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We report on first observation of spin noise in a strongly birefringent semiconductor -- halide perovskite single crystal MAPbI$_3$. The observed spin noise resonance is ascribed to free holes with a record spin dephasing time of 4 ns. The spin dynamics is found to be affected by the residual light absorption of the crystal providing renormalization of the Larmor frequency. Extended spin noise spectroscopy with rotating magnetic field allowed us not only to evaluate the $g$-factor anisotropy, but also to distinguish two different spin subsystems tentatively associated to twinning of the crystal., Comment: 14 pages, 11 figures

We report on first direct observation of spontaneous fluctuations of birefringence in glasses doped with rare-earth (RE) ions. The fluctuations were observed in Nd$^{3+}$- and Yb$^{3+}$-doped glasses as polarization noise of the laser beam transmitted through the sample in the region of the RE-ion absorption. The noise was characterized by a flat (``white'') spectrum in the range of frequencies up to 1 GHz and did not show any dependence on magnetic field. The discovered polarization noise is interpreted in terms of structural dynamics of glasses revealed at low temperatures and usually described in the model of tunneling two-level systems (TLS). High sensitivity of the polarization noise technique to this dynamics is related to small homogeneous width of \textit{f-f} transitions of RE-ions in glasses and small spectral width of the probe laser light. The discovered effect provides a new experimental approach to studying low-temperature structural dynamics of different disordered matrices and interactions of impurities with environment in such media.

Exciton excited states in the quantum well are studied via their effect on the nonradiative broadening of the ground exciton resonance. Dependence of the nonradiative broadening of the ground exciton state on the photon energy of additional laser excitation was measured. Applying magnetic field up to 6 T, we could trace the formation of Landau levels and evolution of the exciton states of size quantization in a 14-nm GaAs/AlGaAs quantum well. Sensitivity of the technique allowed for observation of the second exciton state of size quantization, unavailable for conventional reflectance and photoluminescence spectroscopy. Our interpretation is supported by the numerical calculation of the exciton energies of the heavy-hole and light-hole subsystems. The numerical problems were solved using the finite-difference method on the nonuniform grid. The ground Landau level of the free electron-hole pair was observed and numerically analysed. In addition to energies of the excited states, electron hole distances and exciton-light interaction constant was investigated using the obtained in the numerical procedure exciton wave functions.

It is known that linear birefringence of the medium essentially hinders measuring the Faraday effect. For this reason, optically anisotropic materials have never been considered as objects of the Faraday-rotation-based spin noise spectroscopy (SNS). We show, both theoretically and experimentally, that strong optical anisotropy that may badly suppress the regular Faraday rotation of the medium, practically does not affect the measurement of the spatially uncorrelated spin fluctuations. An important consequence of this result is that the Faraday-rotation noise should be also insensitive to spatially nonuniform birefringence, which makes the SNS applicable to a wide class of optically anisotropic and inhomogeneous materials. We also show that the birefringent media provide additional opportunity to measure spatial spin correlations. Results of the experimental measurements of the spin-noise spectra performed on 4$f$--4$f$ transitions of Nd$^{3+}$ ions in the CaWO$_4$ and LiYF$_4$ crystals well agree with the theory., Comment: 5 pages, 2 figures

We show that in cubic crystals with anisotropic impurity centers the sum of squares of the magnetic resonance (EPR) frequencies is invariant with respect to the magnetic field direction. The connection between such an invariant and the g-tensor components of the impurity is derived for different types of centers. The established regularity is confirmed experimentally for the spin-noise spectra of a CaF2-Nd3+ crystal. We show how this property of the EPR spectra can be efficiently used for the assignment of paramagnetic centers in cubic crystals., Comment: 5 pages, 2 figures

The MAPbI$_3$ halide perovskite single crystals are studied at 5 K temperature using the photoluminescence excitation spectroscopy. Two non-interacting types of states are determined: bound excitons and defect-related states. Excitation of the crystal with light energy below the bound exciton resonance reveals the complex low-density defects emission, otherwise hidden by the emission of bound excitons. A way to separate these defect-related luminescence spectra is proposed, and the thorough study of this emission regime is carried out. The results of this study opens an area of low-density defects and dopants exploration in halide perovskite semiconductors.

