Ultrafast Coherent Control of Individual Electron Spin Qubits

In this chapter, we shall derive how ultrafast optical control can be used in combination with Larmor precession for full SU(2) control of a single quantum dot electron spin. Such ultrafast electron spin control was first reported in Refs. [1–3]. In combination with accurate timing control over the optical fields used to realize this SU(2) control, arbitrary pulse (control) patterns can be applied to the spin [3]. As we will show in Sect. 3.3.2, such pulse sequences can be used to overcome the effects of slowly varying Larmor precession due to variations in the spin’s solid state environment. As a particular example, we will study the effects of the hyperfine interaction between an electron spin and the nuclear spins inside the quantum dot [4–7] – the latter will be discussed in detail in Sect. 3.3.1.