Environmentally induced quantum dynamical phase transition in the spin swapping operation.

Abstract

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 |(up arrow, down arrow)> and |(down arrow, up arrow)>. In NMR, this is achieved turning on and off the spin-spin interaction b=DeltaE that splits the energy levels and induces an oscillation with a natural frequency DeltaE/Planck's. Interaction of strength Planck's/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/Planck's 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 DeltaEtau(SE) similar or greater than Planck's. Beyond a critical interaction with the environment the swapping freezes and the decoherence rate drops as 1/tau(phi) proportional to (b/Planck's)2tau(SE). The transition between quantum dynamical phases occurs when omega proportional to sqrt (b/Planck's)2-(k/tau(SE)2 becomes imaginary, resembling an overdamped classical oscillator. Here, 0< or =k2< or =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.