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International Journal of Modern Physics B

THE DYNAMICS OF GEOMETRIC DISCORD AND ITS TRANSFER IN ATOM-CAVITY-RESERVOIR SYSTEM

Tao Wu, Xue‐Ke Song, Liu Ye

Published Aug 20, 2013• 4 citations
Publisher

Abstract

The dynamics of geometric discord (GD) and its transfer in a dissipative system consisting of two independent atom-cavity-reservoir subsystems under the strong coupling and the weak coupling regimes is studied. It is shown that the GD of the atoms and the cavities oscillatorily decays to zero while the reservoirs begin to present nonzero geometric quantum discord already immediately after t = 0 in the strong coupling regime. However, in the weak coupling regime, the GD between the atoms progressively decays becoming zero and the discord between the reservoirs arises from zero to a steady value, while the cavities remain almost uncorrelated during the evolution. We also show that the amount of GD contained in atoms and reservoirs depends on the purity p and it is proportional to p, the smaller the value of p the smaller the amount of GD. It is worth noting that, in both strong coupling and the weak coupling regimes, the results show that GD initially stored in the atoms will eventually be completely transferred to the reservoirs, independent of the parameters, but the transfer is mediated via the cavities in the strong coupling regime, while it is almost directly in the weak coupling regime.

DOI
10.1142/s0217979213501361

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The dynamics of geometric discord (GD) and its transfer in a dissipative system consisting of two independent atom-cavity-reservoir subsystems under the strong coupling and the weak coupling regimes is studied. It is shown that the GD of the atoms and the cavities oscillatorily decays to zero while the reservoirs begin to present nonzero geometric quantum discord already immediately after t = 0 in the strong coupling regime. However, in the weak coupling regime, the GD between the atoms progressively decays becoming zero and the discord between the reservoirs arises from zero to a steady value, while the cavities remain almost uncorrelated during the evolution. We also show that the amount of GD contained in atoms and reservoirs depends on the purity p and it is proportional to p, the smaller the value of p the smaller the amount of GD. It is worth noting that, in both strong coupling and the weak coupling regimes, the results show that GD initially stored in the atoms will eventually be completely transferred to the reservoirs, independent of the parameters, but the transfer is mediated via the cavities in the strong coupling regime, while it is almost directly in the weak coupling regime.
In this work, the dynamics of quantum correlation (QC) in terms of geometric discord and its transfer coupled with dissipative reservoirs are investigated. Taken two canonical cases where the qubits of interest are initially prepared in extended Werner-like state and W-like states into account, we specifically reveal the dynamical behaviors of the geometric discord as each qubit locally interacts with its surrounding infinite degree-of-freedom reservoir. In the scenarios, the short-term and long-term dynamics of the geometric discord for the qubit- and reservoir-subsystem as well as its transfers between them are observed detailedly. It turns out that the geometric discord of qubit-subsystem decays asymptotically to zero while the counterpart of reservoir-subsystem can revive from time t = 0 to steady value, which sheds light on a transfer of the discord from the qubit-subsystem to the corresponding reservoir-subsystem.
Abstract Using quantum discord (QD) and geometric quantum discord (GQD), quantum correlation dynamics is investigated for two coupled qubits within a multiqubit interacting system in the zero-temperature bosonic reservoir, under both weak and strong qubit-reservoir coupling regimes. The multiqubit system is connected with either a common bosonic reservoir (CBR) or multiple independent bosonic reservoirs (IBRs). In the CBR case, our findings indicate that both QD and GQD can be strengthened by increasing the number of qubits in the multiqubit system. Furthermore, we study the steady state QD and GQD in the strong coupling regime, and find that the stable value in the long-time limit is determined exclusively by the number of qubits. The evolution period of QD and GQD gets longer as the dipole–dipole interaction (DDI) strength increases, which helps prolong the correlation time and thus preserves the quantum correlation under the weak coupling regime. Further analysis reveals notable differences between the CBR and IBRs scenarios. In the IBRs case, the decay of QD and GQD becomes slower compared to the CBR case, with both measures tending to zero at a reduced rate. Moreover, GQD consistently exhibits lower values than QD in both scenarios. These findings provide valuable insights into the selection of appropriate correlation measurement techniques for quantifying quantum correlations.
We investigate the dynamics of geometric quantum correlations for certain decoherence channels and discuss the necessary conditions for the existence of frozen geometric discord. As illustrative examples, we study the phenomenon of double sudden transitions in geometric discord for a system consisting of two noninteracting atoms inserted in two independent dissipative cavities and how the initial state parameters and decay rate of dissipative cavities affect the frozen time during which the geometric discord remains constant. We also explore the dynamics of geometric discord between two noninteracting atoms trapped in a common dissipative cavity and find that the geometric discord exhibits sudden transition between classical and quantum decoherence. Moreover, a nonzero stationary geometric discord can arise in both the independent cavity case and common cavity case.
The dynamics of entanglement and quantum discord between two identical qubits strongly interacting with a common single mode leaky cavity field have been investigated beyond the rotating wave approximation (RWA) by using a recently derived Lindblad type quantum optical master equation [F. Beaudoin, J. M. Gambetta, and A. Blais, Phys. Rev. A 84, 043832 (2011)] that can describe the losses of the cavity field in a strong atom-field coupling regime. Contrary to previous investigations of the same model in the dissipative regime by using the standard Lindblad quantum optical master equation in a strong-coupling regime, the atom-field steady states are found to be cavity decay rate independent and have a very simple structure determined solely by the overlap of initial atomic state with the subradiant state which is valid for all coupling regimes. Non-RWA dynamics are found to have remarkable effects on the steady state quantum discord and entanglement that cannot be achieved under RWA conditions, for instance, they can induce steady state entanglement even for the initial states that have no overlap with the subradiant state. Moreover, the non-RWA dynamics are found to reverse the initial state dependence of steady state entanglement and quantum discord contrary to the RWA case.
Abstract The dynamics of entanglement and quantum discord (QD) between two two-level atoms interacting with two dissipative coupled cavities in the presence of initial atom-cavity correlations is investigated. In comparison with the result of the initial factorized state, we show that the initial state contained quantum correlation of atom-cavity is most robust against the dissipative environment, and the initial atom-cavity correlations, especially the quantum correlation, play a constructive role in the generation of atomic entanglement and QD. Simultaneously, the comparison between Markovian and non-Markovian dynamics, and the influences of inter-cavity hopping rate are also taken into account and analyzed.
In this work, we study the dynamics of quantum correlation (QC) in terms of quantum discord and its transfer for multiqubit systems in dissipative environments. At first, we investigate the dynamics of bipartite QC contained in a three-qubit system that are initially prepared in an extended W-like state with each qubit coupled to an independent reservoir. Subsequently, we study a realistic quantum network of several remote nodes each of which contains two qubits in contact with a common reservoir. For the simplest case of two nodes, we study the dynamics of QC and its transfer from the initially correlated system to the reservoirs and other degrees of freedom. In both models, we pay particular attention to the independent evolution and transfer of QC without the participation of entanglement when the systems of interest are initially prepared in unentangled states. We also observe the occurrence of sudden changes of quantum discord when the systems are initially in mixed states.