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The Land\'e $g$-factor of charge carriers is a key parameter in spin physics controlling spin polarization and spin dynamics. In turn, it delivers information of the electronic band structure in vicinity of the band gap and its modification in nanocrystals provided by strong carrier confinement. The coherent spin dynamics of electrons and holes are investigated in CsPbI$_3$ perovskite nanocrystals with sizes varied from 4 to 16 nm by means of time-resolved Faraday ellipticity at the temperature of 6 K. The Land\'e $g$-factors of the charge carriers are evaluated through the Larmor spin precession in magnetic fields up to 430 mT across the spectral range from 1.69 to 2.25 eV, provided by variation of the nanocrystal size. The spectral dependence of the electron $g$-factor follows the model predictions when accounting for the mixing of the electronic bands with increasing confinement resulting from a decrease of the nanocrystal size. The spectral dependence of the hole $g$-factor, changing from $-0.19$ to $+1.69$, is considerably stronger than expected from the model. We analyze several mechanisms and conclude that none of them can be responsible for this difference. The renormalizations of the electron and hole $g$-factors roughly compensate each other, providing spectral independence for the bright exciton $g$-factor with a value of about $+2.2$., Comment: arXiv admin note: text overlap with arXiv:2407.21610

The coherent spin dynamics of holes are investigated for CsPbBr$_3$ and CsPb(Cl,Br)$_3$ perovskite nanocrystals in a glass matrix using the time-resolved Faraday rotation/ellipticity techniques. In an external magnetic field, pronounced Larmor spin precession of the hole spins is detected across a wide temperature range from 5 to 300 K. The hole Land\'e $g$-factor varies in the range of $0.8-1.5$, in which it increases with increasing high energy shift of the exciton due to enhanced confinement in small nanocrystals. The hole spin dephasing time decreases from 1 ns to 50 ps in this temperature range. Nuclear spin fluctuations have a pronounced impact on the hole spin dynamics. The hyperfine interaction of the holes with nuclear spins modifies their spin polarization decay and induces their spin precession in zero external magnetic field. The results can be well described by the model developed in Ref. 41, from which the hyperfine interaction energy of a hole spin with the nuclear spin fluctuation in range of $2-5$ $\mu$eV is evaluated.

The coherent spin dynamics of electrons and holes in CsPbI3 perovskite nanocrystals in a glass matrix are studied by the time-resolved Faraday ellipticity technique in magnetic fields up to 430 mT across a temperature range from 6 K up to 120 K. The Land\'e g-factors and spin dephasing times are evaluated from the observed Larmor precession of electron and hole spins. The nanocrystal size in the three studied samples varies from about 8 to 16 nm, resulting in exciton transition varying from 1.69 to 1.78 eV at the temperature of 6 K, allowing us to study the corresponding energy dependence of the g-factors. The electron g-factor decreases with increasing confinement energy in the NCs as result of NC size reduction, and also with increasing temperature. The hole g-factor shows the opposite trend. A model analysis shows that the variation of g-factors with NC size arises from the transition energy dependence of the g-factors, which becomes strongly renormalized by temperature.

We study the Hanle and spin polarization recovery effects on resident electrons in a monolayer MoSe$_2$ on EuS. We demonstrate that localized electrons provide the main contribution to the spin dynamics signal at low temperatures below 15~K for small magnetic fields of only a few mT. The spin relaxation of these electrons is determined by random effective magnetic fields due to a contact spin interaction, namely the hyperfine interaction with the nuclei in MoSe$_2$ or the exchange interaction with the magnetic ions of the EuS film. From the magnetic field angular dependence of the spin polarization we evaluate the anisotropy of the intervalley electron $g$-factor and the spin relaxation time. The non-zero in-plane $g$-factor $|g_x|\approx 0.1$, the value of which is comparable to its dispersion, is attributed to randomly localized electrons in the MoSe$_2$ layer., Comment: 6 pages, 4 figures

The coupled electron-nuclear spin system in an InGaAs semiconductor as testbed of nonlinear dynamics can develop auto-oscillations, resembling time-crystalline behavior, when continuously excited by a circularly polarized laser. We expose this system to deviations from continuous driving by periodic modulation of the excitation polarization, revealing a plethora of nonlinear phenomena that depend on modulation frequency and depth. We find ranges in which the system's oscillations are entrained with the modulation frequency. The width of these ranges depends on the polarization modulation depth, resulting in an Arnold tongue. Outside the tongue, the system shows a variety of fractional subharmonic responses connected through bifurcation jets when varying the modulation frequency. Here, each branch in the frequency spectrum forms a devil's staircase. When an entrainment range is approached by going through an increasing order of bifurcations, chaotic behavior emerges. These findings can be described by an advanced model of the periodically pumped electron-nuclear spin system. We discuss the connection of the obtained results to different phases of time matter.

