Higher order spin noise spectroscopy of coherently interacting quan- tum systems

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We want to study coupled quantum mechanical systems by going beyond standard spin noise spectroscopy. Advancing spin noise spectroscopy beyond second order noise spectra opens up a new realm of possibilities including the distinction between homogenous and inhomogeneous broadening, proof of quantum coherence, and testing time-reversal invariance. We will lay a quantum mechanical theoretical foundation for second and higher order spin noise spectroscopy and perform measurements on suitable strongly coupled pairs of nuclear and electron spins in semiconductors (so-called hybrid nuclear qubits).We plan to(i) derive analytical expressions for higher order spin noise spectra from first principles in terms of quantum mechanical propagators using for the first time continuous quantum measurement theory. The full quantum mechanical theory is based on a stochastic version of the Lindblad master equation which includes damping and temperature.(ii) measure standard and higher order spin noise spectra of the In-donor electron in ZnO which is strongly coupled to the 9/2 indium nuclear spin.(iii) compare the spectra with theoretical spectra that we numerically obtain by master equation techniques published earlier by our group.Preliminary work shows that our theoretical approach recovers known expressions for the 2nd order power spectrum. In addition, the perturbation of the system by the measurement process appears naturally in the equations and can be used to quantify the trade-off between perturbation due to high probe beam intensities and increased measurement time for weak intensities.