Environmentally induced Quantum Dynamical Phase Transition in the spin swapping operation

Details Environmentally induced Quantum Dynamical Phase Transition in the spin swapping operation Environmentally induced Quantum Dynamical Phase Transition in the spin swapping operation

2005-04-13

arxiv.org/abs/cond-mat/0504347v4

J. Chem. Phys. 124 (2006) 194507

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

Final version. One figure and some equations corrected, 10 pages, 4 figures

Scientific paper

10.1063/1.2193518

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=\Delta E that splits the energy levels and induces an oscillation with a natural frequency \Delta E/\hbar. Interaction of strength \hbar/\tau_{SE}, with an environment of neighboring spins, degrades this oscillation within a decoherence time scale \tau_{\phi}. While the experimental frequency \omega and decoherence time \tau_{\phi} were expected to be roughly proportional to b/\hbar and \tau_{SE} respectively, we present here experiments that show drastic deviations in both \omega and \tau_{\phi}. By solving the many spin dynamics, we prove that the swapping regime is restricted to \Delta E \tau_{SE} > \hbar. Beyond a critical interaction with the environment the swapping freezes and the decoherence rate drops as 1/\tau_{\phi} \propto (b/\hbar)^2 \tau_{SE}. The transition between quantum dynamical phases occurs when \omega \propto \sqrt{(b/\hbar)^{2}-(k/\tau_{SE})^2} becomes imaginary, resembling an overdamped classical oscillator. Here, 0

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