We investigate the two-pulse photon echo response of excitons in the mixed lead halide perovskite crystal \sample in dependence on the excitation intensity and polarization of the incident laser pulses. Using spectrally narrow picosecond laser pulses, we address localized excitons with long coherence times $T_2 \approx 100\,$ps. This approach offers high sensitivity for the observation of excitation-induced changes in the homogeneous linewidth $\Gamma_2=2\hbar/T_2$ on the $\mu$eV scale. Through intensity-dependent measurements, we evaluate the increase of $\Gamma_2$ by 10~$\mu$eV at an exciton density of 10$^{17}$~cm$^{-3}$ being comparable with the intrinsic linewidth of 14$\,\mu$eV. We observe that the decay of the photon echo and its power dependence are sensitive to the polarization configuration of the excitation pulses, which indicates that spin-dependent exciton-exciton interactions contribute to excitation-induced dephasing. In cross-linear polarization, the decay is faster and its dependence on exciton density is stronger as compared to the co-polarized configuration. Using a two-exciton model accounting for different spin configurations we are able to reproduce the experimental results.

Diluted magnetic semiconductor (DMS) colloidal nanocrystals demonstrate remarkable magneto-optical properties. However, the behavior of circular polarization of their emission in high magnetic fields remains unclear. We measure magneto-optical properties of colloidal CdSe/CdMnS nanoplatelets in high magnetic fields up to 30 T and at cryogenic temperatures. The degree of circular polarization of photoluminescence demonstrates non-monotonous behavior in a magnetic field. In low magnetic fields, the polarization degree is positive, due to an exchange interaction of excitons with localized spins of magnetic Mn ions. The exchange interaction is strong enough to overcome the intrinsic Zeeman splitting, which provides negatively polarized emission in nonmagnetic CdSe/CdS nanoplatelets. After reaching a maximum the polarization degree starts to decrease and reverses the sign to negative in high magnetic fields. The critical magnetic field, in which the sign is reversed, increases when temperature is elevated. We develop a model, which explains this behavior by an interplay of bright and dark exciton recombination.

Optical orientation of carrier spins by circularly polarized light is the basic concept and tool of spin physics in semiconductors. We study the optical orientation of electrons and holes in a crystal of the FA$_{0.9}$Cs$_{0.1}$PbI$_{2.8}$Br$_{0.2}$ lead halide perovskite by means of polarized photoluminescence, time-resolved differential reflectivity, and time-resolved Kerr rotation. At the cryogenic temperature of 1.6 K the optical orientation degree measured for continuous-wave excitaton reaches 6% for localized electrons and 2\% for localized holes. Their contributions are distinguished from each other and from exciton optical orientation through the pronounced Hanle effect in transverse magnetic fields and the polarization recovery effect in longitudinal magnetic fields. The optical orientation degree is highly stable against detuning of the laser photon energy from the band gap by up to 0.25 eV, showing then a gradual decrease for detunings up to 0.9 eV. This evidences the inefficiency of spin relaxation mechanisms for free carriers during their energy relaxation. Spin relaxation for localized electrons and holes is provided by the hyperfine interaction with the nuclear spins. Dynamic polarization of nuclear spins is demonstrated by the Overhauser field reaching 4 mT acting on the electrons and $-76$ mT acting on the holes. This confirms the specifics of lead halide perovskite semiconductors, where the hole hyperfine interaction with the nuclei considerably exceeds that of the electron.

Excitons, as bound states of electrons and holes, embody the solid state analogue of the hydrogen atom, whose quantum spectrum is explained within a classical framework by the Bohr-Sommerfeld atomic model. In a first hydrogenlike approximation the spectra of excitons are also well described by a Rydberg series, however, due to the surrounding crystal environment deviations from this series can be observed. A theoretical treatment of excitons in cuprous oxide needs to include the band structure of the crystal, leading to a prominent fine-structure splitting in the quantum spectra. This is achieved by introducing additional spin degrees of freedom into the system, making the existence and meaningfulness of classical exciton orbits in the physical system a non-trivial question. Recently, we have uncovered the contributions of periodic exciton orbits directly in the quantum mechanical recurrence spectra of cuprous oxide [J. Ertl et al., Phys. Rev. Lett. 129, 067401 (2022)] by application of a scaling technique and fixing the energy of the classical dynamics to a value corresponding to a principle quantum number $n=5$ in the hydrogenlike case. Here, we present a comprehensive derivation of the classical and semiclassical theory of excitons in cuprous oxide. In particular, we investigate the energy dependence of the exciton dynamics. Both the semiclassical and quantum mechanical recurrence spectra exhibit stronger deviations from the hydrogenlike behavior with decreasing energy, which is related to a growing influence of the spin-orbit coupling and thus a higher velocity of the secular motion of the exciton orbits. The excellent agreement between semiclassical and quantum mechanical exciton recurrence spectra demonstrates the validity of the classical and semiclassical approach to excitons in cuprous oxide., Comment: 16 pages, 10 figures, accepted for publication in Phys. Rev. B

