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Cavity-assisted Spin Control

Cavity-assisted all-optical spin manipulation in a QD

Employing the model to the treatment of the resonant coherent interactions with single QDs embedded in realistic device geometries (Fig. 23) allows us to test and identify possible routes for minimisation of the decoherence effects and achievement of reliable generation and detection of the spin state.

 Fig. 23. Shematic representation of a semiconductor microcavity with distributed Bragg mirrors containing a single Quantum Dot as an active medium interacting with the incident polarised ultrashort light pulse (from left).
Consider a microcavity with 6 embedded QWs (QD planes) with half of the initial spin population prepared in the ground state of the first two-level system, and the other half is residing in the excited state of the second two-level system (fig. 16). A sleft-circularly polarised p-pulse is launched from the left microcavity boundary (z=0) and the time dynamics of the electric field vector components at the location of the QW planes is monitored (Fig. 24).

(a)                                                                                         (c)
(b)                                                                                                (d)
Fig. 24. (a) Refractive index profile along the microcavity structure (right axis), containing 6 quantum wells (or planes with QDs) and initial spin population in an ensemble of four-level systems,used to model the electric dipole transitions, initially prepared with half-spin population in the ground state of the first two-level system and a half of the population in the excited state of the second two-level system (see Fig. 16); (b) Spatial distribution of the electric field and the population difference in the first and in the second two-level systems at a particular time after a p-pulse excitation from the left boundary. (c) Magnified view of the cavity with the QWs (planes of QDs) ; (d) Intracavity field and population distributions. 
After some time the field builds up in the cavity, due to the multiple reflections by the Bragg mirrors, and the spin population is inverted with respect to the initial population profile (compare Fig. 24 (c) and (d)). The model allows designing the precise locations of the QW/ QD planes within the cavity, in order to obtain maximum coupling and spin population inversion.

Extension of the model to multi-dimensions: polarised ultrashort pulse interactions with discrete multi-level quantum systems embedded in planar nonlinear optical waveguides and semiconductor microcavities (Fig. 25).

                          (a)                                                          (b)                                                                  (c)

Fig. 25. (a) 3D plot of the refractive index profile across a 5λ-cavity at λ=1.3 mm; bottom DBR AlAs/GaAs 31 pairs; top DBR AlGaAs/Al0.8Ga0.2As 24 pairs; (b) Schematic picture of a planar optical waveguide / microresonator and the E- and H-field vectors configuration of the transverse magnetic guided mode;  transmission boundary conditions at the input/output facets and perfectly reflecting boundary conditions on the side walls are designated by arrows; (c) 2D discretisation scheme: finite differences on a modified 2D-Yee grid with polarisation variables assigned to empty nodes and subsequent averaging procedure

Consider a slab waveguide structure filled with resonantly absorbing/amplifying medium (GaAs) described by an ensemble of four-level systems (e.g. QW/QD medium). The quantum system is prepared initially in the ground state with population equally distributed between the lower-lying levels. We start to propagate s - (left)-circularly polarised pulse (pulse duration Tp=100 fs at λ=800 nm) with a spatial profile of a TM1 guided mode of a parallel mirror waveguide and a hyperbolic secant envelope from the left boundary of the simulated structure z=0. The initial field amplitude E0=2.099´108 Vm-1 is chosen to drive the population in the four-level system through 5 Rabi flops. In Fig. 26 snapshots at a simulation time t=120 fs of the pulse E-field components are given:

                                                                                                                    (a)                                                                                         (b)
Fig. 26. 3D plot of (a)  Ey electric field vector component and (b) Ez component of a TM1 mode - sech pulse (E0=2.099´108 Vm-1) at a time t=120 fs propagating through resonant absorbing 4-level atom medium with initial population equally distributed between the lower-lying levels (see Fig. 16): r11i=+1/2,r33i=+1/2. The spatial step of discretisation along z and y is Dz=2´10-3 µm, Dy=5´10-2 µm, the corresponding time step is Dt=6.66 ´10-18 s.
     3D plots of the macroscopic polarisation induced by the electromagnetic wave in the medium are given in Fig. 27.

Fig. 27. 3D and top view plots of the polarisation components induced by the electromagnetic wave in the 4-level medium. S1 and S7 are the absorptive and dispersive part of the polarisation between level |1ñ and   |2ñ. S6 and S12 are the absorptive and dispersive parts of the polarisation between level |3ñ and  |4ñ.

The population terms are shown in Fig. 28:

Fig. 28. Top line: 3D and top view plots of the population difference S13r22-r11 in the first two-level system. The population in the first two-level system  ( |1ñ ® |2ñis driven through 5 Rabi flops shown in the bottom line (left) at different y-offset cross-sections along the structure, and through 4 Rabi flops in the second two-level system  ( |3ñ ® |4ñ).

The field components, polarisation and populations are shown at the same simulation time of a higher-order TM2 mode pulse in Fig. 29.

Fig. 29. Top line: 3D and top view plots of the electric field vector components of a TM2 mode pulse at t=120 fs (same parameters as in Fig. 28); middle line: population difference S13= r22-r11 in the first two-level system ( |1ñ ® |2ñ); bottom line: population difference in the second two-level system  ( |3ñ ® |4ñ)