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arXiv:2012.04083

Quadratic Models for Engineered Control of Open Quantum Systems

J. P. P. Vieira, Achilleas Lazarides, Tapio Ala-Nissilä

Published Dec 7, 2020• 0 citations
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Abstract

We introduce a framework to model the evolution of a class of open quantum systems whose environments periodically undergo an instantaneous non-unitary evolution stage. For the special case of quadratic models, we show how this approach can generalise the formalism of repeated interactions to allow for the preservation of system-environment correlations. Furthermore, its continuous zero-period limit provides a natural description of the evolution of small systems coupled to large environments in negligibly perturbed steady states. We explore the advantages and limitations of this approach in illustrative applications to thermalisation in a simple hopping ring and to the problem of initialising a qubit chain via environmental engineering.

DOI
10.48550/arxiv.2012.04083

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We introduce a framework to model the evolution of a class of open quantum systems whose environments periodically undergo an instantaneous non-unitary evolution stage. For the special case of quadratic models, we show how this approach can generalise the formalism of repeated interactions to allow for the preservation of system-environment correlations. Furthermore, its continuous zero-period limit provides a natural description of the evolution of small systems coupled to large environments in negligibly perturbed steady states. We explore the advantages and limitations of this approach in illustrative applications to thermalisation in a simple hopping ring and to the problem of initialising a qubit chain via environmental engineering.
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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.
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