Abstract
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.
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Notes
- 1.
For | Ω1(t) | ≠ | Ω2(t) | , there is a net difference in the energy of both ground states, which adds to the energy splitting δ e . In the case of a spin qubit, as we shall derive later, this corresponds to a net magnetic field being applied, parallel to the field causing the Zeeman splitting in the first place.
- 2.
The distribution of quantum dot emission wavelengths reflects their size- and strain distribution due to the self-assembled growth process. In practice, this distribution peaks around 880 nm, and tails off very slowly towards 950–1,000 nm. For quantum dots in the 940 nm range, as were used for the spin echo experiments described in Sect. 3.3.2, there is often less than one quantum dot resonant with the cavity. For the more blue-shifted dots used for spin-photon entanglement verification in Sect. 7, the overall dot density was reduced, yet the cavity is closer to the peak of the distribution. Therefore, typically, more than one quantum dot could be found resonant with the cavity. However, their spectral inhomogeneity still allows for selective excitation of and collection from one particular dot.
- 3.
Higher order terms, due to e.g. dipolar coupling to both electron spin and other nuclear spins do exist, and give rise to some slow dynamics on milliseconds- to seconds timescales, as will be shown in Sect. 3.3.2, but for the current analysis, those can be temporarily ignored.
- 4.
As the (mixed-in) heavy-holes form an effective two-level system, such re-mapping is valid for the low temperatures in typical experiments: the energy separation from the next higher states is typically several meV.
- 5.
Rather: approximately observe the single-shot dynamics in a multishot experiment. The spin-echo results in slightly different dynamics for the nuclear spin bath than true, single-shot free induction decay, and therefore, slightly different decoherence effects. We refer to Refs. [5, 18] and [26] for further details.
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De Greve, K. (2013). Ultrafast Coherent Control of Individual Electron Spin Qubits. In: Towards Solid-State Quantum Repeaters. Springer Theses. Springer, Heidelberg. https://doi.org/10.1007/978-3-319-00074-9_3
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