Our group has successfully employed spin noise spectroscopy (SNS) in semiconductor materials as a new sensitive tool to measure the spincoherence time of electrons in nGaAs nearly interaction free [1]. This approach opens exciting ways to study the spininteraction of free and donorbound electrons, which may be regarded as model system for coupled zerodimensional spinsystems. Noise spectroscopy is an elegant method to unravel properties of a system in thermal equilibrium, without exposing it to unnecessary excitations [2]. Previously utilized techniques to study the spincoherence of charge carriers, like photoluminescence or pumpprobe techniques, had always to rely on the optical above band gap excitation of the material. Therefore a contribution, even though small, of nonequilibrium effects, carrier heating and the spindephasing influence of holes can never be excluded. This is even more of importance if it comes to small size quantum systems. Spin noise spectroscopy in semiconductors empowers us to measure extreme long spin coherence times as long as 234 ns at low temperatures, which may have been masked in the past by effects like those mentioned above. The experiment can easily be extended to study spinspin correlations in coupled quantumdots or phase transitions in semiconductors with magnetic impurities, without imposing a systematic influence on the underlying effects. The inherently low perturbation of this method makes it also very suitable to investigate single electron spins in quantum dots or bound to impurities. We furthermore discuss the measured noise power and spincoherence time in dependence of the probe energy position and the macroscopic ensemble temperature. The results compare very well with a theory based on Poisson distribution probability. The experimental principle is based upon the measurement of the noise spectrum of the below bandgap Faradayrotation in ndoped GaAs at low temperatures with high frequency spectrum analysis techniques. A schematic setup is depicted in Figure 1.
Figure 1: Spin noise Faradayrotation setup: The sample is mounted in a magnetcryostat with optical access in Voigt geometry. A small magnetic field is applied to distinguish the noise from a coincidental spinpolarized ensemble of donorbound electrons against the stronger underlying optical shot noise from the laser source. The Zeemansplitting causes the stochastically spinpolarized ensemble to precess and gives rise to an alternating spinpolarization in the direction of the probelight direction. This yields a Faradayrotation signal with MHz frequencies, which is detected with a balanced receiver setup. 
We have successively enhanced the method of spin noise spectroscopy in the last years. Some of our research highlights are SNS measurements in twodimensional semiconductors [3], the proof of concept to use SNS as a noncontact, spatiallyresolved doping measurement method for direct semiconductors [4], and the introduction of GHz spin noise spectroscopy [5] to overcome the bandwidth limitation of SNS. Current projects are, e.g., the experimental realization of Ultrafast SNS and SNS on Singly charged In(Ga)As/GaAs QDs.
[1] M. Oestreich, M. Römer, R. Haug, and D. Hägele, Spin Noise Spectroscopy in GaAs, Phys. Rev. Lett. 95, 216603 (2005).

[2] S. A. Crooker, D. G. Rickel, A. V. Balatsky, and D. L. Smith, Spectroscopy of spontaneous spin noise as a probe of spin dynamics and magnetic resonance, Nature 431, 49 (2004).

[3] G. Müller, M. Römer, D. Schuh, W. Wegscheider, J. Hübner, and M. Oestreich, Spin noise spectroscopy in GaAs (110) quantum wells: Access to intrinsic spin lifetimes and equilibrium electron dynamics, Phys. Rev. Lett. 101, 206601 (2008).

[4] M. Römer, J. Hübner, and M. Oestreich, Spatially resolved doping concentration measurement in semiconductors via spin noise spectroscopy, Appl. Phys. Lett. 94, 112105 (2009).

[5] G. Müller, M. Römer, J. Hübner, and M. Oestreich, GHz spin noise spectroscopy in ndoped bulk GaAs, Phys. Rev. B 81, 121202(R) (2010).

"Conventional" spin noise spectroscopy is limited by the bandwidth of the balanced photo receiver. This limitation can be overcome by replacing the continuous probe laser by a pulsed probe laser with a repitition rate of, e.g., 80 MHz. The stroboscopic effect maps domains of the noise power spectrum that reside continuously probed above the detection bandwith onto the detection bandwidth of the balanced receiver. These domains are centered around the multiple of the probe repitition rate (80 MHz) and have a width equal to the bandwidth of the balanced receiver. The effective slow down of spin fluctuations within the domains enables us to perform spin noise spectroscopy at ultrahigh frequencies up to several GHz [1].
The continuous bandwidth of the spin noise power spectrum up to theoretical 1 THz becomes accessible by applying a second probe pulse train in addition to the first one [2]. Two synchronized Ti:Sapphire lasers are used to provide the appropriate probe pulse sequence. The repitition rates of the lasers are slightly detuned to create a constantly increasing time delay Δt between both probe pulse trains. Although the detector cannot resolve two successive spin noise signals shifted by Δt, the average signal of both Faraday rotation angles can be used to get information about the correlation of both spin noise signals. Recording the correlation in dependence on Δt yields the autocorrelation of the spin noise and, hence, the continuous spin noise power spectrum.
The application of ultrafast spin noise spectroscopy is envisioned for studying magnetic phase transitions, for discovering incoherent dissipative dynamics of, e.g., current driven magnetic domain wall motion, and many other areas ranging from incoherent reaction dynamics in chemistry to noise in high frequency electronic devices [2].
[1] G. Müller, M. Römer, J. Hübner, and M. Oestreich, GHz spin noise spectroscopy in ndoped bulk GaAs, Phys. Rev. B 81, 121202(R) (2010).

