Coherent population trapping combined with cycling transitions for quantum dot hole spins using triplet trion states

Optical spin rotations and cycling transitions for measurement are normally incompatible in quantum dots, presenting a fundamental problem for quantum information applications. Here we show that for a hole spin this problem can be addressed using a trion with one hole in an excited orbital, where strong spin-orbit interaction tilts the spin. Then, a particular trion triplet forms a double $Lambda$ system, even in a Faraday magnetic field, which we use to demonstrate fast hole spin initialization and coherent population trapping. The lowest trion transitions still strongly preserve spin, thus combining fast optical spin control with cycling transitions for spin readout.