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Coherent optical spin control

The successful implementation of quantum computation requires the choice of a long-lived quantum property of a scalable physical system in which to encode our bit of information. The spin of a single electron provides a two-level system and is a natural candidate for realisation of a quantum bit (qubit). Among the huge variety of proposed schemes to realise quantum computing, one of the front runners is now considered to be the charged quantum dot (QD) mainly due to the long spin-flip and spin decoherence times of the localised spin. One promising approach is to optically address individual carrier spins in semiconductor QDs and to manipulate them through optically excited states (charged excitons).

Consider a scheme of how the trion, with energy configuration (Fig. 20), permits the readout of a single electron spin during the spin relaxation. 

Fig. 20. Schematic representation of the initial spin-down and spin-up electron states in a single negatively-charged quantum dot (a,b) and the ground trion state, formed by a two electrons in a singlet state (with opposite spin orientations) and a hole, created by s -(c) and s+(d) light; (e) Equivalent energy-level diagram of a ground singlet negatively charged exciton (trion) X - state in a single quantum dot.

The optically created trion state radiatively decays to the initial state with spontaneous emission decay rate G. Transitions of population occur between lower-lying states due to electron spin flip relaxation processes (hyperfine interaction with the lattice ions nuclei) with rate g1, and between the upper-lying levels due to phonon assisted hole spin relaxation process. The electron and hole spin decoherence rates are denoted by g2 and Gt, correspondingly We have originally derived master pseudospin equations describing the coherent spin dynamics induced by an ultrashort polarised optical excitation through optical orientation mechanism, taking into account the dissipation in the system through spin-relaxation and spin decoherence processes.

The model is applied to trace the time evolution of the population of the trion |−3/2ñ state, following a s - or s + pulse excitation, at a point within a single modulation-doped GaAs/AlGaAs self-assembled QD for |ñ and |ñ initial electron spin states, which represents a measure of the intensity of the polarised time-resolved (TR) photoluminescence (PL) from the ground trion state (Fig. 21).

Fig. 21. Refractive index profile of a single QD embedded between two Al0.3Ga0.7As barriers (right y-axis), the electric field vector components and the populations of all four levels (left y-axis) at a particular time (see plot title).

The long-lived electron spin coherence left behind a single resonant ultrashort optical excitation of the electron-trion transition in a charged quantum dot is simulated both in the low- and high-intensity Rabi oscillation regime. The time evolution of the electric field vector components of a s--polarized optical pulse (with pulse duration Tp=1.3 ps), resonant with the trion transition and the corresponding spin population of all four states are shown in Fig. 22 A (low-excitation limit E0=550 V m−1), B (a p-pulse with E0=3´106 Vm−1) and C (a 12p-pulse  with E0=4´107 Vm−1) for (a) initially  |ñ populated state and (b) initial |ñ state. 

Fig. 22. Time evolution of the electric field vector components of a s --polarised optical pulse (Tp=1.3 ps) resonant with the trion transition and the corresponding spin population of all four states (a) and (b), (c) comparison between the TRPL traces corresponding to initial spin orientation shown in the rightmost column for excitations with the same helicity. The horizontal lines represent the time dynamics at 3 different initial electric field amplitudes (A:E0=550 V m−1, B: a p-pulse with E0=3´106 Vm−1, C: a 12p-pulse  with E0=4´107 Vm−1)

The polarised Time-Resolved Photo-Luminescence (TRPL), denoted by the blue curves in (a) and (b), are plotted on the same graph in (c). Note that at high excitation intensity (C), the optical field amplitude saturates and the short-time dynamics exhibits Rabi oscillations of the spin population. The number of the full Rabi flops is determined by the pulse area 12p yielding six full Rabi flops. In all three cases sufficiently long time interval exists (~400 ps) within which a differentiation between the two initial spin states can be made with great fidelity. The polarised PL shape for spin-down and spin-up initial states is considerably different: while the polarized PL for initial spin-down state exhibits exponential decay (blue curve), the PL for initial spin-up state is a non-monotonic function of time with characteristic rising time, reaching a maximum and a subsequent decay (red curve). The simulations imply two distinct ways of reliable single-shot coherent initial spin state detection, namely, through the pulse echo appearing at later times following the initial excitation, specific only to initial state with spin-up orientation (Fig 22 A,B,C (b)), and through the shape of the polarized PL trace in time showing a maximum again for this initial state in contrast to the single-exponential decay characterizing the spin-down initial state (Fig 22 A,B,C (c)). The simulations show the onset of the high-intensity optical Rabi oscillation regime suppressing the spin-relaxation processes.

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