Rydberg excitons (analogues of Rydberg atoms in condensed matter systems) are highly excited bound electron-hole states with large Bohr radii. The interaction between them as well as exciton coupling to light may lead to strong optical nonlinearity, with applications in sensing and quantum information processing. Here, we achieve strong effective photon-photon interactions (Kerr-like optical nonlinearity) via the Rydberg blockade phenomenon and the hybridisation of excitons and photons forming polaritons in a Cu$_2$O-filled microresonators. Under pulsed resonant excitation polariton resonance frequencies are renormalised due to the reduction of the photon-exciton coupling with increasing exciton density. Theoretical analysis shows that the Rydberg blockade plays a major role in the experimentally observed scaling of the polariton nonlinearity coefficient as $\propto n^{4.4 \pm 1.8}$ for principal quantum numbers up to n = 7. Such high principal quantum numbers studied in a polariton system for the first time are essential for realisation of high Rydberg optical nonlinearities, which paves the way towards quantum optical applications and fundamental studies of strongly-correlated photonic (polaritonic) states in a solid state system.

Cesium lead bromide (CsPbBr$_3$) is a representative material of the emerging class of lead halide perovskite semiconductors that possess remarkable optoelectronic properties. Its optical properties in the vicinity of the band gap energy are greatly contributed by excitons, which form exciton-polaritons due to strong light-matter interactions. We examine exciton-polaritons in solution-grown CsPbBr$_3$ crystals by means of circularly-polarized reflection spectroscopy measured in high magnetic fields up to 60 T. The excited 2P exciton state is measured by two-photon absorption. Comprehensive modeling and analysis provides detailed quantitative information about the exciton-polariton parameters: exciton binding energy of 32.5 meV, oscillator strength characterized by longitudinal-tranverse splitting of 5.3 meV, damping of 6.7 meV, reduced exciton mass of $0.18 m_0$, exciton diamagnetic shift of 1.6 $\mu$eV/T$^2$, and exciton Land\'e factor $g_X=+2.35$. We show that the exciton states can be well described within a hydrogen-like model with an effective dielectric constant of 8.7. From the measured exciton longitudinal-transverse splitting we evaluate the Kane energy of $E_p=15$ eV, which is in reasonable agreement with values of $11.8-12.5$ eV derived from the carrier effective masses., Comment: 16 pager, 7 figures

Optical orientation of carrier spins by circularly polarized light is the basis of spin physics in semiconductors. Here, we demonstrate strong optical orientation of 85\%, approaching the ultimate limit of unity, for excitons in FA$_{0.9}$Cs$_{0.1}$PbI$_{2.8}$Br$_{0.2}$ lead halide perovskite bulk crystals. Time-resolved photoluminescence allows us to distinguish excitons with 60~ps lifetime from electron-hole recombination in the spin dynamics detected via coherent spin quantum beats in magnetic field. We reveal electron-hole spin correlations through linear polarization beats after circularly polarized excitation. Detuning of the excitation energy from the exciton resonance up to 0.5~eV does not reduce the optical orientation, evidencing clean chiral selection rules in agreement with atomistic calculations, and suppressed spin relaxation of electrons and holes even with large kinetic energies.

The tunability of the optical properties of lead halide perovskite nanocrystals makes them highly appealing for applications. Both, halide anion exchange and quantum confinement pave the way for tailoring their band gap energy. For spintronics applications, the Land\'e g-factors of electrons and hole are of great importance. By means of the empirical tight-binding and $\textbf{k}\cdot\textbf{p}$ methods, we calculate them for nanocrystals of the class of all-inorganic lead halide perovskites CsPb$X_3$ ($X = \text{I},\,\text{Br},\,\text{Cl}$). The hole g-factor as function of the band gap follows the universal dependence found for bulk perovskites, while for the electrons a considerable modification is predicted. Based on the $\textbf{k}\cdot\textbf{p}$ analysis we conclude that this difference arises from the interaction of the bottom conduction band with the spin-orbit split electron states. The model predictions are confirmed by experimental data for the electron and hole g-factors in CsPbI3 nanocrystals placed in a glass matrix, measured by time-resolved Faraday ellipticity in a magnetic field at cryogenic temperatures.

