Time-periodic interaction between a spin-pair: A quantum master equation approach

Abstract

Quantum master equations describe the dynamics of open quantum systems. Such systems might be subjected to external drives and internal interactions such as direct dipolar couplings. Both the external drives and the internal interactions could be oscillatory functions of time. In particular, a spin pair undergoing magic angle sample spinning experiences such oscillatory interactions in time. In the present work, we analyze a spin pair with a time-periodic interaction by using our recently-proposed fluctuation-regulated quantum master equation [PRA, 97, 063837 (2018)] (FRQME). FRQME helps calculate the first as well as the second-order effects of all time-dependent interactions Hamiltonians. Using FRQME, we find the usual sideband pattern and also have shown the linewidths of the sidebands as a function of the coupling strength, the period of oscillation, and an environmental parameter. We show that at high spinning speed, the sidebands would have a Lorentzian shape. We predict that the dipolar contributions to the sidebands’ linewidths are smaller for a shorter correlation time of the environmental fluctuations.