Spatiotemporal spin noise spectroscopy is combined with dynamic light scattering in order to reach spatial resolutions down to ∼λ/10. Applied to a system of localized electron spins, an insulating n-doped CdTe layer, this allows us to reveal long spin jump distances ∼ 2.7 μm. Spin noise spectra at large wave vectors q (q 1) provide a snapshot of the spin dynamics before jump (therefore not affected by spin motion), while at smaller q, spin motion sets in. This allows us to unravel the contributions of spin-orbit and hyperfine fields in the electron spin relaxation and to determine self-consistently all parameters relevant to the spin dynamics. We propose a phenomenological equation inspired by studies of atomic jump diffusion by neutron scattering, which includes the relevant spin relaxation mechanisms and the effect of time of flight of the spin fluctuation across the laser spot. This modeling reproduces all experimental results.

We report on the dynamics of electron spins in n-doped CdTe layers that differs significantly from the expected response derived from the studies dedicated to electron spin relaxation in n-GaAs. At zero magnetic field, the electron spin noise spectra exhibit a two-peak structure-a zero-frequency line and a satellite-that we attribute to the electron spin precession in a frozen random nuclear spin distribution. This implies a surprisingly long electron spin correlation time whatever the doping level, even above the Mott transition. Using spatiotemporal spin noise spectroscopy, we demonstrate that the observation of a satellite in the spin noise spectra and a fast spin diffusion are mutually exclusive. This is consistent with a shortening of the electron spin correlation time due to hopping between donors. We interpret our data via a model assuming that the low temperature spin relaxation is due to hopping between donors in presence of hyperfine and anisotropic exchange interactions. Most of our results can be interpreted in this framework. First, a transition from inhomogeneous to homogeneous broadening of the spin noise peaks and the disappearance of the satellite are observed when the hopping rate becomes larger than the Larmor period induced by the local nuclear fields. In the regime of homogeneous broadening the ratio between the spin diffusion constant and the spin relaxation rate has a value in good agreement with the Dresselhaus constant. In the regime of inhomogeneous broadening, most of the samples exhibit a broadening consistent with the distribution of local nuclear fields. We obtain a new estimate of the hyperfine constants in CdTe and a value of 0.10 Tesla for the maximum nuclear field. Finally, our study also reveals a puzzle as our samples behave as if the active donor concentration was reduced by several orders of magnitudes with respect to the nominal values.

We report on the potential of a new spin noise spectroscopy approach by demonstrating all-optical probing of spatiotemporal spin fluctuations. This is achieved by homodyne mixing of a spatially phase-modulated local oscillator with spin-flip scattered light, from which the frequency and wave vector dependence of the spin noise power is unveiled. As a first application of the method we measure the spatiotemporal spin noise in weakly n-doped CdTe layers, from which the electron spin diffusion constant and spin relaxation rates are determined. The absence of spatial spin correlations is also shown for this particular system.

Cooling of nuclear spins in doped semiconductors via their dynamic polarization by optical pumping is a powerful method for harnessing ubiquitous fluctuations of nuclear spin, which constitute a well-known decoherence channel for the electronic spins. The idea of spin cooling is based on the hypothesis of spin temperature, which states that nuclear spin system (NSS) reaches an internal thermal equilibrium long before it comes to equilibrium with the external bath (crystal lattice). Although thermodynamic framework has been successfully employed for the description of a variety of the experimental data, a rigorous check of this concept in semiconductors was impossible until recently, in particular at low magnetic field. The reason for that is the lack of experimental techniques allowing nonperturbative optical control over adiabatic transformation of the NSS.We have recently developed such methods, based on off-resonant Faraday rotation and spin noise spectroscopy [1, 2]. Using these techniques, combined with dark-interval photoluminescence spectroscopy, we established a comprehensive picture of the nuclear spin relaxation efficiency, its magnetic field, temperature, and carrier concentration dependence in doped GaAs, a model system in the field of nuclear spin physics in semiconductors [3-5]. We also analyzed the interplay between four relevant relaxation mechanisms: hyperfine interaction, quadrupole interaction, spin diffusion and Korringa mechanisms.Understanding of field dependence of NSS dynamics allowed us to obtain a new insight into the NSS thermodynamics, and verify the spin temperature concept in GaAs bulk material and microcavities [6]. We have demonstrated, that NSS exactly follows the predictions of the spin temperature theory, despite the quadrupole interaction that was earlier reported to disrupt nuclear spin thermalization in quantum dots [7]. Our results open a way for the deep cooling of nuclear spins in semiconductor structures, with the prospect of realizing nuclear spin-ordered states for high-fidelity spin-photon interfaces.This work is supported by a joint grant of the Russian Foundation for Basic Research (RFBR, Grant No. 16-52-041301-4 and National Center for Scientific Research (CNRS, PRC SPINCOOL No. 148362)References:[1] R. Giri et al, Physical Review Letters, 111, 087603 (2013)[2] I. I. Ryzhov et al, Applied Physics Letters, 106, 242405 (2015)[3] M. Kotur et al, Physical Review B, 94(8), 081201 (2016)[4] M. Vladimirova et al, Physical Review B, 95, 125312 (2017)[5] M. Kotur et al, eprint arXiv:1802.05013 (2018)[6] M. Vladimirova et al, Physical Review B, 97, 041301 (2018)[7] P. Maletinsky et al, Nature Physics, 5, 407 (2009)