Compositional engineering of the optical properties of hybrid organic-inorganic lead halide perovskites is one of the cornerstones for the realization of efficient solar cells and tailored light-emitting devices. We study the effect of compositional disorder on coherent exciton dynamics in a mixed FA$_{0.9}$Cs$_{0.1}$PbI$_{2.8}$Br$_{0.2}$ perovskite crystal using photon echo spectroscopy. We reveal that the homogeneous linewidth of excitons can be as narrow as 16$\mu$eV at a temperature of 1.5K. The corresponding exciton coherence time of $T_2=83$ps is exceptionally long being attributed to the localization of excitons due to variation of composition at the scale of ten to hundreds of nanometers. From spectral and temperature dependences of the two- and three-pulse photon echo decay we conclude that for low-energy excitons, pure decoherence associated with elastic scattering on phonons is comparable with the exciton lifetime, while for excitons with higher energies, inelastic scattering to lower energy states via phonon emission dominates.

The versatile potential of lead halide perovskites and two-dimensional materials is merged in the Ruddlesen-Popper perovskites having outstanding optical properties. Here, the coherent spin dynamics in Ruddlesen-Popper (PEA)$_2$PbI$_4$ perovskites are investigated by picosecond pump-probe Kerr rotation in an external magnetic field. The Larmor spin precession of resident electrons with a spin dephasing time of 190~ps is identified. The longitudinal spin relaxation time in weak magnetic fields measured by the spin inertia method is as long as 25~$\mu$s. A significant anisotropy of the electron $g$-factor with the in-plane value of $+2.45$ and out-of-plane value of $+2.05$ is found. The exciton out-of-plane $g$-factor is measured to be of $+1.6$ by magneto-reflectivity. This work contributes to the understanding of the spin-dependent properties of two-dimensional perovskites and their spin dynamics.

The seminal work by T. Kazimierczuk et al. [Nature 514, 343 (2014)] has shown the existence of highly excited exciton states in a regime, where the correspondence principle is applicable and quantum mechanics turns into classical mechanics, however, any interpretation of exciton spectra based on a classical approach to excitons is still missing. Here, we close this gap by computing and comparing quantum mechanical and semiclassical recurrence spectra of cuprous oxide. We show that the quantum mechanical recurrence spectra exhibit peaks, which, by application of semiclassical theories and a scaling transformation, can be directly related to classical periodic exciton orbits. The application of semiclassical theories to exciton physics requires the detailed analysis of the classical exciton dynamics, including three-dimensional orbits, which strongly deviate from hydrogenlike Keplerian orbits. Our findings illuminate important aspects of excitons in semiconductors by directly relating the quantum mechanical band-structure splittings of excitons to the corresponding classical exciton dynamics., Comment: Article 6 pages, 3 figures and Supplemental material 7 pages, 2 figures. Accepted for publication in Physical Review Letters; Incomplete labeling in Figs. 2 and 3 corrected

Streak cameras are one of the most common and convenient devices to measure pulsed emission e.g. from semiconductor lightsources with picosecond time resolution. However, they are most sensitive in the visible range and possess low or negligible efficiency in the infrared and telecom regime. In this work, we present a frequency conversion based on sum-frequency generation that converts infrared to visible signals while preserving their temporal properties, making them detectable with a streak camera. We demonstrate and verify the functionality of our device by converting the emission from a quantum dot laser., Comment: 6 figures

For low-density plasmas, the classical limit described by the Debye-H\"uckel theory is still considered as an appropriate description even though a clear experimental proof of this paradigm is lacking due to the problems in determining the plasma-induced shift of single-particle energies in atomic systems. We show that Rydberg excitons in states with a high principal quantum number are highly sensitive probes for their surrounding making it possible to unravel accurately the basic properties of low-density non-degenerate electron-hole plasmas. To this end, we accurately measure the parameters of Rydberg excitons such as energies and linewidths in absorption spectra of bulk cuprous oxide crystals in which a tailored electron-hole plasma has been generated optically. Since from the absorption spectra exciton energies, as well as the shift of the single-particle energies given by the band edge, can be directly derived, the measurements allow us to determine the plasma density and temperature independently, which has been a notoriously hard problem in semiconductor physics. Our analysis shows unambiguously that the impact of the plasma cannot be described by the classical Debye model, but requires a quantum many-body theory, not only for the semiconductor plasma investigated here, but in general. Furthermore, it reveals a new exciton scattering mechanism with coupled plasmon-phonon modes becoming important even at very low plasma densities.

