Environmentally induced quantum dynamical phase transition in the spin swapping operation

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 vertical bar up arrow, down arrow > and vertical bar down arrow, up arrow >. 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/h. Interaction of strength h/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/h 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)greater than or similar to h. Beyond a critical interaction with the environment the swapping freezes and the decoherence rate drops as 1/tau(phi)proportional to(b/h)(2)tau(SE). The transition between quantum dynamical phases occurs when omega proportional to root(b/h)(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. (c) 2006 American Institute of Physics.