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 ∣↑, ↓⟩ 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∕ℏ. Interaction of strength ℏ∕τSE, with an environment of neighboring spins, degrades this oscillation within a decoherence time scale τϕ. While the experimental frequency ω and decoherence time τϕ were expected to be roughly proportional to b∕ℏ and τSE, respectively, we present here experiments that show drastic deviations in both ω and τϕ. By solving the many spin dynamics, we prove that the swapping regime is restricted to ΔEτSE≳ℏ. Beyond a critical interaction with the environment the swapping freezes and the decoherence rate drops as 1∕τϕ∝(b∕ℏ)2τSE. The transition between quantum dynamical phases occurs when ω∝(b∕ℏ)2−(k∕τSE)2 becomes imaginary, resembling an overdamped classical oscillator. Here, 0⩽k2⩽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.