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<k^2<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.
Categories: cond-mat.mes-hall nlin.CD physics.chem-ph quant-ph