Environmentally induced Quantum Dynamical Phase Transition in the spin swapping operation

GONZALO AGUSTÍN ÁLVAREZ; ERNESTO PABLO DANIELI; PATRICIA REBECA LEVSTEIN; HORACIO MIGUEL PASTAWSKI

JOURNAL OF CHEMICAL PHYSICS

AMER INST PHYSICS

Lugar: New York; Año: 2006 vol. 124 p. 194507 - 194507

0021-9606

Quantum information processing relies on coherent quantum dynamics for a precise control of itsbasic 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=Delta E that splits the energy levels and induces an oscillation with a natural frequency Delta E/ hbar. Interaction of strength hbar/tSE, with an environment of neighboring spins, degrades this oscillation within a decoherence time scale tf. While the experimental frequency w and decoherence time tf were expected to be roughly proportional to b/h and tSE, respectively, we present here experiments that show drasticdeviations in both w and tf. By solving the many spin dynamics, we prove that the swapping regime is restricted to Delta E tSE ³ hbar. Beyond a critical interaction with the environment the swapping freezes and the decoherence rate drops as 1/tf µ (b/ hbar)^2 tSE. The transition between quantum dynamical phases occurs when w µ Ö[(b/ hbar)^2-(k/tSE)^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.