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We report measurements of the longitudinal and transverse spin relaxation times of holes in an ensemble of self-assembled InAs/InAlGaAs quantum dots (QDs), emitting in the telecom spectral range. The spin coherence of a single carrier is determined using spin mode-locking in the inhomogeneous ensemble of QDs. Modeling the signal allows us to extract the hole spin coherence time to be in the range of T$_2 = 0.02-0.4$ $\mu$s. The longitudinal spin relaxation time T$_1 = 0.5$ $\mu$s is measured using the spin inertia method.

Crystals spontaneously break the continuous translation symmetry in space, despite the invariance of the underlying energy function. This has triggered suggestions of time crystals analogously lifting translational invariance in time. Originally suggested for closed thermodynamic systems in equilibrium, no-go theorems prevent the existence of time crystals. Proposals for open systems out of equilibrium led to the observation of discrete time crystals subject to external periodic driving to which they respond with a sub-harmonic response. A continuous time crystal is an autonomous system that develops periodic auto-oscillations when exposed to a continuous, time-independent driving, as recently demonstrated for the density in an atomic Bose-Einstein condensate with a crystal lifetime of a few ms. Here we demonstrate an ultra-robust continuous time crystal in the nonlinear electron-nuclear spin system of a tailored semiconductor with a coherence time exceeding hours. Varying the experimental parameters reveals huge stability ranges of this time crystal, but allows one also to enter chaotic regimes, where aperiodic behavior appears corresponding to melting of the crystal. This novel phase of matter opens the possibility to study systems with nonlinear interactions in an unprecedented way., Comment: 12 figures, 17 pages

The class of Ruddlesden-Popper type (PEA)$_2$PbI$_4$ perovskites comprises two-dimensional (2D) structures whose optical properties are determined by excitons with a large binding energy of about 260 meV. It complements the family of other 2D semiconductor materials by having the band structure typical for lead halide perovskites, that can be considered as inverted compared to conventional III-V and II-VI semiconductors. Accordingly, novel spin phenomena can be expected for them. Spin-flip Raman scattering is used here to measure the Zeeman splitting of electrons and holes in a magnetic field up to 10 T. From the recorded data, the electron and hole Land\'e factors ($g$-factors) are evaluated, their signs are determined, and their anisotropies are measured. The electron $g$-factor value changes from $+2.11$ out-of-plane to $+2.50$ in-plane, while the hole $g$-factor ranges between $-0.13$ and $-0.51$. The spin flips of the resident carriers are arranged via their interaction with photogenerated excitons. Also the double spin-flip process, where a resident electron and a resident hole interact with the same exciton, is observed showing a cumulative Raman shift. Dynamic nuclear spin polarization induced by spin-polarized holes is detected in corresponding changes of the hole Zeeman splitting. An Overhauser field of the polarized nuclei acting on the holes as large as $0.6$ T can be achieved.

Coherent control of ensembles of light emitters by means of multi-wave mixing processes is key for the realization of high capacity optical quantum memories and information processing devices. In this context, semiconductor quantum dots placed in optical microcavities represent excellent candidates to explore strong light-matter interactions beyond the limits of perturbative non-linear optics and control the unitary evolution of optically driven quantum systems. In this work, we demonstrate that a sequence of two optical picosecond pulses can be used to establish coherent control over the phase evolution of the ensemble of trions in (In,Ga)As quantum dots independent of their initial quantum state. Our approach is based on coherent transfer between degenerate multi-wave-mixing signals in the strong field limit where Rabi rotations in multi-level systems take place. In particular, we use the two-pulse photon echo sequence to uncover the coherent dynamics of the trion ensemble, whereas the areas of two additional control pulses serve as tuning knobs for adjusting the magnitude and timing of the coherent emission. Furthermore, we make use of the spin degeneracy of ground and excited state of trions to control the polarization state of the emitted signal. Surprisingly, we reveal that the use of optical control pulses, whose durations are comparable to the dephasing time of the ensemble, lifts the temporal degeneracy between wave-mixing processes of different order. This phenomenon is manifested in a significant modification of the temporal shape of the coherent optical response for strong optical fields. Lifting the temporal degeneracy allows to smoothly trace the transition from the perturbative to the regime of Rabi rotations and opens up new possibilities for the optical investigation of complex energy level structures in so far unexplored material systems.

The photovoltaic and optoelectronic properties of lead halide perovskite semiconductors are controlled by excitons, so that investigation of their fundamental properties is of critical importance. The exciton Land\'e or g-factor g_X is the key parameter, determining the exciton Zeeman spin splitting in magnetic fields. The exciton, electron and hole carrier g-factors provide information on the band structure, including its anisotropy, and the parameters contributing to the electron and hole effective masses. We measure g_X by reflectivity in magnetic fields up to 60 T for lead halide perovskite crystals. The materials band gap energies at a liquid helium temperature vary widely across the visible spectral range from 1.520 up to 3.213 eV in hybrid organic-inorganic and fully inorganic perovskites with different cations and halogens: FA_{0.9}Cs_{0.1}PbI_{2.8}Br_{0.2], MAPbI_{3}, FAPbBr_{3}, CsPbBr_{3}, and MAPb(Br_{0.05}Cl_{0.95})_{3}. We find the exciton g-factors to be nearly constant, ranging from +2.3 to +2.7. Thus, the strong dependences of the electron and hole g-factors on the band gap roughly compensate each other when combining to the exciton g-factor. The same is true for the anisotropies of the carrier g-factors, resulting in a nearly isotropic exciton g-factor. The experimental data are compared favorably with model calculation results.