The functionality of phonon-based quantum devices largely depends on the efficiency of interaction of phonons with other excitations. For phonon frequencies above 20 GHz, generation and detection of the phonon quanta can be monitored through photons. The photon-phonon interaction can be enormously strengthened by involving an intermediate resonant quasiparticle, e.g. an exciton, with which a photon forms a polariton. In this work, we discover a giant photoelasticity of exciton-polaritons in a short-period superlattice and exploit it for detecting propagating acoustic phonons. We demonstrate that 42 GHz coherent phonons can be detected with extremely high sensitivity in the time domain Brillouin oscillations by probing with photons in the spectral vicinity of the polariton resonance., Comment: 6 pages, 3 figures, Supplemental Materials

Hypersonic phononic bandgap structures confine acoustic vibrations whose wavelength is commensurate with that of light, and have been studied using either time- or frequency-domain optical spectroscopy. Pulsed pump-probe lasers are the preferred instruments for characterizing periodic multilayer stacks from common vacuum deposition techniques, but the detection mechanism requires the injected sound wave to maintain coherence during propagation. Beyond acoustic Bragg mirrors, frequency-domain studies using a tandem Fabry-Perot interferometer (TFPI) find dispersions of two- and three-dimensional phononic crystals (PnCs) even for highly disordered samples, but with the caveat that PnCs must be transparent. Here, we demonstrate a hybrid technique for overcoming the limitations that time- and frequency-domain approaches exhibit separately: We inject coherent phonons into a non-transparent PnC using a pulsed laser and acquire the acoustic transmission spectrum on a TFPI, where pumped appear alongside spontaneously excited (i.e. incoherent) phonons. Choosing a metallic Bragg mirror for illustration, we determine the bandgap and compare with conventional time-domain spectroscopy, finding resolution of the hybrid approach to match that of a state-of-the-art asynchronous optical sampling setup. Thus, the hybrid pump-probe technique retains key performance features of the established one and going forward will likely be preferred for disordered samples., Comment: 18 pages, 4 figures, 54 references

We experimentally and numerically investigate the exchange interaction of the yellow excitons in cuprous oxide. By varying the material parameters in the numerical calculations, we can interpret experimental findings and understand their origin in the complex band structure and central-cell corrections. In particular, we experimentally observe the reversal of the ortho- and paraexciton for the $2S$ yellow exciton, and explain this phenomenon by an avoided crossing with the green $1S$ orthoexciton in a detailed numerical analysis. Furthermore, we discuss the exchange splitting as a function of the principal quantum number $n$ and its deviation from the $n^{-3}$ behavior expected from a hydrogenlike model. We also explain why the observed exchange splitting of the green $1S$ exciton is more than twice the splitting of the yellow $1S$ state., Comment: 9 pages, 4 figures, accepted for publication in Phys. Rev. B

Within a new paradigm for communications on the nanoscale, high-frequency surface acoustic waves are becoming effective data carrier and encoder. On-chip communications require acoustic wave propagation along nano-corrugated surfaces which strongly scatter traditional Rayleigh waves. Here we propose the delivery of information using subsurface acoustic waves with hypersound frequencies ~20 GHz, which is a nanoscale analogue of subsurface sound waves in the ocean. A bunch of subsurface hypersound modes is generated by pulsed optical excitation in a multilayer semiconductor structure with a metallic nanograting on top. The guided hypersound modes propagate coherently beneath the nanograting, retaining the surface imprinted information, on a distance of more than 50 {\mu}m which essentially exceeds the propagation length of Rayleigh waves. The concept is suitable for interfacing single photon emitters, such as buried quantum dots, carrying coherent spin excitations in magnonic devices, and encoding the signals for optical communications at the nanoscale., Comment: 18 pages (inc. references), 5 figures

The recombination dynamics and spin polarization of excitons in CdSe nanocrystals synthesized in a glass matrix are investigated using polarized photoluminescence in high magnetic fields up to 30 Tesla. The dynamics are accelerated by increasing temperature and magnetic field, confirming the dark exciton nature of the low-temperature photoluminescence (PL). The circularly polarized PL in magnetic fields reveals several unusual appearances: (i) a spectral dependence of the polarization degree, (ii) its low saturation value, and (iii) a stronger intensity of the Zeeman component which is higher in energy. The latter feature is the most surprising being in contradiction with the thermal population of the exciton spin sublevels. The same contradiction was previously observed in the ensemble of wet-chemically synthesized CdSe nanocrystals, but was not understood. We present a theory which explains all the observed features and shows that the inverted ordering of the circular polarized PL maxima from the ensemble of nanocrystals is a result of competition between the zero phonon (ZPL) and one optical phonon (1PL) assisted emission of the dark excitons. The essential aspects of the theoretical model are different polarization properties of the dark exciton emission via ZPL and 1PL recombination channels and the inhomogeneous broadening of the PL spectrum from the ensemble of nanocrystals exceeding the optical phonon energy.

