Environmentally induced Quantum Dynamical Phase Transition in the spin swapping operation

TL;DR

This paper investigates how environmental interactions induce a quantum dynamical phase transition in spin swapping operations, revealing a critical point where the dynamics freeze due to the Quantum Zeno effect, with implications for quantum control.

Contribution

The study demonstrates the existence of a quantum dynamical phase transition in spin systems influenced by environment-induced decoherence, providing a theoretical framework and experimental validation.

Findings

Swapping oscillation frequency deviates from expected proportionality to interaction strength.

A critical environmental interaction strength causes the swapping to freeze, reducing decoherence rate.

Transition occurs when the oscillation frequency becomes imaginary, indicating overdamped behavior.

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=\Delta E that splits the energy levels and induces an oscillation with a natural frequency \Delta E/\hbar. Interaction of strength \hbar/\tau_{SE}, with an environment of neighboring spins, degrades this oscillation within a decoherence time scale \tau_{\phi}. While the experimental frequency \omega and decoherence time \tau_{\phi} were expected to be roughly proportional to b/\hbar and \tau_{SE} respectively, we present here experiments that show drastic deviations in both \omega and \tau_{\phi}. By solving the many spin dynamics, we prove that the swapping regime is restricted to \Delta E \tau_{SE} > \hbar. Beyond a critical interaction with the environment the swapping freezes and the decoherence rate drops as 1/\tau_{\phi} \propto (b/\hbar)^2 \tau_{SE}. The transition between quantum dynamical phases occurs when \omega \propto \sqrt{(b/\hbar)^{2}-(k/\tau_{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.