  We describe the effect of geometric phases induced by either classical or
quantum electric fields acting on single electron spins in quantum dots in the
presence of spin-orbit coupling. On one hand, applied electric fields can be
used to control the geometric phases, which allows performing quantum coherent
spin manipulations without using high-frequency magnetic fields. On the other
hand, fluctuating fields induce random geometric phases that lead to spin
relaxation and dephasing, thus limiting the use of such spins as qubits. We
estimate the decay rates due to piezoelectric phonons and conduction electrons
in the circuit, both representing dominant electric noise sources with
characteristically differing power spectra.