Coherent many-body states are highly promising for robust and scalable quantum information processing. While far-reaching theoretical predictions have been made for various implementations, direct experimental evidence of their appealing properties can be challenging. Here, we demonstrate coherent optical manipulation of the nuclear spin ensemble in the lead halide perovskite semiconductor FAPbBr$_3$ (FA=formamidinium), targeting a long-postulated collective dark state that is insensitive to optical pumping. Via optical orientation of localized hole spins we drive the nuclear many-body system into an entangled state, requiring a weak magnetic field of only a few Millitesla strength at cryogenic temperatures. During its fast build-up, the nuclear polarization along the optical axis remains small, while the transverse nuclear spin fluctuations are strongly reduced, corresponding to spin squeezing as evidenced by a strong violation of the generalized nuclear squeezing-inequality with $\xi_s < 0.3$. The dark state evidenced in this process corresponds to an approximately 750-body entanglement between the nuclei. Dark nuclear spin states can be exploited to store quantum information benefiting from their long-lived many-body coherence and to perform quantum measurements with a precision beyond the standard limit.

The exciton recombination and spin dynamics in (In,Al)As/AlAs quantum dots (QDs) with indirect band gap and type-I band alignment are studied. The negligible (less than $0.2~\mu$eV) value of the anisotropic exchange interaction in these QDs prevents a mixing of the excitonic basis states with pure spin and allows for the formation of spin polarized bright excitons for quasi-resonant circularly polarized excitation. In a longitudinal magnetic field, the recombination and spin dynamics of the excitons are controlled by the hyperfine interaction between the electron and nuclear spins. A QD blockade by dark excitons is observed in magnetic field eliminating the impact of the nuclear spin fluctuations. A kinetic equation model, which accounts for the population dynamics of the bright and dark exciton states as well as for the spin dynamics, has been developed, which allows for a quantitative description of the experimental data., Comment: 17 pages, 11 figures

Quantum measurement back action is fundamentally unavoidable when manipulating electron spins. Here we demonstrate that this back action can be efficiently exploited to tune the spin relaxation of localized electrons induced by the hyperfine interaction. In optical pump-probe experiments, powerful probe pulses suppress the spin relaxation of electrons on Si donors in an InGaAs epilayer due to the quantum Zeno effect. By contrast, an increase of the probe power leads to a speed up of the spin relaxation for electrons in InGaAs quantum dots due to the quantum anti-Zeno effect. The microscopic description shows that the transition between the two regimes occurs when the spin dephasing time is comparable to the probe pulse repetition period., Comment: 6+5 pages, 2+8 figures

We report on the experimental and theoretical studies of optical alignment and optical orientation effects in an ensemble of core/shell CdSe/CdS colloidal nanoplatelets. The dependences of three Stokes parameters on the magnetic field applied in the Faraday geometry are measured under continuous wave resonant excitation of the exciton photoluminescence. Theoretical model is developed to take into account both bright and dark exciton states in the case of strong electron and hole exchange interaction and random in-plane orientation of the nanoplatelets in ensemble. The data analysis allows us to estimate the time and energy parameters of the bright and dark excitons. The optical alignment effect enables identification of the exciton and trion contributions to the photoluminescence spectrum even in the absence of a clear spectral line resolution., Comment: main paper (17 pages) and SI (6 pages)

A trion magnetic polaron formed by the exchange interaction of a positively charged exciton (trion) with localized spins of Mn$^{2+}$ ions is found experimentally in a 4\,nm wide Cd$_{0.98}$Mn$_{0.02}$Te/Cd$_{0.78}$Mn$_{0.02}$Mg$_{0.2}$Te quantum well containing resident holes. The experiment is performed at a temperature of 1.6 K using resonant excitation of the trion with circularly polarized light. The trion is formed from a resident hole, which is in a hole magnetic polaron state, and a photogenerated electron-hole pair. The dynamical evolution from the hole magnetic polaron to the trion magnetic polaron is accompanied by a spin-flip of the electron, which results in negative circular polarization of the photoluminescence. The degree of circular polarization reaches $-8\%$ at zero magnetic field and strongly decreases in transverse magnetic fields exceeding 0.2 T. Our model considerations show that different localization sizes of the resident and photogenerated holes and the resulting difference in their exchange interaction with the Mn$^{2+}$ spins maintains Mn spin polarization. The resulting exchange field of Mn acting on the electron provides a robust spin polarization of the trion magnetic polaron. We evaluate the electron exchange energy in the T$^+$MP to be 0.19~meV, and the T$^+$MP binding energy to be about 0.5 - 1 meV.

