a unique steady state-even in regimes where the standard Monte Carlo wavefunction method fails to produce one. Furthermore, we show that this framework facilitates transitions between distinct steady-state phases, governed by tunable parameters such as the interaction strength and a non-Hermiticity control parameter introduced via the rate operator formalism.

arXiv:2609.02490 [quant-ph]

(or arXiv:2609.02490v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2609.02490 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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