[2] S. Starosielec and D. Hägele, Ultrafast spin noise spectroscopy, Appl. Phys. Lett. 93, 051116 (2008).

The strong localization of carriers in semiconductor quantum dots (~ 10 nm) weakens the highly efficient DyakonovPerel spin relaxation mechanism and enhances the spin relaxation due to hyperfine interaction. For negatively charged quantum dots, i.e., for electrons the hyperfine interaction with the randomly oriented ambient nuclear spins leads to spin relaxation times of about 500 ps [1]. The main contribution to hyperfine interaction for electrons is the Fermi contact term. For the ptype holes in the valence band the hyperfine interaction is of dipoledipole nature which is considerably smaller than the Fermi contact interaction. Accordingly, the hole spin relaxation time in quantum dots is even longer compared to electrons and of the order of 10 ns. These long spin relaxation times have drawn much attention in the last years on positively charged quantum dots and they are especially examined as a possible candidate for qubit implementation in solidstate based quantum information devices.
By means of a density gradient quantum dot (QD)sample containing In(Ga)As/GaAs quantum dots partially charged by holes stemming from a carbon background doping the spin relaxation time of the trapped holes is investigated by spin noise spectroscopy. Two Bragg mirrors enclosing the quantum dot region build a high finesse cavity facilitating spin noise measurements in backward direction. The measurements are carried out with a homebuilt probeinset for helium dewars that realizes an intrinsically longterm stable optical measurement system. The probeinset is equipped with a twodimensional vector magnetic field (up to 30 mT) and a threedimensional piezo positioning system.
Our experiments are carried out on an ensemble of quantum dots with a magnetic field parallel to the probe laser. The measurements reveal two distinct spin lifetimes of the trapped heavy holes that differ from each other by one order of magnitude [2]. The fast spin dephasing time T_2 of 27 ns is attributed to a spin orientation perpendicular to the randomly oriented nuclear magnetic field and agrees with previous measurements of Eble et al. [3]. The second spin lifetime T_l of 215 ns stems from the parallel spin orientation at which the stochastic nature of the nuclear magnetic field does not lead to spin dephasing in the quantum dot ensemble. Especially the very long T_l heavyhole spin relaxation time is significantly influenced by the laser excitation and, hence, a crucial parameter in the experiment. The size of the quantum dot ensemble is a second relevant parameter and spin noise measurements on single quantum dots are a prospective intention of our group.
[1] P.F. Braun et al., Direct Observation of the Electron Spin Relaxation Induced by Nuclei in Quantum Dots, Phys. Rev. Lett. 94, 116601 (2005).

[2] R. Dahbashi et al., Measurement of heavyhole spin dephasing in (InGa)As quantum dots, Appl. Phys. Lett. 100, 031906 (2012).

[3] B. Eble et al., HoleNuclear Spin Interaction in Quantum Dots, Phys. Rev. Lett. 102, 146601 (2009).

The ability to engineer the electron g factor in semiconductor structures is important for the coherent manipulation of electron spins and potential quantum information processing. An accurate knowledge of the effective electron g factor g* of the base material is required. However, the measured lowtemperature values of g* in GaAs vary by more than 10 % [13]. Furthermore, the g factor is one of the key parameters of semiconductors, and therefore well suited as a test parameter for band structure calculations. Former measurements of the temperature dependence of g* in GaAs have revealed a huge discrepancy to k·p calculations [4]. We performed detailed high precision measurements of the electron Landé factor g* in weakly ndoped GaAs determined by optical time and polarizationresolved spin quantum beat (SQB) spectroscopy (left figure: streak camera image of SQBs). The discrepancy between the measured temperature dependence of g* and accurate k·p calculations is confirmed and explained by a strong temperaturedependent interband matrix element [5]. At low temperatures, we find a strong interaction between the electron and nuclear spin system. The resulting dynamic nuclear polarization (DNP) and subsequent nuclear spin diffusion cause an effective magnetic field which drastically affects the measured g*. The value of the bare g* can be determined accurately by monitoring the timedependent nuclear polarization. Contemporaneously, these measurements allow an insight into nuclear spin dynamics. We systematically investigate the dependence of g* on excitation polarization, excitation energy, excitation density, external magnetic field, and temperature.
[1] C. Weisbuch and C. Hermann, Phys. Rev. B 15, 816 (1977).

[3] M. Seck, M. Potemski, and P. Wyder, Phys. Rev. B 56, 7422 (1997).

[3] J. S. Colton et al., Phys. Rev. B 67, 165315 (2003).

[4] M. Oestreich and W.W. Rühle, Phys. Rev. Lett. 74, 2315 (1995).

