Electron spin tomography through counting statistics: a quantum trajectory approach

We investigate the dynamics of electron spin qubits in quantum dots. Measurement of the qubit state is realized by a charge current through the dot. The dynamics is described in the framework of the quantum trajectory approach, widely used in quantum optics, and we show that it can be applied successfully to problems in condensed matter physics. The relevant master equation dynamics is unravelled to simulate stochastic tunneling events of the current through the dot.Quantum trajectories are then used to extract the counting statistics of the current. We show how, in combination with an electron spin resonance (ESR) field, counting statistics can be employed for quantum state tomography of the qubit state. Further, it is shown how decoherence and relaxation time scales can be estimated with the help of counting statistics, in the time domain. Finally, we discuss a setup for single shot measurement of the qubit state without the need for spin-polarized leads.