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 |+,-> 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/\hbar. Interaction of strength \hbar/τ_{SE}, with an environment of neighboring spins, degrades this oscillation within a decoherence time scale τ_ϕ. While the experimental frequency ωand decoherence time τ_ϕ were expected to be roughly proportional to b/\hbar and τ_{SE} respectively, we present here experiments that show drastic deviations in both ωand τ_ϕ. By solving the many spin dynamics, we prove that the swapping regime is restricted to ΔE τ_{SE} > \hbar. Beyond a critical interaction with the environment the swapping freezes and the decoherence rate drops as 1/τ_ϕ \propto (b/\hbar)^2 τ_{SE}. The transition between quantum dynamical phases occurs when ω\propto \sqrt{(b/\hbar)^{2}-(k/τ_{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.