Bose-Einstein condensates of exciton-polaritons are known for their fascinating coherent and polarization properties. The spin state of the condensate is reflected in polarization of the exciton-polariton emission, with temporal fluctuations of this polarization being, in general, capable of reflecting quantum statistics of polaritons in the condensate. To study the polarization properties of optically trapped polariton condensates, we take advantage of the spin noise spectroscopy technique. The ratio between the noise of ellipticity of the condensate emission and its polarization plane rotation noise is found to be dependent, in a nontrivial way, on the intensity of CW nonresonant laser pumping. We show that the interplay between the ellipticity and the rotation noise can be explained in terms of the competition between the self-induced Larmor precession of the condensate pseudospin and the static polarization anisotropy of the microcavity., Comment: 5 pages, 3 figures

Spin noise spectroscopy is a method of magnetic resonance widely used, nowadays, in atomic and semiconductor research. Classical objects of the EPR spectroscopy - dielectrics with paramagnetic impurities - seemed to be unsuitable for this technique because of large widths of allowed optical transitions and, therefore, low specific Faraday rotation (FR). We show, however, that the FR noise detected at the wavelength of a weak optical transition (with low regular FR) may increase by many orders of magnitude as its homogeneous width decreases. This spin-noise gain effect, numerically described by the ratio of the inhomogeneous linewidth to homogeneous, relates primarily to forbidden intraconfigurational transitions of impurity ions with unfilled inner electronic shells. Specifically, for the f-f transitions of rare-earth ions in crystals, this factor may reach 10$^8$. In this paper, we report on the first successful application of spin noise spectroscopy for detecting magnetic resonance of rare-earth ions in crystals., Comment: 5 pages, 3 figures

In the spin noise spectroscopy, the magnetic susceptibility spectrum is known to be provided by the spin-system untouched by any external perturbation, or, better to say, disturbed only by its thermal bath. We propose a new version of the spin noise spectroscopy, with the detected magnetization (Faraday-rotation) noise being stimulated by an external fluctuating magnetic field with a quasi-white spectrum. Experimental study of the stimulated spin noise performed on a $\text{BaF}_2 : \text{U}^{3+}$ crystal in a longitudinal magnetic field has revealed specific features of this approach and allowed us to identify the Van-Vleck and population-related contributions to the AC susceptibility of the system and to discover unusual magnetic-field dependence of the longitudinal spin relaxation rate in low magnetic fields. It is shown that spectra of the stimulated and spontaneous spin noise, being both closely related to the spin-system magnetic susceptibility, are still essentially different. Distinctions between the two types of the spin-noise spectra and two approaches to the spin noise spectroscopy are discussed., Comment: 6 pages, 6 figures

We report the observation of tens of minor lines of the combinational spin-flip Raman scattering in a CdTe:Mn quantum well by means of the high-resolution optical spectroscopy. Classification of this manifold leads to four characteristic values of energy, that correspond to four different types of pair clusters of Mn ions: the nearest, second, third etc. neighbors. All the four energies show up in a single experiment with a very high precision, providing experimental grounds for a deeper understanding of the d-d exchange interactions in a diluted magnetic semiconductor and demonstrating the capacity of the employed method. The major (nearest-neighbor) exchange constant J_1 = 6.15 K was found to consent with its previously reported value. Other detected characteristic energies are as follows: J_{(2)} = 1.80 K, J_{(3)} = 1.39 K, J_{(4)} = 0.81 K., Comment: 11 pages, 2 figures

Nuclear spin relaxation is studied in n-GaAs thick layers and microcavity samples with different electron densities. We reveal that both in metallic samples where electrons are free and mobile, and in insulating samples, where electrons are localized, nuclear spin relaxation is strongly enhanced at low magnetic field. The origin of this effect could reside in the quadrupole interaction between nuclei and fluctuating electron charges, that has been proposed to drive nuclear spin dynamics at low magnetic fields in the insulating samples. The characteristic values of these magnetic fields are given by dipole-dipole interaction between nuclei in bulk samples, and are greatly enhanced in microcavities, presumably due to additional strain, inherent to micro and nanostructures., Comment: 11 pages, 4 figures

The single scattering theory is applied to spin noise spectroscopy (SNS). The case of two Gaussian probe beams tilted with respect to each other is analysed. It is shown that SNS signal in this case carry information about spatial correlations of studied gyrotropic medium., Comment: 13 pages, 1 figure

We report on experimental study of the exciton-polariton emission (PE) polarization noise below and above the polariton lasing threshold under continuous wave nonresonant excitation. The experiments were performed with a high-Q graded 5{\lambda}/2 GaAs/AlGaAs microcavity with three quantum wells in the strong coupling regime. The PE polarization noise substantially exceeded in magnitude the shot noise level and, in the studied frequency range (up to 650 MHz), had a flat spectrum. We have found that the PE polarization noise magnitude dependence on the pump intensity showed specific features that had no analogy in power dependences of the PE intensity and intensity noise. Particularly, the linear polarization fluctuations normalized by the emission intensity showed a remarkably non-monotonic dependence on the pump power. A theoretical model describing the observed peculiarity of the PE polarization noise is proposed., Comment: 5 pages, 4 figures