We discuss the implications of a small indium content (3%) in a GaAs epilayer on the electron- and nuclear-spin relaxation due to enhanced quadrupolar effects induced by the strain. Using the weakly perturbative spin-noise spectroscopy, we study the electron-spin relaxation dynamics without explicit excitation. The observed temperature dependence indicates the presence of localized states, which have an increased interaction with the surrounding nuclear spins. Time-resolved spin-noise spectroscopy is then applied to study the relaxation dynamics of the optically pumped nuclear-spin system. It shows a multi-exponential decay with time components, ranging from several seconds to hundreds of seconds. Further, we provide a measurement of the local magnetic field acting between the nuclear spins and discover a strong contribution of quadrupole effects. Finally, we apply the nuclear spin diffusion model, that allows us to estimate the concentration of the localized carrier states and to determine the nuclear spin diffusion constant characteristic for this system., Comment: 13 pages, 9 figures

The spin physics of perovskite nanocrystals with confined electrons or holes is attracting increasing attention, both for fundamental studies and spintronic applications. Here, stable CsPb(Cl$_{0.5}$Br$_{0.5}$)$_3$ lead halide perovskite nanocrystals embedded in a fluorophosphate glass matrix are studied by time-resolved optical spectroscopy to unravel the coherent spin dynamics of holes and their interaction with nuclear spins of the $^{207}$Pb isotope. We demonstrate the spin mode locking effect provided by the synchronization of the Larmor precession of single hole spins in each nanocrystal in the ensemble that are excited periodically by a laser in an external magnetic field. The mode locking is enhanced by nuclei-induced frequency focusing. An ensemble spin dephasing time $T_2^*$ of a nanosecond and a single hole spin coherence time of $T_2=13\,$ns are measured. The developed theoretical model accounting for the mode locking and nuclear focusing for randomly oriented nanocrystals with perovskite band structure describes the experimental data very well., Comment: Main paper of 9 pages and 3 figures. Supplementary material of 16 pages and 12 figures

We study Rabi rotations arising in intensity-dependent photon echoes from an ensemble of self-assembled InGaAs quantum dots. To achieve a uniform distribution of intensities within the excited ensemble, we introduce flattop intensity profiles of picosecond laser pulses. This allows us to overcome the damping of Rabi rotations imposed by the spatial inhomogeneity of Rabi frequencies by a Gaussian laser profile. Using photon echo polarimetry, we distinguish between the coherent optical responses from exciton and trion ensembles. Here, we demonstrate that a photo-induced charging of the quantum dots leads to a significant reduction of the number of neutral quantum dots under resonant excitation with intensive optical pulses with areas exceeding $\frac{\pi}{2}$. The trion ensemble shows robust Rabi rotations when the area of the refocussing pulse is increased up to 5.5$\pi$. We analyze the remaining attenuation of Rabi rotations by theoretical modeling of excitation induced dephasing, inhomogeneity of dipole moments, and coupling to acoustic phonons. The latter is identified as the dominating mechanism resulting in a loss of optical coherence during the action of the involved optical pulses.

The ability to extend the time scale of the coherent optical response from large ensembles of quantum emitters is highly appealing for applications in quantum information devices. In semiconductor nanostructures, spin degrees of freedom can be used as auxiliary, powerful tools to modify the coherent optical dynamics. Here, we apply this approach to negatively charged (In,Ga)As/GaAs self-assembled quantum dots which are considered as excellent quantum emitters with robust optical coherence and high bandwidth. We study 3-pulse spin-dependent photon echoes subject to moderate transverse magnetic fields up to 1 T. We demonstrate that the timescale of coherent optical response can be extended by at least an order of magnitude by the field. Without magnetic field, the photon echo decays with $T_ 2$ = 0.45 ns which is determined by the radiative lifetime of trions $T_1$ = 0.27 ns. In the presence of the transverse magnetic field, the decay of the photon echo signal is given by spin dephasing time of the ensemble of resident electrons $T_{2,e}$ ~ 4 ns. We demonstrate that the non-zero transverse g-factor of the heavy holes in the trion state plays a crucial role in the temporal evolution and magnetic field dependence of the long-lived photon echo signal., Comment: 9 pages, 4 figures, Supplementary material

Methylammonium lead triiodine (MAPbI$_3$) is a material representative of the hybrid organic-inorganic lead halide perovskites which attract currently great attention due to their photovoltaic efficiency and bright optoelectronic properties. Here, the coherent spin dynamics of charge carriers and spin dependent phenomena induced by the carrier interaction with nuclear spins are studied in MAPbI$_3$ single crystals, using time-resolved Kerr rotation at cryogenic temperatures in magnetic fields up to 3 T. Spin dephasing times up to a few nanoseconds and a longitudinal spin relaxation time of 37 ns are measured. The Larmor spin precession of both resident electrons and holes is identified in the Kerr rotation signals. The Land\'e factors ($g$-factors) in the orthorhombic crystal phase show a strong anisotropy, ranging for the holes from $-0.28$ to $-0.71$ and for the electrons from $+2.46$ to $+2.98$, while the $g$-factor dispersion of about 1% is rather small. An exciton $g$-factor of $+2.3$ is measured by magneto-reflectivity. A dynamic nuclear polarization by means of spin polarized electrons and holes is achieved in tilted magnetic fields giving access to the carrier-nuclei exchange interaction and the nuclei spin relaxation time exceeding 16 minutes.