The ability to generate and control strong long-range interactions via highly excited electronic states has been the foundation for recent breakthroughs in a host of areas, from atomic and molecular physics [1, 2] to quantum optics [3, 4] and technology [5-7]. Rydberg excitons provide a promising solid-state realization of such highly excited states, for which record-breaking orbital sizes of up to a micrometer have indeed been observed in cuprous oxide semiconductors [8]. Here, we demonstrate the generation and control of strong exciton interactions in this material by optically producing two distinct quantum states of Rydberg excitons. This makes two-color pump-probe experiments possible that allow for a detailed probing of the interactions. Our experiments reveal the emergence of strong spatial correlations and an inter-state Rydberg blockade that extends over remarkably large distances of several micrometers. The generated many-body states of semiconductor excitons exhibit universal properties that only depend on the shape of the interaction potential and yield clear evidence for its vastly extended-range and power-law character., Comment: Main script: 7 pages, 3 figures. Supplementary file 15 pages, 5 figures

In this study we analyze the transmission spectrum of a thin plate of Cuprous Oxide in the range of the absorption of the yellow exciton states with the coherent transfer matrix method. We demonstrate that, in contrast to the usual analysis using Beer's law, which turns out to be a rather good approximation only in the spectral region of high principal quantum numbers, a consistent quantitative description over the whole spectral range under consideration is possible. This leads to new and more accurate parameters not only for the Rydberg exciton states, but also for the strengths of indirect transitions. Furthermore, the results have consequences on the determination of the density of electron-hole pairs after optical excitation.

Optical harmonic generation on excitons is found in ZnSe/BeTe quantum wells with type-II band alignment. Two experimental approaches with spectrally-broad femtosecond laser pulses and spectrally-narrow picosecond pulses are used for spectroscopic studies by means of second and third harmonic generation (SHG and THG). The SHG signal is symmetry-forbidden for light propagation along the structure's growth axis, which is the [001] crystal axis, but can be induced by an external magnetic field. The THG signal is detected at zero magnetic field and its intensity is field independent. A group theory analysis of SHG and THG rotational anisotropy diagrams allows us to identify the involved excitation mechanisms., Comment: 11 pages, 17 figures

We study optical harmonic generation on the 1S exciton-polariton in the semiconductor ZnSe. Intense and spectrally narrow exciton resonances are found in optical second (SHG), third (THG), and fourth (FHG) harmonic generation spectra. The resonances are shifted to higher energy by 3.2 meV from the exciton energy in the linear reflectivity spectrum. Additional resonances are observed in the THG and FHG spectra and assigned to combinations of incident and backscattered photons in the crystal. Rotational anisotropy diagrams are measured and further information on the origin of the optical harmonic generation and the involved exciton states is obtained by a symmetry analysis using group theory in combination with a microscopic consideration., Comment: 14 pages, 14 figures, submitted to PRB

Experimental and theoretical investigations of excitons in cuprous oxide have revealed a significant fine-structure splitting of the excitonic Rydberg states caused by a strong impact of the valence band structure. We provide a semiclassical interpretation of that splitting by investigating the classical dynamics of the excitonic electron-hole pair beyond the hydrogen-like model. Considering the slow motion of Rydberg excitons in coordinate space compared to the fast dynamics of quasispin and hole spin we use an adiabatic approach and energy surfaces in momentum space for the computation of the exciton dynamics. We observe quasi-periodic motion on near-integrable tori. Semiclassical torus quantization yields the energy regions of the fine-structure splitting of $n$-manifolds in agreement with quantum mechanical computations., Comment: 5 pages, 3 figures

Recently Second Harmonic Generation (SHG) for the yellow exciton series in cuprous oxide has been demonstrated [J. Mund et al., Phys. Rev. B 98, 085203 (2018)]. Assuming perfect $O_{\mathrm{h}}$ symmetry, SHG is forbidden along certain high-symmetry axes. Perturbations can break this symmetry and forbidden transitions may become allowed. We investigate theoretically the effect of external magnetic fields on the yellow exciton lines of cuprous oxide. We identify two mechanisms by which an applied magnetic field can induce a second harmonic signal in a forbidden direction. First of all, a magnetic field by itself generally lifts the selection rules. In the Voigt configuration, an additional magneto-Stark electric field appears. This also induces certain SHG processes differing from those induced by the magnetic field alone. Complementary to the manuscript by A. Farenbruch et al. [Phys. Rev. B, submitted], we perform a full numerical diagonalization of the exciton Hamiltonian including the complex valence band structure. Numerical results are compared with experimental data., Comment: 14 pages, 6 figures

Energy harvesting is a modern concept which makes dissipated heat useful by transferring thermal energy to other excitations. Most of the existing principles for energy harvesting are realized in systems which are heated continuously, for example generating DC voltage in thermoelectric devices. Here we present the concept of high-frequency energy harvesting where the dissipated heat in a sample excites resonant magnons in a 5-nm thick ferromagnetic metal layer. The sample is excited by femtosecond laser pulses with a repetition rate of 10 GHz which results in temperature modulation at the same frequency with amplitude ~0.1 K. The alternating temperature excites magnons in the ferromagnetic nanolayer which are detected by measuring the net magnetization precession. When the magnon frequency is brought onto resonance with the optical excitation, a 12-fold increase of the amplitude of precession indicates efficient resonant heat transfer from the lattice to coherent magnons. The demonstrated principle may be used for energy harvesting in various nanodevices operating at GHz and sub-THz frequency ranges., Comment: Manuscript: 12 pages, 3 figures; Supplemental information: 7 pages; 4 figures, 3 tables

