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arXiv:1901.04952 · Optik

Time evolution of entanglement and trace distance in an atom-cavity system described with random walk and non-random walk states

M. Mohammadi, Safa Jami

Published Dec 20, 2018• 3 citations
arXivHTMLPDF
DOI
10.1016/j.ijleo.2018.12.096

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We study the time evolution of three quantifiers of nonclassical correlations, namely uncertainty-induced nonlocality (UIN), trace distance discord (TDD), and logarithmic negativity (LN), in a hybrid spin–cavity system with anisotropic XY interactions and two-photon spin-field coupling. We examine how the interaction parameters, including the anisotropy strength, initial photon number, spin–cavity coupling, spin–spin interaction, and spin–cavity detuning, influence the resulting two-qubit correlations. Our results show that both spin–cavity and spin–spin couplings can efficiently generate UIN, TDD, and entanglement, each exhibiting distinct oscillatory features, and we further evaluate the robustness of these features as the other interaction parameters increase. In the presence of cavity dissipation and spontaneous emission, entanglement is rapidly suppressed and may undergo entanglement sudden death, whereas UIN and TDD remain noticeably nonzero over longer times despite the damping of their oscillations. Overall, our findings provide a comparative characterization of entanglement and discord-like correlations in a dissipative spin–cavity platform and highlight the greater persistence of UIN- and TDD-type correlations within the present dissipative framework.
We investigate the time evolution of the chirality reduced density matrix for a discrete-time quantum walk on a one-dimensional lattice. The matrix is obtained by tracing out the spatial degree of freedom. We analyze the standard case, without decoherence, and the situation in which decoherence appears in the form of broken links in the lattice. By examining the trace distance for possible pairs of initial states as a function of time, we conclude that the evolution of the reduced density matrix is non-Markovian, in the sense defined by Breuer, Laine, and Piilo [Phys. Rev. Lett. 103, 210401 (2009)]. As the level of noise increases, the dynamics approaches a Markovian process. The highest non-Markovianity corresponds to the case without decoherence. The reduced density matrix tends always to a well-defined limit that we calculate, but only in the decoherence-free case is this limit nontrivial.