The Land\'e or $g$-factors of charge carriers are decisive for the spin-dependent phenomena in solids and provide also information about the underlying electronic band structure. We present a comprehensive set of experimental data for values and anisotropies of the electron and hole Land\'e factors in hybrid organic-inorganic (MAPbI$_3$, MAPb(Br$_{0.5}$Cl$_{0.5}$)$_3$, MAPb(Br$_{0.05}$Cl$_{0.95}$)$_3$, FAPbBr$_3$, FA$_{0.9}$Cs$_{0.1}$PbI$_{2.8}$Br$_{0.2}$) and all-inorganic (CsPbBr$_3$) lead halide perovskites, determined by pump-probe Kerr rotation and spin-flip Raman scattering in magnetic fields up to 10~T at cryogenic temperatures. Further, we use first-principles DFT calculations in combination with tight-binding and $\mathbf k \cdot \mathbf p$ approaches to calculate microscopically the Land\'e factors. The results demonstrate their universal dependence on the band gap energy across the different perovskite material classes, which can be summarized in a universal semi-phenomenological expression, in good agreement with experiment.

Lead halide perovskites show remarkable performance when used in photovoltaic and optoelectronic devices. However, the peculiarities of light-matter interactions in these materials in general are far from being fully explored experimentally and theoretically. Here we specifically address the energy level order of optical transitions and demonstrate photon echos in a methylammonium lead triiodide single crystal, thereby determining the optical coherence times $T_2$ for excitons and biexcitons at cryogenic temperature to be 0.79 ps and 0.67 ps, respectively. Most importantly, we have developed an experimental photon-echo polarimetry method that not only identifies the contributions from exciton and biexciton complexes, but also allows accurate determination of the biexciton binding energy of 2.4 meV, even though the period of quantum beats between excitons and biexcitons is much longer than the coherence times of the resonances. Our experimental and theoretical analysis methods contribute to the understanding of the complex mechanism of quasiparticle interactions at moderate pump density and show that even in high-quality perovskite crystals and at very low temperatures, inhomogeneous broadening of excitonic transitions due to local crystal potential fluctuations is a source of optical dephasing.

The optical spectra of antiferromagnetic copper metaborate CuB$_2$O$_4$ are characterized by an exceptionally rich structure of narrow absorption lines due to electronic transitions within the magnetic Cu$^{2+}$ ions, but their unambiguous identification and behavior in magnetic field remain far from being fully understood. We studied the polarized magneto-absorption spectra of this tetragonal antiferromagnet with a high spectral resolution in the range of $1.4055-1.4065$ eV in magnetic fields up to 9.5 T and temperatures from 1.6 up to $T_N = 20$ K. We observed a set of eight absorption lines at $T=1.6$ K in magnetic fields exceeding 1.4 T which we identified as arising from Frenkel excitons related to the ground and the first excited state of Cu$^{2+}$ ions. The number of these excitons is defined by the presence of the four Cu$^{2+}$ ions with the doubly-degenerate spin state $S = 1/2$ at the 4$b$ positions in the crystallographic unit cell. The energies of these excitons are determined the exchange interaction of 0.5 meV of Cu$^{2+}$ ions in the excited state with surrounding ions and by the Davydov splitting of 0.12 meV. In large magnetic field the observed Zeeman splitting is controlled by the anisotropic $g$-factors of both the ground and excited states. We developed a theoretical model of Frenkel excitons in magnetic field that accounts for specific features of the spin structure and exchange interactions in CuB$_2$O$_4$. The model was used for fitting the experimental data and evaluation of Frenkel exciton parameters, such as the Davydov splitting, the molecular exchange energy, and the $g$-factors of the ground and excited states of the Cu$^{2+}$ ions., Comment: 13 pages, 8 figures

The spin-noise spectroscopy (SNS) method implies high efficiency of conversion of the spin-system magnetization to the Faraday rotation angle. Generally, this efficiency cannot be estimated using the characteristics of the regular magneto-optical activity of a paramagnet. However, it may be drastically enhanced in systems with strong inhomogeneous broadening of the optical transitions. This enhancement leads to the giant spin-noise gain effect and previously allowed one to apply the SNS to rare-earth-activated crystals. We show that the nonlinear resonant Faraday effect can be used to measure the homogeneous width of the inhomogeneously broadened transition and, thus, to estimate the applicability of the SNS to this type of paramagnet. We present the theoretical description of the effect and perform measurements on intraconfigurational ($4f$-$4f$) transitions of the trivalent rare-earth ions of neodymium and ytterbium in fluorite-based crystals. The proposed experimental approach establishes new links between the effects of nonlinear optics and spin-noise characteristics of crystals with paramagnetic impurities and offers new ways of research in the physics of impurity crystals., Comment: 9 pages, 7 figures, 1 table

