Harmonic dual dressing of spin one-half systems

Controlled modifications of the quantum magnetic response are produced in dressed systems by a high frequency, strong and not-resonant electromagnetic field. This quantum control is greatly enhanced and enriched by the harmonic, commensurable and orthogonally oriented dual dressing theoretically discussed here. The secondary field enables a fine tuning of the qubit response, with control parameters amplitude, harmonic content, spatial orientation and phase relation. Our analysis is based on a perturbative approach and includes few numerical solutions. The long-time dynamics is described in terms of an anisotropic effective static magnetic field representing the handle for the system full engineering. Through a low-order harmonic mixing the bichromatic driving generates a rectified static field acting on the spin. The Zeeman response becomes anisotropic in a triaxial geometry and includes a quadratic contribution. Our dressing increases the two-level energy splitting, improving the spin detection sensitivity. On the low field direction it compensates the static fields applied in different geometries. A resonant spin exchange between two species having very different magnetic response as electron and nucleus is allowed by the dressing. The spin temporal evolution includes a micromotion at harmonics of the driving frequency whose role in the spin detection is examined and can be exploited in quantum information. The results presented here lay a foundation for additional applications to be harnessed in quantum simulations.