[5] J. Hübner et al., Phys. Rev. B 79, 193307 (2009).

Collaboration with R. Winkler
The electron spin excitation and detection using the spindependent selection rules for optical transitions provide a powerful tool for the investigation of spin dynamics in semiconductor quantum wells.[1] While the optical spin orientation for excitation in growth direction is well understood, few investigations have focused on the inplane orientation of electron spins. Yet it is, indeed, the latter orientation that is most interesting for several new spintronic devices such as edgeemitting quantum well lasers. Both accurate experimental investigations of optical orientation and a realistic theoretical treatment of this geometry are highly required, and these topics are the subject of our work. We study the optical orientation of electron spins in GaAs quantum wells using a light beam propagating parallel to the plane of the twodimensional (2D) system. A circularly polarized laser pulse is focused on the cleaved edge of the quantum wells thus creating spinpolarized electrons in the wells. Application of an inplane magnetic field perpendicular to the excitation direction leads to spin precession which we observe in the optical emission along the growth direction of the 2D system. From the polarization and timeresolved photoluminescence, we obtain the initial degree of electron spin polarization P_0 which is studied as a function of the excitation energy. In comparison with the optical orientation for excitation in growth direction, we observe a qualitatively different behavior of the energy dependence of P_0. While the former geometry yields a high degree of P_0 for excitation of the lowest heavyhole exciton, we now measure that P_0 is close to 0 near the HH1:E1 resonance. Above this resonance, we observe a significant spin orientation with a sign that is independent of the excitation energy. We compare our experimental data with accurate numerical calculations of the inplane excitonic absorption taking fully into account electronhole Coulomb correlations and heavyhole lighthole coupling. Our investigation shows that the direction of the optical excitation and detection is a new promising degree of freedom for the design of spintronic devices.
[1] S. Pfalz, R. Winkler, T. Nowitzki, D. Reuter, A.D. Wieck, D. Hägele, and M. Oestreich, Phys. Rev. B 71, 165305 (2005).

Collaboration with
We demonstrate a reduction of the threshold of a semiconductor laser by optically pumping spinpolarized electrons in the gain medium. [1] Polarized electrons couple selectively to one of two possible lasing light modes which effectively reduces the threshold by up to 50 % compared to conventional pumping with unpolarized electrons. We theoretically show that our concept can be generalized to an electrically pumped laser. The threshold current is an important figure of merit for every semiconductor laser and most important for applications, e.g., in telecommunication or reader heads in CD or DVD drives. Our research extends recent results of fundamental research to the first genuine proof that a spintronic device with obvious advantages over traditional electronics is possible.
[1] J. Rudolph et al., Laser threshold reduction in a spintronic device, Appl. Phys. Lett. 82, 4516 (2003).

For full understanding of the spin dynamics in an equilibrium system we use Rubidium gas as sample for spin noise spectroscopy (SNS). While linear spin noise spectroscopy is fully understood [1,2], nonlinear effects which occur in the atomic resonances still need explanations. Noise experiments with longitudinal magnetic field are frequently performed, but the transverseBfield method as used in SNS is used very rarely. We measure the nonlinearities and evaluate the complete theoretical model which describes the system. By comparing the measurements with theoretical curves, we get very good agreement for the evaluated theoretical Bloch equations [3]. Additionally, we prepare measurements on cold Rubidium atoms. Simulations show that it should be possible to measure the spin dynamics of cold gases.
[1] E. Aleksandrov and V. Zapassky, MagneticResonance In The FaradayRotation Noise Spectrum, ZhETF 81, 132 (1981).

[2] S. A. Crooker, D. G. Rickel, A. V. Balatsky, and D. L. Smith, Spectroscopy of spontaneous spin noise as a probe of spin dynamics and magnetic resonance, Nature 431, 49 (2004).

[3] H. Horn, G. M. Müller, E. Rasel, L. Santos, J. Hübner, and M. Oestreich, Spinnoise spectroscopy under resonant optical probing conditions: Coherent and nonlinear effects, Phys. Rev. A 84, 043851 (2011).

[4] C.H.H. Schulte, G.M. Müller, H. Horn, J. Hübner, and M. Oestreich, Analyzing atomic noise with a consumer sound card, Am. J. Phys.(2011)

We observe signatures of stimulated bosonic scattering of excitons, a precursor of BoseEinsteinCondensation (BEC), in the photoluminescence of semiconductor quantum wells. The optical decay of a spinless molecule of two excitons (biexciton) into an exciton and a photon with opposite angular momenta is subject to bosonic enhancement in the presence of other excitons. In a gas of biexcitons and spin polarized excitons the bosonic enhancement breaks the symmetry of two equivalent biexciton decay channels leading to circularly polarized luminescence of the biexciton with the sign opposite to the circularly polarized exciton luminescence. Comparison of experiment and many body theory corroborates stimulated scattering of excitons, but excludes the presence of a fully condensed BEClike state.
[1] D. Hägele, S. Pfalz, and M. Oestreich, Phys. Rev. Lett. 103, 146402 (2009). 