Strong coupling between light and the fundamental excitations of a two-dimensional electron gas (2DEG) are of foundational importance both to pure physics and to the understanding and development of future photonic nanotechnologies. Here we study the relationship between spin polarization of a 2DEG in a monolayer semiconductor, MoSe$_2$, and light-matter interactions modified by a zero-dimensional optical microcavity. We find robust spin-susceptibility of the 2DEG to simultaneously enhance and suppress trion-polariton formation in opposite photon helicities. This leads to observation of a giant effective valley Zeeman splitting for trion-polaritons (g-factor >20), exceeding the purely trionic splitting by over five times. Going further, we observe robust effective optical non-linearity arising from the highly non-linear behaviour of the valley-specific strong light-matter coupling regime, and allowing all-optical tuning of the polaritonic Zeeman splitting from 4 to >10 meV. Our experiments lay the groundwork for engineering quantum-Hall-like phases with true unidirectionality in monolayer semiconductors, accompanied by giant effective photonic non-linearities rooted in many-body exciton-electron correlations.

We study experimentally and theoretically the temperature dependence of transverse magnetic routing of light emission from hybrid plasmonic-semiconductor quantum well structures where the exciton emission from the quantum well is routed into surface plasmon polaritons propagating along a nearby semiconductor-metal interface. In II-VI and III-V direct band semiconductors the magnitude of routing is governed by the circular polarization of exciton optical transitions, that is induced by a magnetic field. For structures comprising a (Cd,Mn)Te/(Cd,Mg)Te diluted magnetic semiconductor quantum well we observe a strong directionality of the emission up to 15% at low temperature of 20 K and magnetic field of 485 mT due to giant Zeeman splitting of holes mediated via the strong exchange interaction with Mn$^{2+}$ ions. For increasing temperatures towards room-temperature the magnetic susceptibility decreases and the directionality strongly decreases to 4% at T = 45 K. We also propose an alternative design based on a non-magnetic (In,Ga)As/(In,Al)As quantum well structure, suitable for higher temperatures. According to our calculations, such structure can demonstrate emission directionality up to 5% for temperatures below 200 K and moderate magnetic fields of 1 T., Comment: 15 pages, 10 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

A novel spin orientation mechanism - dynamic electron spin polarization has been recently suggested in Phys. Rev. Lett. $\mathbf{125}$, 156801 (2020). It takes place for unpolarized optical excitation in weak magnetic fields of the order of a few millitesla. In this paper we demonstrate experimentally and theoretically that the dynamic electron spin polarization degree changes sign as a function of time, strength of the applied magnetic field and its direction. The studies are performed on indirect band-gap (In,Al)As/AlAs quantum dots and their results are explained in the framework of a theoretical model developed for our experimental setting., Comment: 14 pages, 16 figures

We reveal the existence of a large in-plane heavy-hole $g$ factor in symmetric self-assembled (001) (In,Ga)As/GaAs quantum dots due to warping of valence band states. This warping dominates over the well-established mechanism associated with a reduced symmetry of quantum dots and the corresponding mixing of heavy-hole and light-hole states. The effect of band warping is manifested in a unique angular dependence of a trion photon echo signal on the direction of external magnetic field with respect to the sample axes. It results in a uniform magnetic-field-induced optical anisotropy for the entire quantum dot ensemble which is a prerequisite for realization of spin quantum memories and spin-photon entanglement in the ensemble., Comment: 5 pages, 3 figures, supplementary information: 10 pages, 10 figs

Spin waves in magnetic microresonators are at the core of modern magnonics. Here we demonstrate a new method of tunable excitation of different spin wave modes in magnetic microdisks by using a train of laser pulses coming at a repetition rate higher than the decay rate of spin precession. The microdisks are etched in a transparent bismuth iron garnet film and the light pulses influence the spins nonthermally through the inverse Faraday effect. The high repetition rate of the laser stimulus of 10 GHz establishes an interplay between the spin wave resonances in the frequency and momentum domains. As a result, scanning of the focused laser spot near the disk boarder changes interference pattern of the magnons and leads to a resonant dependence of the spin wave amplitude on the external magnetic field. Apart from that, we achieved a switching between volume and surface spin waves by a small variation of the external magnetic field.

The selective cooling of $^{75}$As spins by optical pumping followed by adiabatic demagnetization in the rotating frame is realized in a nominally undoped GaAs/(Al,Ga)As quantum well. The rotation of 6 kG strong Overhauser field at the $^{75}$As Larmor frequency of 5.5 MHz is evidenced by the dynamic Hanle effect. Despite the presence of the quadrupole induced nuclear spin splitting, it is shown that the rotating $^{75}$As magnetization is uniquely determined by the spin temperature of coupled spin-spin and quadrupole reservoirs. The dependence of heat capacity of these reservoirs on the external magnetic field direction with respect to crystal and structure axes is investigated. The lowest nuclear spin temperature achieved is 0.54 $\mu$K, which is the record low value for semiconductors and semiconductor nanostructures.

