Environmentally induced Quantum Dynamical Phase Transition in the swapping operation

GONZALO A. ÁLVAREZ; ERNESTO P. DANIELI; PATRICIA R. LEVSTEIN; HORACIO M. PASTAWSKI

Córdoba, Argentina

Simposio; Quantum symposium. Time of Challenges: Harnessing the Uncertainties of the Quantum World (with the presence of Ahmed Zewail, Novel Price in Chemistry,1999); 2005

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/τSE, with an environment of neighboring spins, degrades this oscillation within a decoherence time scale τf. While the experimental frequency ω and decoherence time τf were expected to be roughly proportional to b/hbar and τSE respectively, we present here experiments that show drastic deviations in both ω and τf. By solving the many spin dynamics, we prove that the swapping regime is restricted to ΔEτSE>hbar. Beyond a critical interaction with the environment the swapping freezes and the decoherence rate drops as 1/τf µ (b/hbar)²τSE. The transition between quantum dynamical phases occurs when ωµ√((b/hbar)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.