Finite-frequency shot noise as a spin-relaxation probe in quantum dots

Long spin-relaxation times are an important prerequisite for spin-based quantum information processing. However, conventional pulsed-gate techniques for measuring spin relaxation in a quantum dot operate only at large energy splitting. An alternative is to measure a transient effective charge $e^*$ [1], or equivalently, the zero-frequency noise. However, multi-level systems often exhibit several decay rates due to distinct physical mechanisms, where a more refined approach is necessary. We have formulated a theory of the frequency-dependent current noise through a multilevel system in the dynamical channel blockade regime, including the effects of multiple relaxation processes. This theory gives a one-to-one correspondence between the form of the frequency-dependent Fano factor and the relevant relaxation rates and can therefore be used to determine these rates through a measurement of the current noise. We have applied it to the case of a quantum-dot spin diode (or spin valve) and to a double quantum dot in the Pauli spin blockade regime.\\[4pt] [1] F. Qassemi, W. A. Coish and F. K. Wilhelm, Phys. Rev. Lett. \textbf{102}, 176806 (2009)