We demonstrate the realization of the resonant spin amplification (RSA) effect in Faraday geometry where a magnetic field is applied parallel to the optically induced spin polarization so that no RSA is expected. However, model considerations predict that it can be realized for a central spin interacting with a fluctuating spin environment. As a demonstrator, we choose an ensemble of singly-charged (In,Ga)As/GaAs quantum dots, where the resident electron spins interact with the surrounding nuclear spins. The observation of RSA in Faraday geometry requires intense pump pulses with a high repetition rate and can be enhanced by means of the spin-inertia effect. Potentially, it provides the most direct and reliable tool to measure the longitudinal $g$ factor of the charge carriers., Comment: 7 pages including 4 figures; 8 pages supplement including 4 figures

The dynamics of the coupled electron-nuclear spin system is studied in an ensemble of singly-charged (In,Ga)As/GaAs quantum dots (QDs) using periodic optical excitation at 1 GHz repetition rate. In combination with the electron-nuclei interaction, the highly repetitive excitation allows us to lock the electron spins into magnetic resonance in a transverse external magnetic field. Sweeping the field to higher values, the locking leads to an effective "diamagnetic" response of significant strength due to dynamic nuclear polarization, which shields the QD electrons at least partly from the external field and can even keep the internal magnetic field constant up to 1.3 T field variation. We model the effect through a magnetic field-dependent polarization rate of the nuclei, from which we suggest a strategy for adjusting the nuclear polarization through the detuning between optical excitation and electronic transition, in addition to tuning the magnetic field., Comment: 12 pages, 9 figures

The coherent electron spin dynamics of an ensemble of singly charged (In,Ga)As/GaAs quantum dots in a transverse magnetic field is driven by periodic optical excitation at 1 GHz repetition frequency. Despite the strong inhomogeneity of the electron $g$ factor, the spectral spread of optical transitions, and the broad distribution of nuclear spin fluctuations, we are able to push the whole ensemble of excited spins into a single Larmor precession mode that is commensurate with the laser repetition frequency. Furthermore, we demonstrate that an optical detuning of the pump pulses from the probed optical transitions induces a directed dynamic nuclear polarization and leads to a discretization of the total magnetic field acting on the electron ensemble. Finally, we show that the highly periodic optical excitation can be used as universal tool for strongly reducing the nuclear spin fluctuations and preparation of a robust nuclear environment for subsequent manipulation of the electron spins, also at varying operation frequencies., Comment: 14 pages, 7 figures

Optical control of electronic spins is the basis for ultrafast spintronics: circularly polarized light in combination with spin-orbit coupling of the electronic states allows for spin manipulation in condensed matter. However, the conventional approach is limited to spin orientation along one particular orientation that is dictated by the direction of photon propagation. Plasmonics opens new capabilities, allowing one to tailor the light polarization at the nanoscale. Here, we demonstrate ultrafast optical excitation of electron spin on femtosecond time scales via plasmon to exciton spin conversion. By time-resolving the THz spin dynamics in a hybrid (Cd,Mn)Te quantum well structure covered with a metallic grating, we unambiguously determine the orientation of the photoexcited electron spins which is locked to the propagation direction of surface plasmon-polaritons. Using the spin of the incident photons as additional degree of freedom, one can orient the photoexcited electron spin at will in a two-dimensional plane., Comment: main text 23 pages, 5 figures. Supplementing material with 6 figures

We report on theoretical and experimental study of the spin polarization recovery and Hanle effect for the charge carriers interacting with the fluctuating nuclear spins in the semiconductor structures. We start the theoretical description from the simplest model of static and isotropic nuclear spin fluctuations. Then we describe the modification of the polarization recovery and Hanle curves due to the anisotropy of the hyperfine interaction, finite nuclear spin correlation time, and the strong pulsed spin excitation. For the latter case, we describe the resonance spin amplification effect in the Faraday geometry and discuss the manifestations of the quantum Zeno effect. The set of the experimental results for various structures and experimental conditions is chosen to highlight the specific effects predicted theoretically. We show that the spin polarization recovery is a very valuable tool for addressing carrier spin dynamics in semiconductors and their nanostructures., Comment: 16 pages, 15 figures

This work presents micromagnetic simulations in ferromagnetic nanogratings for the full range of directions of an applied in-plane external magnetic field. We focus on the modification of the magnon mode characteristics when the magnetic field orientation is gradually changed between the classical Damon-Eshbach (DE) and backward-volume (BV) geometries. We found that in a specific range of field directions, the magnon mode parameters differ significantly from the parameters in the classical cases, namely, the modes are characterized by complex spatial distributions and have low group velocities. The center of this range corresponds to the direction of the external magnetic field, which gives the maximal nonuniform distribution of the static magnetization in the nanogratings., Comment: 20 pages, 15 figures

