Theory of phonon-induced spin relaxation in coupled lateral quantum dots*

Electron spins in lateral quantum dots at GaAs/GaAlAs interfaces relax in milliseconds. Spin relaxation here means transitions from the upper to the lower Zeeman split orbital ground state, at an applied magnetic field. Both spin-orbit and electron-phonon couplings are needed for spin flips between spectrally distinct and opposite-spin states. We have carried out realistic numerical and analytical calculations of spin relaxation and spin dynamics in single and coupled lateral quantum dots [1]. Our results agree with existing experiments on single dots, while predict interesting effects for coupled dots. Most important, spin relaxation in coupled dots is dominated by spin hot spots--anticrossings of states of opposite spins--at practical couplings (say, 0.1 meV). Spin hot spots reduce spin relaxation to nanoseconds! Fortunately, spin hot spots are strongly anisotropic and there can be (rather singular) configurations, we call them {\it easy passages}, in which spin relaxation slows down to milliseconds as in single dots. For a (001) plane, for example, an easy passage occurs if coupled dots are oriented along [110] and the in-plane magnetic field lies perpendicular, along [1$\overline{1}$0]. This configuration should be used for spin-based quantum information processing. This easy passage also protects spin qubits from electrical field disturbances which occur in ``on-chip" single electron spin resonance experiments, as will be demonstrated theoretically using density matrix formalism for electron spins in the presence of both dissipation and driving oscillating electric and magnetic field [2]. \\ \noindent [1] P. Stano and J. Fabian, Phys. Rev. Lett. 96, 186602 (2006).\\ \noindent [2] P. Stano and J. Fabian, cond-mat/0611228.