Cooling of nuclear spin system (NSS) in doped semiconductors via dynamic polarization by optical pumping is a powerful method for harnessing ubiquitous fluctuations of nuclear spin. The idea of NSS cooling is based on the hypothesis of spin temperature, which states that NSS reaches an internal thermal equilibrium long before it comes to equilibrium with the external bath (crystal lattice). Although thermodynamic framework has been successfully employed for the description of a variety of the experimental data, a rigorous check of this concept in semiconductors was impossible until recently, in particular at low magnetic field. The reason for that is the lack of experimental techniques allowing nonperturbative optical control over adiabatic transformation of the NSS. We have recently developed such methods, based on off-resonant Faraday rotation and spin noise spectroscopy [1,2]. Using these techniques, combined with photoluminescence spectroscopy, we established a comprehensive picture of the nuclear spin relaxation efficiency, its magnetic field, temperature, and carrier concentration dependence in both n- and p-doped GaAs, a model system in the field of nuclear spin physics in semiconductors [3-5]. We also analyzed the interplay between four relevant relaxation mechanisms: hyperfine interaction, quadrupole interaction, spin diffusion towards paramagnetic impurities, and Korringa mechanisms. Figure 1 illustrates these processes in a nuclei-electron coupled system. Understanding of field dependence of NSS dynamics allowed us to obtain a new insight into the NSS thermodynamics, and verify the spin temperature concept in GaAs bulk material and microcavities [6]. We have demonstrated that NSS exactly follows the predictions of the spin temperature theory, despite the quadrupole interaction that was earlier reported to disrupt nuclear spin thermalization in quantum dots [7]. These results open a way for the deep cooling of nuclear spins in semiconductor structures, with the prospect of realizing nuclear spin-ordered states for high-fidelity spin-photon interfaces. References[1] R. Giri et al, Physical Review Letters, 111, 087603 (2013)[2] I. I. Ryzhov et al, Applied Physics Letters, 106, 242405 (2015)[3] M. Kotur et al, Physical Review B, 94, 081201(R) (2016)[4] M. Vladimirova et al, Physical Review B, 95, 125312 (2017)[5] M. Kotur et al, Physical Review B, 97, 165206 (2018)[6] M. Vladimirova et al, Physical Review B, 97, 041301 (2018)[7] P. Maletinsky et al, Nature Physics, 5, 407 (2009)

Density and spin dynamics of indirect excitons in asymmetric GaAs/AlGaAs coupled quantum wells is studied by time-resolved photoluminescence. Under electric bias applied in the growth direction the lifetime of indirect excitons formed by an electron in a wide and hole in a narrow quantum well reaches 12 ns, while the circular polarisation lifetime is about 5 ns. The structure is suited for further studies of dark indirect excitons by time-resolved pump-probe spectroscopy

spin fluctuations in atomic vapors and in semiconductors. As such it is quite attractive for probing non-perturbatively electrons or nuclear spins in atomic vapours or in semiconductors, particularly when the laser is detuned from optical resonances, an aspect which has triggered considerable interest to spin noise spectroscopy in recent years. The signal in spin noise spectroscopy can be considered as arising from intensity fluctuations due to the interference between the light scattered by Raman spin-flip excitations and the probe laser. This suggests that homodyne or heterodyne detection of spin noise by mixing of the Raman signal with a local oscillator is feasible, which we have demonstrated recently [1]. This opportunity is essential to spin noise spectroscopy because it allows us to increase its sensitivity and accessible frequency range.Homodyne and/or heterodyne detection of spin noise for scattered light directions different from that of the probe should give access to spatio-temporal spin correlations [2], and therefore could considerably extend the application range of spin noise spectroscopy. Here we demonstrate non-collinear homodyne detection of spin noise in n-doped CdTe epilayers. This allows us to exploit different scattering geometries based on spin-flip Raman selection rules. We are able to measure simultaneously different fluctuating spin components by homodyne mixing in different space directions, and also for different local oscillator polarizations. [1] S. Cronenberger and D. Scalbert, Review of Scientific Instruments 87, 093111 (2016).[2] G. G. Kozlov, I. I. Ryzhov, and V. S. Zapasskii, Phys. Rev. A 95, 043810 (2017).