Synchronization transition in dipole-coupled two-level systems with positional disorder

TL;DR

This paper investigates a phase transition in the decoherence dynamics of disordered dipole-coupled two-level systems, revealing a transition from disorder-dominated decay to synchronized, collective oscillations at a critical filling fraction.

Contribution

The study introduces a mean-field theory capturing the synchronization transition in disordered dipolar systems and links it to observable decoherence dynamics.

Findings

Decoherence exhibits a phase transition at critical filling p_c ≈ 0.15.

Below p_c, the Ramsey signal decays with a timescale T_2 ∝ p^{-3/2}.

Above p_c, the system shows persistent oscillations and diverging T_2 for large N.

Abstract

We study the decoherence dynamics of dipole-coupled two-level quantum systems in Ramsey-type experiments. We focus on large networks of two-level systems, confined to two spatial dimensions and with positional disorder giving rise to disordered dipolar couplings. This setting is relevant for modeling the decoherence dynamics of the rotational excitations of polar molecules confined to deep optical lattices, where disorder arises from the random filling of lattice sites with occupation probability $p$. We show that the decoherence dynamics exhibits a phase transition at a critical filling $p_c\simeq 0.15$. For $p<p_c$ the dynamics is disorder-dominated and the Ramsey interference signal decays on a timescale $T_2 \propto p^{-3/2}$. For $p>p_c$ the dipolar interactions dominate the disorder, and the system behaves as a collective spin-ordered phase, representing synchronization of the two-level systems and persistent Ramsey oscillations with divergent $T_2$ for large systems. For a finite number of two-level systems, $N$, the spin-ordered phase at $p> p_c$ undergoes a crossover to a collective spin-squeezed state on a timescale $\tau_{\rm sq} \propto \sqrt{N}$. We develop a self-consistent mean-field theory that is capable of capturing the synchronization transition at $p_c$, and provide an intuitive theoretical picture that describes the phase transition in the long-time dynamics. We also show that the decoherence dynamics appear to be ergodic in the vicinity of $p_c$, the long-time behaviour being well described by the predictions of equilibrium thermodynamics. The results are supported by the results of exact diagonalization studies of small systems.