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 ΔEℏ. 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 bℏ 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 ΔE τSE ℏ. Beyond a critical interaction with the environment the swapping freezes and the decoherence rate drops as 1 τφ ≳ (bℏ)2 τSE. The transition between quantum dynamical phases occurs when ω≳ (bℏ)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.