Dynamics of quantum and classical correlations in the three-qubit multiphoton Tavis-Cummings model with a vacuum resonator field
Eugene K. Bashkirov, Alexander R. Bagrov; Samara National Research University, Samara, Russia;
Abstract
The paper presents an exact analytical solution of the nonstationary Schr\"odinger equation for a three-qubit multiphoton Tavis-Cummings model with a vacuum resonator field. The solution is obtained for a general pure state of qubits and for any photon transition multiplicity. The explicit expressions for the temporal wave function of the full system and all reduced density matrices of the qubits are obtained. Based on these results, analytical formulas for two measures of quantum correlations -- pairwise negativity and symmetric quantum discord -- are derived. The dynamics of correlations is numerically studied for two initial separable states of the qubits: one with three excited qubits and the other with two excited qubits and one in the ground state. It is shown that increasing the photon transition multiplicity leads to the suppression of classical correlations for the first state, while symmetric quantum discord persists and negativity becomes nonzero, which indicates the emergence of entanglement with sudden death effects. For the second state, the dynamics of correlations of atomic pairs acquires a regular periodic structure with characteristic periods for zero values and maxima; at the moments of correlation vanishing, the system returns to the initial separable state, while at the maxima it transforms into a state similar to the Werner state. Effects of sudden revival and sudden death of entanglement are revealed with characteristic time intervals, with the region of entanglement presence exceeding the interval of its absence. It is established that in the regions of sudden death of entanglement, symmetric quantum discord retains nonzero values, which is due to a significant degree of mixedness of the states of the qubit subsystems. Thus, symmetric quantum discord allows one to reveal a broader spectrum of quantum correlations than pairwise negativity, confirming the non-equivalence of the two measures.
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Eugene K. Bashkirov
Samara National Research University
Russia
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