Theory of phonon-induced spin relaxation in a structured phononic reservoir

Abstract

By combining Markovian and non-Markovian open quantum system theory with finite-element simulations, we develop a theory of electron spin relaxation in a structured phononic reservoir. This problem is crucial for understanding spin dynamics in hybrid systems involving mechanical modes, as well as for the design of devices combining spin degrees of freedom with photonic and phononic architectures, where the phonon density of states is modulated in the relevant spectral range corresponding to moderate magnetic fields. Taking a QD in a phononic waveguide as a representative and technologically relevant example, we show that spin relaxation in such environments is much more complex than in bulk. While the relaxation rates are typically an order of magnitude higher than in bulk, there are parameter windows where the relaxation is suppressed by many orders of magnitude due to gaps in mode dispersion and selection rules imposed by mode symmetry. At the border between these two sectors, van Hove singularities in phonon dispersion lead to singularities in relaxation rates, for which we develop power-law scaling and propose a non-Markovian description of the dynamics, revealing polaronic dressing of the spin into slow acoustic modes.