Recently reported optical nuclear orientation in the $n$-doped GaAs microcavity under pumping in nominal transparency region of the crystal [Appl. Phys. Lett. $\mathbf{106}$, 242405 (2015)] has arisen a number of questions, the main of them concerning mechanisms of angular momentum transfer from the light to the nuclear spin system and the nature of the light-related magnetic fields accompanying the optical nuclear polarization. In this paper, we use the spin noise spectroscopy for magnetometric purposes, particularly, to study effective fields acting upon electron spin system of an $n$-GaAs layer inside a high-Q microcavity in the presence of elliptically polarized probe beam. In addition to the external magnetic field applied to the sample in the Voigt geometry and the Overhauser field created by optically oriented nuclei, the spin noise spectrum reveals an additional effective, "optical," magnetic field produced by elliptically polarized probe itself. This field is directed along the light propagation axis, with its sign being determined by the sign of the probe helicity and its magnitude depending on degree of circular polarization and intensity of the probe beam. We analyze properties of this optical magnetic field and suggest that it results from the optical Stark effect in the field of the elliptically polarized electromagnetic wave., Comment: 9+ pages, 7 figures

We exploit spin noise spectroscopy (SNS) to directly observe build-up of dynamic nuclear polarization and relaxation of a perturbed nuclear spin-system to its equilibrium state in a single-shot experiment. The SNS experiments were performed on a layer of bulk $n$-type GaAs embedded into a high-finesse microcavity with negative detuning. The dynamic nuclear spin polarization is observed as a shift of the peak in the electron spin noise spectrum due to the build-up of the Overhauser field acting on the electron spin. The relaxation dynamics of nuclear spin system was revealed in the time-resolved SNS experiments where the exponential decay of the Overhauser field with characteristic timescale of hundreds of seconds was detected. We show that elliptically polarized laser beam tuned in resonance with the cavity mode, whose energy corresponds to nominal transparency of the semiconductor, can nevertheless produce a sizable nuclear polarization., Comment: 4 pages and 3 figures

The spin-fluctuations-related Kerr rotation noise of the optical beam reflected from a microcavity with a quantum well in the intermirror gap is studied. In the regime of anti-crossing of the cavity polariton branches, the several hundred times enhancement of the noise signal, or giant noise, is observed. The effect of the amplification of the noise signal is explained by the nonlinear instability of the microcavity. In the frame of the developed model of built-in amplifier, the non-trivial properties of the noise signal in the regime of the negative detuning of microcavity are described., Comment: 10 pages, 5 figures

The optical gyrotropy noise of a high-finesse semiconductor Bragg microcavity with an embedded quantum well (QW) is studied at different detunings of the photon mode and the QW exciton resonances. A strong suppression of the noise magnitude for the photon mode frequencies lying above exciton resonances is found. We show that such a critical behavior of the observed optical noise power is specific of asymmetric Fabry-Perot resonators. As follows from our analysis, at a certain level of intracavity loss, the reflectivity of the asymmetric resonator vanishes, while the polarimetric sensitivity to the gyrotropy changes dramatically when moving across the critical point. The results of model calculations are in a good agreement with our experimental data on the spin noise in a single-quantum-well microcavity and are confirmed also by the spectra of the photo-induced Kerr rotation in the pump-probe experiments., Comment: 6 pages, 5 figures

We report on the first experimental observation of spin noise in a single semiconductor quantum well embedded into a microcavity. The great cavity-enhanced sensitivity to fluctuations of optical anisotropy has allowed us to measure the Kerr rotation and ellipticity noise spectra in the strong coupling regime. The spin noise spectra clearly show two resonant features: a conventional magneto-resonant component shifting towards higher frequencies with magnetic field and an unusual "nonmagnetic" component centered at zero frequency and getting suppressed with increasing magnetic field. We attribute the first of them to the Larmor precession of free electron spins, while the second one being presumably due to hyperfine electron-nuclei spin interactions., Comment: 5 pages, 6 figures + supplement (4 pages, 1 figure)

We attract attention to the fact that the ultimate (shot-noise-limited) polarimetric sensitivity can be enhanced by orders of magnitude leaving the photon flux incident onto the photodetector on the same low level. This opportunity is of crucial importance for present-day spin noise spectroscopy, where a direct increase of sensitivity by increasing the probe beam power is strongly restricted by the admissible input power of the broadband photodetectors. The gain in sensitivity is achieved by replacing the 45-deg polarization geometry commonly used in conventional schemes with balanced detectors by geometries with stronger polarization extinction. The efficiency of these high-extinction polarization geometries with enhancement of the detected signal by more than an order of magnitude is demonstrated by measurements of the spin noise spectra of bulk n:GaAs in the spectral range 835-918 nm. It is shown that the inevitable growth of the probe beam power with the sensitivity gain makes spin noise spectroscopy much more perturbative, but, at the same time, opens up fresh opportunities for studying nonlinear interactions of strong light fields with spin ensembles., Comment: 8 pages, 9 figures