Temporal order in periodically driven spins in star-shaped clusters

TL;DR

This study demonstrates that star-shaped clusters of nuclear spins exhibit stable period-two magnetization oscillations under inexact pulse sequences, revealing a robust temporal order influenced by Ising coupling and initial magnetization.

Contribution

The paper provides experimental evidence of stable temporal order in large spin clusters driven periodically, highlighting the role of Ising interactions and initial magnetization in maintaining periodicity.

Findings

Period-two oscillations are robust against bath effects.

Amplitude decay depends on pulse inaccuracy.

Stable period increases with initial magnetization.

Abstract

We experimentally study the response of star-shaped clusters of initially unentangled $N=4$, 10 and 37 nuclear spin-$\frac{1}{2}$ moments to an inexact $\pi$-pulse sequence, and show that an Ising coupling between the centre and the satellite spins results in robust period-two magnetization oscillations. The period is stable against bath-effects but the amplitude decays with a time scale that depends on the inexactness of the pulse. Simulations reveal a semiclassical picture where the rigidity of the period is due to a randomizing effect of the Larmor precession under the magnetization of surrounding spins. The time scales with stable periodicity increase with net initial magnetization even in the presence of perturbations, indicating a robust temporal ordered phase for large systems with finite magnetization per spin.