Environmentally induced Quantum Dynamical Phase Transition in the spin swapping operation

Alvarez, Gonzalo Agustin; Danieli, Ernesto Pablo; Levstein, Patricia Rebeca; Pastawski, Horacio Miguel

Environmentally induced Quantum Dynamical Phase Transition in the spin swapping operation

Authors

Alvarez, Gonzalo Agustin

Danieli, Ernesto Pablo

Levstein, Patricia Rebeca

Pastawski, Horacio Miguel

Description

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.
Final version. One figure and some equations corrected, 10 pages, 4 figures