Dynamical regimes of a quantum SWAP gate beyond the Fermi golden rule

AXEL D. DENTE; RAÚL A. BUSTOS-MARÚN; HORACIO M. PASTAWSKI

PHYSICAL REVIEW A - ATOMIC, MOLECULAR AND OPTICAL PHYSICS

American Physical Society

Lugar: Ridge N.Y.; Año: 2008 vol. 78 p. 1 - 8

1050-2947

Dynamical regimes of a quantum SWAP gate beyond the Fermi golden rule Axel D. Dente,1 Raúl A. Bustos-Marún,1,2 and Horacio M. Pastawski1Axel D. Dente,1 Raúl A. Bustos-Marún,1,2 and Horacio M. Pastawski11 Raúl A. Bustos-Marún,1,2 and Horacio M. Pastawski1 1Facultad de Matemática, Astronomía y Física, and Instituto de Física (CONICET), Universidad Nacional de Córdoba, Ciudad Universitaria, 5000 Córdoba, Argentina 2Departamento de Fisicoquímica. Facultad de Ciencias Químicas, Universidad Nacional de Córdoba, Ciudad Universitaria, 5000 Córdoba, Argentina 2Departamento de Fisicoquímica. Facultad de Ciencias Químicas, Universidad Nacional de Córdoba, Ciudad Universitaria, 5000 Córdoba, Argentina Received 6 October 2008 We discuss how the bath’s memory affects the dynamics of a SWAP gate. We present an exactly solvable model that shows various dynamical transitions when treated beyond the Fermi golden rule. By moving continuously a single parameter, the unperturbed Rabi frequency, we sweep through different analytic properties of the density of states: -I collapsed resonances that split at an exceptional point in II two resolved resonances;  III out-of-band resonances; IV virtual states; and V pure point spectrum. We associate them with distinctive dynamical regimes: overdamped, damped oscillations, environment controlled quantum diffusion, anomalous diffusion, and localized dynamics, respectively. The frequency of the SWAP gate depends differently on the unperturbed Rabi frequency. In region I there is no oscillation at all, while in the regions III and IV the oscillation frequency is particularly stable because it is determined by the environment’s band width. The anomalous diffusion could be used as a signature for the presence of the elusive virtual states. We discuss how the bath’s memory affects the dynamics of a SWAP gate. We present an exactly solvable model that shows various dynamical transitions when treated beyond the Fermi golden rule. By moving continuously a single parameter, the unperturbed Rabi frequency, we sweep through different analytic properties of the density of states: -I collapsed resonances that split at an exceptional point in II two resolved resonances;  III out-of-band resonances; IV virtual states; and V pure point spectrum. We associate them with distinctive dynamical regimes: overdamped, damped oscillations, environment controlled quantum diffusion, anomalous diffusion, and localized dynamics, respectively. The frequency of the SWAP gate depends differently on the unperturbed Rabi frequency. In region I there is no oscillation at all, while in the regions III and IV the oscillation frequency is particularly stable because it is determined by the environment’s band width. The anomalous diffusion could be used as a signature for the presence of the elusive virtual states. We discuss how the bath’s memory affects the dynamics of a SWAP gate. We present an exactly solvable model that shows various dynamical transitions when treated beyond the Fermi golden rule. By moving continuously a single parameter, the unperturbed Rabi frequency, we sweep through different analytic properties of the density of states: -I collapsed resonances that split at an exceptional point in II two resolved resonances;  III out-of-band resonances; IV virtual states; and V pure point spectrum. We associate them with distinctive dynamical regimes: overdamped, damped oscillations, environment controlled quantum diffusion, anomalous diffusion, and localized dynamics, respectively. The frequency of the SWAP gate depends differently on the unperturbed Rabi frequency. In region I there is no oscillation at all, while in the regions III and IV the oscillation frequency is particularly stable because it is determined by the environment’s band width. The anomalous diffusion could be used as a signature for the presence of the elusive virtual states. We discuss how the bath’s memory affects the dynamics of a SWAP gate. We present an exactly solvable model that shows various dynamical transitions when treated beyond the Fermi golden rule. By moving continuously a single parameter, the unperturbed Rabi frequency, we sweep through different analytic properties of the density of states: -I collapsed resonances that split at an exceptional point in II two resolved resonances;  III out-of-band resonances; IV virtual states; and V pure point spectrum. We associate them with distinctive dynamical regimes: overdamped, damped oscillations, environment controlled quantum diffusion, anomalous diffusion, and localized dynamics, respectively. The frequency of the SWAP gate depends differently on the unperturbed Rabi frequency. In region I there is no oscillation at all, while in the regions III and IV the oscillation frequency is particularly stable because it is determined by the environment’s band width. The anomalous diffusion could be used as a signature for the presence of the elusive virtual states.