There is a great desire to extend ultrasonic techniques to the imaging and characterization of nanoobjects. This can be achieved by picosecond ultrasonics, where by using ultrafast lasers it is possible to generate and detect acoustic waves with frequencies up to terahertz and wavelengths down to nanometers. In our work we present a picosecond ultrasonics setup based on miniaturized mode-locked semiconductor lasers, whose performance allows us to obtain the necessary power, pulse duration and repetition rate. Using such a laser, we measure the ultrasonic echo signal with picosecond resolution in a Al film deposited on a semiconductor substrate. We show that the obtained signal is as good as the signal obtained with a standard bulky mode-locked Ti-Sa laser. The experiments pave the way for designing integrated portable picosecond ultrasonic setups on the basis of miniaturized semiconductor lasers., Comment: 9 pages, 4 figures

CdSe colloidal nanoplatelets are studied by spin-flip Raman scattering in magnetic fields up to 5 T. We find pronounced Raman lines shifted from the excitation laser energy by an electron Zeeman splitting. Their polarization selection rules correspond to those expected for scattering mediated by excitons interacting with resident electrons. Surprisingly, Raman signals shifted by twice the electron Zeeman splitting are also observed. The theoretical analysis and experimental dependencies show that the mechanism responsible for the double flip involves two resident electrons interacting with a photoexcited exciton. Effects related to various orientations of the nanoplatelets in the ensemble and different orientations of the magnetic field are analyzed.

The surface of nominally diamagnetic colloidal CdSe nanoplatelets can demonstrate paramagnetism owing to the uncompensated spins of dangling bonds (DBSs). We reveal that by optical spectroscopy in high magnetic fields up to 15 Tesla using the exciton spin as probe of the surface magnetism. The strongly nonlinear magnetic field dependence of the circular polarization of the exciton emission is determined by the DBS and exciton spin polarization as well as by the spin-dependent recombination of dark excitons. The sign of the exciton-DBS exchange interaction can be adjusted by the nanoplatelet growth conditions.

Strong coupling between two quanta of different excitations leads to the formation of a hybridized state which paves a way for exploiting new degrees of freedom to control phenomena with high efficiency and precision. A magnon polaron is the hybridized state of a phonon and a magnon, the elementary quanta of lattice vibrations and spin waves in a magnetically-ordered material. A magnon polaron can be formed at the intersection of the magnon and phonon dispersions, where their frequencies coincide. The observation of magnon polarons in the time domain has remained extremely challenging because the weak interaction of magnons and phonons and their short lifetimes jeopardize the strong coupling required for the formation of a hybridized state. Here, we overcome these limitations by spatial matching of magnons and phonons in a metallic ferromagnet with a nanoscale periodic surface pattern. The spatial overlap of the selected phonon and magnon modes formed in the periodic ferromagnetic structure results in a high coupling strength which, in combination with their long lifetimes allows us to find clear evidence of an optically excited magnon polaron. We show that the symmetries of the localized magnon and phonon states play a crucial role in the magnon polaron formation and its manifestation in the optically excited magnetic transients., Comment: 18 pages, 4 figures + Supplementary materials (available through the corresponding link given in References)

Coherent spin dynamics in colloidal CdSe quantum dots (QDs) typically show two spin components with different Larmor frequencies, whose origin is an open question. We exploit the photocharging approach to identify their origin and find that surface states play a key role in the appearance of the spin signals. By controlling the photocharging with electron or hole acceptors, we show that the specific spin component can be enhanced by the choice of acceptor type. In core/shell CdSe/ZnS QDs, the spin signals are significantly weaker. Our results exclude the neutral exciton as the spin origin and suggest that both Larmor frequencies are related to the coherent spin precession of electrons in photocharged QDs. The lower frequency is due to the electron confined in the middle of the QD, and the higher frequency to the electron additionally localized in the vicinity of the surface., Comment: 35 pages, 16 figures

The lead halide perovskites demonstrate huge potential for optoelectronic applications, high energy radiation detectors, light emitting devices and solar energy harvesting. Those materials exhibit strong spin-orbit coupling enabling efficient optical orientation of carrier spins in perovskite-based devices with performance controlled by a magnetic field. Perovskites are promising for spintronics due to substantial bulk and structure inversion asymmetry, however, their spin properties are not studied in detail. Here we show that elaborated time-resolved spectroscopy involving strong magnetic fields can be successfully used for perovskites. We perform a comprehensive study of high-quality CsPbBr$_3$ crystals by measuring the exciton and charge carrier $g$-factors, spin relaxation times and hyperfine interaction of carrier and nuclear spins by means of coherent spin dynamics. Owing to their "inverted" band structure, perovskites represent appealing model systems for semiconductor spintronics exploiting the valence band hole spins, while in conventional semiconductors the conduction band electrons are considered for spin functionality., Comment: 8 pages, 3 figures + supplementary information

