Abstract
We investigate the time evolution and asymptotic behavior of a system of two two-level atoms (qubits) interacting off-resonance with a single mode radiation field. The two atoms are coupled to each other through dipole–dipole as well as Ising interactions. An exact analytic solution for the system dynamics that spans the entire phase space is provided. We focus on initial states that cause the system to evolve to entanglement sudden death (ESD) between the two atoms. We find that combining the Ising and dipole–dipole interactions is very powerful in controlling the entanglement dynamics and ESD compared with either one of them separately. Their effects on eliminating ESD may add up constructively or destructively depending on the type of Ising interaction (Ferromagnetic or anti-Ferromagnetic), the detuning parameter value, and the initial state of the system. The asymptotic behavior of the ESD is found to depend substantially on the initial state of the system, where ESD can be entirely eliminated by tuning the system parameters except in the case of an initial correlated Bell state. Interestingly, the entanglement, atomic population and quantum correlation between the two atoms and the field synchronize and reach asymptotically quasi-steady dynamic states. Each one of them ends up as a continuous irregular oscillation, where the collapse periods vanish, with a limited amplitude and an approximately constant mean value that depend on the initial state and the system parameters choice. This indicates an asymptotic continuous exchange of energy (and strong quantum correlation) between the atoms and the field takes place, accompanied by diminished ESD for these chosen setups of the system. This system can be realized in spin states of quantum dots or Rydberg atoms in optical cavities, and superconducting or hybrid qubits in linear resonators.
Highlights
Studying the quantum phenomena in systems of atoms coupled to radiation fields has been in the center of interest in physics since the Jaynes–Cummings model was introduced in 1963 [1]
Embedding superconducting qubits in a superconducting microwave resonator was a huge step toward utilizing these systems in quantum information processing (QIP) [7,8,9] and establishing the new field of circuit quantum electrodynamics, where close and distant superconducting qubits can be coupled through local interactions or microwave photons [10,11,12,13,14]
We presented an exact analytic solution for the time evolution of the system that spans its entire parameter phase space starting from any initial state
Summary
Studying the quantum phenomena in systems of atoms coupled to radiation fields has been in the center of interest in physics since the Jaynes–Cummings model was introduced in 1963 [1]. We provide an exact analytic study of the system dynamics while considering simultaneously the effect of the two types of interactions, dipole–dipole and Ising, which can be modeled as a Heisenberg spin 1/2 XXZ interaction This system is important for its own sake as a model of two coupled spins interacting with a bosonic bath, as well as for its impact on the field of cavity (circuit) QED and its implementations in QIP. It can be realized in electron spin states in quantum dots or Rydberg atoms in optical cavities as well as in superconducting or hybrid qubits in linear resonators.
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