Fundamental bounds on many-body spin cluster intensities

TL;DR

This paper establishes fundamental bounds on the observable intensities of multiple-quantum coherences in large spin systems, revealing a transition that can be mitigated by hyperpolarization, thus enabling larger spin cluster observations.

Contribution

It introduces a fundamental limit on MQC intensities in large systems and shows how hyperpolarization can overcome the traditional size restrictions.

Findings

Identifies a sharp transition in observable MQC intensities with increasing coherence order.

Shows the transition point scales with system size and polarization.

Suggests hyperpolarization can extend observable spin cluster sizes.

Abstract

Multiple-quantum coherence (MQC) spectroscopy is a powerful technique for probing spin clusters, offering insights into diverse materials and quantum many-body systems. However, prior experiments have revealed a rapid decay in MQC intensities as the coherence order increases, restricting observable cluster sizes to the square root of the total system size. In this work, we establish fundamental bounds on observable MQC intensities in the thermodynamic limit outside the weak polarisation limit. We identify a sharp transition point in the observable MQC intensities as the coherence order grows. This transition points fragments the state space into two components consisting of observable and unobservable spin clusters. Notably, we find that this transition point is directly proportional to the size $N$ and polarization $p$ of the system, suggesting that the aforementioned square root limitation can be overcome through hyperpolarization techniques. Our results provide important experimental guidelines for the observation of large spin cluster phenomena.