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arXiv:1511.04929 · Systems & Control Letters

Linear quantum systems with diagonal passive Hamiltonian and a single dissipative channel

Shan Ma, Ian R. Petersen, Matthew J. Woolley

Published Dec 22, 2016• 12 citations
arXivHTMLPDF
DOI
10.1016/j.sysconle.2016.11.013

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We study an imaginary Stark ladder model, and we propose a realization of the model in a dissipative chain with linearly increasing site-dependent dissipation strength. Due to the existence of KKK symmetry and passive PT\mathcal{PT}PT symmetry, the model exhibits quite a different feature from its Hermitian counterpart. With the increase of dissipation strength, the system first undergoes a passive PT\mathcal{PT}PT-symmetry breaking transition, with the shifted eigenvalues changing from real to complex, and then a KKK-symmetry restoring transition, characterized by the emergence of a pure imaginary spectrum with equal spacing. Accordingly, the eigenstates change from PT\mathcal{PT}PT-unbroken extended states to PT\mathcal{PT}PT-broken states, and finally to Stark-localized states. In the framework of the quantum open system governed by the Lindblad equation with linearly increasing site-dependent dissipation, we unveil that the dynamical evolution of a single-particle correlation function is governed by the Hamiltonian of the imaginary Stark ladder model. By studying the dynamical evolution of the density distribution under various initial states, we demonstrate that the damping dynamics displays distinct behaviors in different regions. A localized damping is observed in the strong dissipation limit.
The paper considers the problem of equalization of passive linear quantum systems. While our previous work was concerned with the analysis and synthesis of passive equalizers, in this paper we analyze coherent quantum equalizers whose annihilation (respectively, creation) operator dynamics in the Heisenberg picture are driven by both quadratures of the channel output field. We show that the characteristics of the input field must be taken into consideration when choosing the type of the equalizing filter. In particular, we show that for thermal fields allowing the filter to process both quadratures of the channel output may not improve mean square accuracy of the input field estimate, in comparison with passive filters. This situation changes when the input field is `squeezed'.