Month: May 2006

Environmentally induced quantum dynamical phase transition in the spin swapping operation | Journal of Chemical Physics

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Environmentally induced quantum dynamical phase transition in the spin swapping operation

Gonzalo A. Álvarez, Ernesto P. Danieli, Patricia R. Levstein, and Horacio M. Pastawski

Facultad de Matemática, Astronomía y Física, Universidad Nacional de Córdoba, Ciudad Universitaria, 5000, Córdoba, Argentina

via Environmentally induced quantum dynamical phase transition in the spin swapping operation | Browse – Journal of Chemical Physics.

Quantum information processing relies on coherent quantum dynamics for a precise control of its basic operations. A swapping gate in a two-spin system exchanges the degenerate states ∣↑, ↓⟩ and ∣↓, ↑⟩. In NMR, this is achieved turning on and off the spin-spin interaction b = ΔE that splits the energy levels and induces an oscillation with a natural frequency ΔE/. Interaction of strength /τSE, with an environment of neighboring spins, degrades this oscillation within a decoherence time scale τϕ. While the experimental frequency ω and decoherence time τϕ were expected to be roughly proportional to b/ and τSE, respectively, we present here experiments that show drastic deviations in both ω and τϕ. By solving the many spin dynamics, we prove that the swapping regime is restricted to ΔEτSE. Beyond a critical interaction with the environment the swapping freezes and the decoherence rate drops as 1/τϕ∝(b/)2τSE. The transition between quantum dynamical phases occurs when ωmath becomes imaginary, resembling an overdamped classical oscillator. Here, 0 ⩽ k2 ⩽ 1 depends only on the anisotropy of the system-environment interaction, being 0 for isotropic and 1 for XY interactions. This critical onset of a phase dominated by the quantum Zeno effect opens up new opportunities for controlling quantum dynamics.

© 2006 American Institute of Physics

Decoherence rate and oscillation frequency in the spin swapping of a 13C-1H system. Data points are obtained from cross polarization experiments. The zero plateau in the frequency and the parabolic behavior of the decoherence rate are indicative of an over-damped Zeno phase. Solid lines are the prediction of our model.
Decoherence rate and oscillation frequency in the spin swapping of a 13C-1H system. Data points are obtained from cross polarization experiments. The zero plateau in the frequency and the parabolic behavior of the decoherence rate are indicative of an over-damped Zeno phase. Solid lines are the prediction of our model.
Quantum dynamical phase diagram for the spin swapping operation. The figure shows the frequency dependence on system-environment (SE) interaction anisotropy pXY and the ratio among the internal and the SE interaction. The projection plane determines the phase diagram where the transition between the swapping phase into the Zeno phase (frequency null) is manifested. Values of pXY for typical SE interaction
Quantum dynamical phase diagram for the spin swapping operation. The figure shows the frequency dependence on system-environment (SE) interaction anisotropy pXY and the ratio among the internal and the SE interaction. The projection plane determines the phase diagram where the transition between the swapping phase into the Zeno phase (frequency null) is manifested. Values of pXY for typical SE interaction