We suggest a new spin orientation mechanism for localized electrons: $dynamic~electron~spin~polarization~provided~by~nuclear~spin~fluctuations$. The angular momentum for the electrons is gained from the nuclear spin system via the hyperfine interaction in a weak magnetic field. For this the sample is illuminated by an unpolarized light, which directly polarizes neither the electrons nor the nuclei. We predict, that for the electrons bound in localized excitons 100% spin polarization can be reached in longitudinal magnetic fields of a few millitesla. The proof of principle experiment is performed on momentum-indirect excitons in (In,Al)As/AlAs quantum dots, where in a magnetic field of 17 mT the electron spin polarization of 30% is measured., Comment: 6+9 pages, 3+9 figures

Semiconductor quantum dots are excellent candidates for ultrafast coherent manipulation of qubits by laser pulses on picosecond timescales or even faster. In inhomogeneous ensembles a macroscopic optical polarization decays rapidly due to dephasing, which, however, is reversible in photon echoes carrying complete information about the coherent ensemble dynamics. Control of the echo emission time is mandatory for applications. Here, we propose a novel concept to reach this goal. In a two-pulse photon echo sequence, we apply an additional resonant control pulse with multiple of 2pi area. Depending on its arrival time, the control slows down dephasing or rephasing of the exciton ensemble during its action. We demonstrate for self-assembled (In,Ga)As quantum dots that the photon echo emission time can be retarded or advanced by 5 ps relative to its nominal appearance time without control. This versatile protocol may be used to obtain significantly longer temporal shifts for suitably tailored control pulses., Comment: 13 pages, 8 figures

We study the spin dynamics in a high-mobility two-dimensional electron gas confined in a GaAs/AlGaAs quantum well. An unusual magnetic field dependence of the spin relaxation is found: as the magnetic field becomes stronger, the spin relaxation time first increases quadratically but then changes to a linear dependence, before it eventually becomes oscillatory, whereby the longitudinal and transverse times reach maximal values at even and odd filling Landau level factors, respectively. We show that the suppression of spin relaxation is due to the effect of electron gyration on the spin-orbit field, while the oscillations correspond to oscillations of the density of states appearing at low temperatures and high magnetic fields. The transition from quadratic to linear dependence can be related to a transition from classical to Bohm diffusion and reflects an anomalous behavior of the two-dimensional electron gas analogous to that observed in magnetized plasmas., Comment: 10 pages, 3 figures

Excitons in diluted magnetic semiconductors represent excellent probes for studying the magnetic properties of these materials. Various magneto-optical effects, which depend sensitively on the exchange interaction of the excitons with the localized spins of the magnetic ions can be used for probing. Here, we study core/shell CdSe/(Cd,Mn)S colloidal nanoplatelets hosting diluted magnetic semiconductor layers. The inclusion of the magnetic Mn$^{2+}$ ions is evidenced by three magneto-optical techniques using high magnetic fields up to 15 T: polarized photoluminescence, optically detected magnetic resonance, and spin-flip Raman scattering. In particular, information on the Mn$^{2+}$ concentration in the CdS shell layers can be obtained from the spin-lattice relaxation dynamics of the Mn$^{2+}$ spin system.

The Lorentz reciprocity principle is a fundamental concept that governs light propagation in any optically linear medium in zero magnetic field. Here, we demonstrate experimentally a novel mechanism of reciprocity breaking in nonlinear optics driven by the toroidal moment. Using high-resolution femtosecond spectroscopy at optical electronic resonances in the magnetoelectric antiferromagnet CuB$_2$O$_4$, we show that by controlling the nonlinear interference of coherent sources of second harmonic generation originating from the toroidal spin order, applied magnetic field, and noncentrosymmetric crystal structure, we induce a huge nonreciprocity approaching 100% for opposite magnetic fields. The experimental results are corroborated by a convincing theoretical analysis based on the magnetic and crystal symmetry. These findings open new degrees of freedom in the nonlinear physics of electronic and magnetic structures and pave the way for future nonreciprocal spin-optronic devices operating on the femtosecond time scale., Comment: 20 pages, 8 figures, 2 tables

We develop a simple method for measuring the electron spin relaxation times $T_1$, $T_2$ and $T_2^*$ in semiconductors and demonstrate its exemplary application to $n$-type GaAs. Using an abrupt variation of the magnetic field acting on electron spins, we detect the spin evolution by measuring the Faraday rotation of a short laser pulse. Depending on the magnetic field orientation, this allows us to measure either the longitudinal spin relaxation time $T_1$ or the inhomogeneous transverse spin dephasing time $T_2^*$. In order to determine the homogeneous spin coherence time $T_2$, we apply a pulse of an oscillating radiofrequency (rf) field resonant with the Larmor frequency and detect the subsequent decay of the spin precession. The amplitude of the rf-driven spin precession is significantly enhanced upon additional optical pumping along the magnetic field., Comment: 9 pages, 5 figures, 1 table

