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arXiv:1811.00335 · Quantum Information Processing

Analytical solution and entanglement swapping of a double Jaynes–Cummings model in non-Markovian environments

Hong‐Mei Zou, Mao-Fa Fang

Published May 3, 2015• 30 citations
arXivHTMLPDF
DOI
10.1007/s11128-015-1006-0

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We investigate the influence of phonon degrees of freedom on the qubit dynamics in Jaynes-Cummings (JC) model. A strong qubit-phonon coupling is considered giving rise to Jaynes-Cummings-Holstein (JCH) model. Under anti-adiabatic conditions, we perform a unitary transformation to make the underlying problem tractable through Redfield-type non-Markovian master equation. Analytical expression for the time-dependent coherence is obtained, incorporating both cavity-induced dissipation and phonon-induced dressing effects. The dynamics of JC model is highly non-Markovian for a narrow spectral width and finite detuning. However, a non-zero phonon coupling suppresses these non-Markovian features by effectively reducing the qubit-cavity interaction strength. {It is observed that polaronic dressing effectively supresses the detuning effects. Furthermore, the coherence-based non-Markovianity measure shows an order-of-magnitude suppression in the JCH model, indicating a new dynamical regime, while memory effects extend over a wider range of spectral densities than in the JC model.
We investigate the dynamics of nonclassical correlations including concurrence and local quantum uncertainty in the damped Jaynes–Cummings model with an initial system–reservoir correlation. The dynamics of qubit–reservoir correlation and the influence of non-Markovian effect are studied. Furthermore, we consider the double damped Jaynes–Cummings model consisting of two noninteracting qubits locally coupled to independent reservoirs and explore the properties of both qubit–qubit and reservoir–reservoir correlations. The influences of initial correlation and non-Markovian effect on the dynamics of nonclassical correlations are analyzed. It is found that the dynamics for both qubit–qubit and reservoir–reservoir correlations can be significantly changed by the initial correlation and the non-Markovian effect. Finally, we explore the sudden changes of local quantum uncertainty and find that they are closely related to the initial system–environment entanglement.