Using a Lindbladian approach to model decoherence in two coupled nuclear spins via correlated phase-damping and amplitude damping noise channels

In this work, we studied the relaxation dynamics of coherences of different order present in a system of two coupled nuclear spins. We used a previously designed model for intrinsic noise present in such systems which considers the Lindblad master equation for Markovian relaxation. We experimentally created zero-, single- and double- quantum coherences in several two-spin systems and performed a complete state tomography and computed state fidelity. We experimentally measured the decay of zero- and double- quantum coherences in these systems. The experimental data fitted well to a model that considers the main noise channels to be a correlated phase damping channel acting simultaneously on both spins in conjunction with a generalized amplitude damping channel acting independently on both spins. The differential relaxation of multiple-quantum coherences can be ascribed to the action of a correlated phase damping channel acting simultaneously on both the spins.