The effect of a lateral electric current on the photoluminescence H-band of an AlGaAs/GaAs heterostructure is investigated. The photoluminescence intensity and optical orientation of electrons contributing to the H-band are studied by means of continuous wave and time-resolved photoluminescence spectroscopy and time-resolved Kerr rotation. It is shown that the H-band is due to recombination of the heavy holes localized at the heterointerface with photoexcited electrons attracted to the heterointerface from the GaAs layer. Two lines with significantly different decay times constitute the H-band: a short-lived high-energy one and a long-lived low-energy one. The high-energy line originates from recombination of electrons freely moving along the structure plane, while the low-energy one is due to recombination of donor-bound electrons near the interface. Application of the lateral electric field of ~ 100-200 V/cm results in a quenching of both lines. This quenching is due to a decrease of electron concentration near the heterointerface as a result of a photocurrent-induced heating of electrons in the GaAs layer. On the contrary, electrons near the heterointerface are effectively cooled, so the donors near the interface are not completely empty up to ~ 100 V/cm, which is in stark contrast with the case of bulk materials. The optical spin polarization of the donor-bound electrons near the heterointerface weakly depends on the electric field. Their polarization kinetics is determined by the spin dephasing in the hyperfine fields of the lattice nuclei. The long spin memory time (> 40 ns) can be associated with suppression of the Bir-Aronov-Pikus mechanism of spin relaxation for electrons., Comment: 21 pages, 7 figures

We report on the experimental and theoretical investigation of magnetic-field-induced second harmonic generation (SHG) and two-photon absorption (TPA) of excited exciton states ($n \geq 3$) of the yellow series in Cu$_2$O. In this centrosymmetric material, SHG can occur due to constructive interplay of electric dipole and electric quadrupole/magnetic dipole transitions for light propagating along the low-symmetry directions [111] or [112]. By application of a magnetic field in Voigt configuration, SHG gets also allowed for excitation along the [110]-axis and even the high-symmetry cubic direction [001]. Combining a symmetry analysis and a microscopic theory, we uncover the two key contributions to the magnetic-field-induced SHG: the Zeeman effect and the magneto-Stark effect. We demonstrate systematic dependencies of the SHG intensity on the linear polarization angles of the ingoing fundamental laser and the outgoing SHG beam. In general, the resulting contour plots in combination with a symmetry analysis allow one to determine uniquely the character of involved transitions. Moreover, we can separate in magnetic field the Zeeman and the magneto-Stark effect through appropriate choice of the experimental geometry and polarization configuration. We present a microscopic theory of the second harmonic generation of excitons in a centrosymmetric cubic semiconductor taking into account the symmetry and the band structure of cuprous oxide. Based on the developed microscopic theory we identify the main contributions to the second-order nonlinear susceptibility of $S$-, $P$- and $D$-excitons. We analyze the redistribution of SHG intensities between the excitonic states both in the absence and presence of the magnetic field and show good agreement with the experimental data. With increasing exciton principal quantum number the magneto-Stark effect overpowers the influence of the Zeeman effect.

We use the two-pulse spin-dependent photon echo technique to study the in-plane hole spin anisotropy in a 20~nm-thick CdTe/Cd$_{0.76}$Mg$_{0.24}$Te single quantum well by exciting the donor-bound exciton resonance. We take advantage of the photon echo sensitivity to the relative phase of the electron and hole spin precession and study various interactions contributing to the hole in-plane spin properties. The main contribution is found to arise from the crystal cubic symmetry described by the Luttinger parameter $q=0.095$, which is substantially larger than the one theoretically expected for CdTe or found in other quantum well structures. Another contribution is induced by the strain within the quantum well. These two contributions manifest as different harmonics of the spin precession frequencies in the photon echo experiment, when strength and orientation of the Voigt magnetic field are varied. The magnitude of the effective in-plane hole $g$ factor is found to vary in the range $|\tilde{g_h}|$=0.125--0.160 in the well plane., Comment: 7 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

We study the quantum beats in the polarization of the photon echo from donor-bound exciton ensembles in semiconductor quantum wells. To induce these quantum beats, a sequence composed of a circularly polarized and a linearly polarized picosecond laser pulse in combination with an external transverse magnetic field is used. This results in an oscillatory behavior of the photon echo amplitude, detected in the $\sigma^+$ and $\sigma^-$ circular polarizations, occurring with opposite phases relative to each other. The beating frequency is the sum of the Larmor frequencies of the resident electron and the heavy hole when the second pulse is polarized along the magnetic field. The beating frequency is, on the other hand, the difference of these Larmor frequencies when the second pulse is polarized orthogonal to the magnetic field. The measurement of both beating frequencies serves as a method to determine precisely the in-plane hole $g$ factor, including its sign. We apply this technique to observe the quantum beats in the polarization of the photon echo from the donor-bound excitons in a 20-nm-thick CdTe/Cd$_{0.76}$Mg$_{0.24}$Te quantum well. From these quantum beats we obtain the in-plane heavy hole $g$ factor $g_h=-0.143\pm0.005$., Comment: 4 pages, 4 figures