Spin amplification in realistic systems

Spin amplification increases the number of excited spins in an ensemble if there is one excitation present already, while the zero-excitation state is left unchanged in the ideal case. We show that spin amplification is possible to implement in noisy and disordered spin ensembles, such as flux qubits, using only a global time-dependent drive field. The drive field envelope is found using optimal control techniques. Compared to the previous spin amplification protocols that assumed an idealized spin ensemble described by the nearest-neighbor Ising model, we include realistic long-range interactions, inhomogeneous broadening and finite life times of the flux qubit spins. Optimal control can find the drive-field envelopes that implement spin amplification in the new regime where the gate time is short compared to the time scale associated with the interaction between the spins. Spin amplification could be used for sensing of single spins and anything that could be converted into single spins, such as photons. The developed techniques can also be used to implement other types of gates. This could increase the types of gates that are possible to realize in realistic spin ensembles using one or several drive fields.