The experiment is performed on a QD sample containing a single layer of In- GaAs/GaAs QDs embedded in a n-doped field effect structure. The i-GaAs tun- nelling barrier separating the QD layer from the back contact is 25 nm thick. An AlAs/GaAs superlattice was grown 10 nm above the QD layer to prevent hole tun- nelling. 176 nm above the QD layer, on the sample surface, a 5 nm thick semi- transparent NiCr top gate electrode was evaporated. By applying a voltage to the top gate with respect to the back contact, the electronic conduction band levels in the QDs can be shifted with respect to the Fermi energy of the back contact. This allows a controlled charging of the dot with single electrons [16]. Furthermore, the electric field experienced by the QD induces an dc-Stark-effect that can be used to fine tune the excitonic resonance energy of the QD in situ. To charge the QD with a hole a bias is applied to the structure, at which the neutral excitonic state is not bound anymore, but the electron will tunnel out of the QD into the back contact, leaving behind a hole. We generate the hole by non-resonantly, optically pumping the wetting layer as for a PL experiment [21]. A tunable narrow band laser is tuned into resonance with the transition of the positively charged exciton (X1+). The transmitted laser power is detected by a Si-photodiode and monitored
as a function of the energy detuning between the laser and the excitonic transition. The sample and the photodiode are mounted in a fiber-based confocal microscope that is immersed in a liquid helium bath cryostat, operating at 4.2 K. For noise deduction lock-in technique is used [18, 22].
In Fig. 11.1 the transmission spectra of the negative and positive exciton is plotted as a function of the energy detuning. For both charging states the transmission signal was measured for circular and linearly polarized resonant laser excitation. The polarization of the non-resonant laser has no effect, since the spin information
Chapter 11
of the excited electrons and holes is lost in the relaxation process. It is clear from the spectra that for the negative exciton the polarization makes no difference for the transmission contrast. This finding, we interpret in a way that the two spin states of the resident electron are equally populated and hence the transition is unpolarized. For the positive excitation the situation is different. Here, for perfect circular polarization one would expect to see no contrast in the transmission signal even at zero magnetic field [14]. This is because perfectly circularly polarized light only pumps one of the two possible transitions of the X1+. In Fig. 11.2(a) the inset shows the schematic transitions of theX1+. In the case of σ− polarized light,
the hole spin up ground-state ⇑ is coupled to the electron spin up state ↑. In the excited state the electron spin is exposed to the Overhauser field; the magnetic field generated by the magnetic moments of the nuclei. The magnitude of this field is of the order of a few mT [11, 12]. The electron spin will precess around the Overhauser field which will have a non-zero component (BNxy) perpendicular to the QD growth direction. This leads to an oscillation of the occupancy of the two excited states, | ⇑⇓↑>and | ⇑⇓↓>. The limited lifetime of the excited state of the order of≈1 ns will lead to a decay into the hole spin up ground state. The vanishing hyperfine interaction of the hole spin with the nuclei leads to a long lifetime of the hole in this spin state. Similar to the electron spin pumping scheme, as presented in [4],
0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.00 0.02 0.04 0.06 0.08 0.10 B (T) N o rm a liz e d tr ansm issi on cont ra st ı- ı+ (a) ı- 0.0 0.5 1.0 1.5 2.0 2.5 0.0 0.1 0.2 B (T) N o rm a liz e d tr ansm issi on cont ra st (b) ʌ
Figure 11.2: Normalized transmission contrast ΔT(B)/2ΔT(B= 0) versus the applied magnetic
field B for two different polarizations (σ− (a) and π (b)). The line is a fit of the theory to the
data as explained in the text. The inset shows the level scheme of the X1+ at zero magnetic
field. The ground and excited states are coupled via a σ+ or σ− polarized light field. The spin
of the photogenerated electron will precess around the Overhauser field, which will lead to spin
shelving into the hole spin down state for pureσ− optical pumping and into the spin up state for
σ+ pumping. The hole spin lifetime is limited by the non-resonant exciton generation rate.
the described process leads to an optical pumping of the hole spin, and hence to a vanishing transmission contrast of the pumped optical σ− transition. If, however, the polarization of the resonant laser field is not perfectly circular, the same laser field will “repump” the hole spin with the ratio of the power of the two circular polarization components of the laser field [14, 4]. In our case the fiber-based setup scrambles the polarization of the laser field, and it is very challenging to feed a laser field with an arbitrary polarization into the fiber that will leave the fiber with a perfect circular polarization. We can only use the QD response itself to measure the degree of polarization and the signal to noise ratio limits the resolution to a ratio of σ+/σ− in this case to 1/5. In Fig. 11.1 the remaining signal for circular polarization of the X1+ is due to this imperfection of the circular polarization.
By applying a magnetic field in growth direction to the QD the ground and excited states are split by the Zeeman energy EZ,e,h = ge,hμBB. This energy lifts the de-
generacy of the two optical transitions. Hence, the optical repump of the signal is decreased, due to the imperfect laser field polarization [14]. In Fig. 11.2 (a) the amplitude of transmission contrast for the circular excitation is plotted as a function of the magnetic field. The contrast is normalized to the maximum contrast at low power [23] that would correspond to a 100 % occupancy of the hole spin up ground state | ⇑>. For equal occupancy the normalized transmission contrast would be 0.5. The normalized transmission contrast shows a minimum for a magnetic field of ≈ 100 mT due to the reduced repump. For a larger magnetic field the signal recovers because the Zeeman splitting of the electronic levels reduces the hyperfine interaction. The line is a fit to the data with the theory based on the optical Bloch equations for two coupled two level systems, as described in detail in ref. [14]. To fit the data the parameters where chosen as follows. The perpendicular component of the Overhauser field BxyN = 46 mT. The Rabi energy for the optical transitions where: Ωσ− = 3.8 μeV, Ωσ+ = 1.6μeV. The g-factors for the electron and hole
where ge = −0.66 and gh = −1.32 corresponding to optical measurements as re-
ported in ref. [9]. The electron precession frequency in the excited state is assumed to be ΩN = 0.2 μeV, leading to a hole spin lifetime Th
1 = 16 ns. For linearly po-
larized resonant excitation, the normalized transmission contrast is plotted in Fig. 11.2 (b). Again the line is a fit to the data using the same parameters as before only that now Ωσ− = Ωσ+ = 2.7 μT, as expected for linearly polarized light. It
has to be stated that the spectra that where calculated with the above mentioned theory, did not reproduce the measured spectra at low magnetic fields (B <30 mT). Therefor, we apply the theory only to the data at a magnetic field B <30 mT. For the linear polarization we see again a reduction of the transmission contrast for a small magnetic field ≈ 100 mT, which arises from the energy detuning of the two optical transitions and hence to a more efficient optical spin pumping, with respect to the zero field situation.
Chapter 11