Fundamental bounds on many-body spin cluster intensities

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 (N ≫ 1) outside the weak polarization region. We identify a sharp decay in the observable MQC intensities as the coherence order grows. This transition regime fragments the state space into two components consisting of observable and unobservable multiple-quantum coherences. Notably, we find that the center of the transition region is directly proportional to 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 selective observation of large spin cluster phenomena.