The dephasing mechanisms of p-shell and s-shell excitons in an InAs self-assembled quantum dot ensemble are examined using two-dimensional coherent spectroscopy (2DCS). 2DCS provides a comprehensive picture of how the energy level structure of dots affects the exciton dephasing rates and recombination lifetimes. We find that at low temperatures, dephasing of s-shell excitons is lifetime limited, whereas p-shell excitons exhibit significant pure dephasing due to scattering between degenerate spin states. At elevated temperatures, quadratic exciton-phonon coupling plays an important role in both s-shell and p-shell exciton dephasing. We show that multiple p-shell states are also responsible for stronger phonon dephasing for these transitions

We present an investigation of the electron spin dynamics in an ensemble of singly-charged quantum dots subject to an external magnetic field and laser pumping with circularly polarized light. The spectral laser width is tailored such that different groups of quantum dots are coherently pumped. Surprisingly, the dephasing time $T^*$ of the electron spin polarization depends only weakly on the laser spectral width. These findings can be consistently explained by a cluster theory of coupled quantum dots with a long range electronic spin-spin interaction. We present a numerical simulation of the spin dynamics based on the central spin model that includes a quantum mechanical description of the laser pulses as well as a time-independent Heisenberg interaction between each pair of electron spins. We discuss the individual dephasing contributions stemming from the Overhauser field, the distribution of the electron $g$-factors and the electronic spin-spin interaction as well as the spectral width of the laser pulse. This analysis reveals the counterbalancing effect of the total dephasing time when increasing the spectral laser width. On one hand, the deviations of the electron $g$-factors increase. On the other hand, an increasing number of coherently pumped electron spins synchronize due to the spin-spin interaction. We find an excellent agreement between the experimental data and the dephasing time in the simulation using an exponential distribution of Heisenberg couplings with a mean value $\overline{J}\approx 0.26\,\mathrm{\mu eV}$.

Dark excitons are of fundamental importance for a wide variety of processes in semiconductors, but are difficult to investigate using optical techniques due to their weak interaction with light fields. We reveal and characterize dark excitons injected by non-resonant pulsed excitation in a semiconductor microcavity structure containing InGaAs/GaAs quantum wells by monitoring their interactions with the bright lower polariton mode. We find a surprisingly long dark exciton lifetime of more than 20 ns which is longer than the time delay between two consecutive pulses. This creates a memory effect that we clearly observe through the variation of the time-resolved transmission signal. We propose a rate equation model that provides a quantitative agreement with the experimental data., Comment: 16 pages, 8 figures

We present a novel spectroscopic technique for second harmonic generation (SHG) using femtosecond laser pulses at 30~kHz repetition rate, which nevertheless provides high spectral resolution limited only by the spectrometer. The potential of this method is demonstrated by applying it to the yellow exciton series of Cu$_2$O. Besides even parity states with $S-$ and $D-$ envelope, we also observe odd parity, $P-$ excitons with linewidths down to 100 $\mu$eV, despite of the broad excitation laser spectrum with a full width at half maximum of 14~meV. The underlying light-matter interaction mechanisms of SHG are elaborated by a group theoretical analysis which allows us to determine the linear and circular polarization dependences, in good agreement with experiment., Comment: 9 pages, 8 figures

Periodic laser pulsing of singly charged semiconductor quantum dots in an external magnetic field leads to a synchronization of the spin dynamics with the optical excitation. The pumped electron spins partially rephase prior to each laser pulse, causing a revival of electron spin polarization with its maximum at the incidence time of a laser pulse. The amplitude of this revival is amplified by the frequency focusing of the surrounding nuclear spins. Two complementary theoretical approaches for simulating up to 20 million laser pulses are developed and employed that are able to bridge between 11 orders of magnitude in time: a fully quantum mechanical description limited to small nuclear bath sizes and a technique based on the classical equations of motion applicable for a large number of nuclear spins. We present experimental data of the nonmonotonic revival amplitude as function of the magnetic field applied perpendicular to the optical axis. The dependence of the revival amplitude on the external field with a profound minimum at $4\;$T is reproduced by both of our theoretical approaches and is ascribed to the nuclear Zeeman effect. Since the nuclear Larmor precession determines the electronic resonance condition, it also defines the number of electron spin revolutions between pump pulses, the orientation of the electron spin at the incidence time of a pump pulse, and the resulting revival amplitude. The magnetic field of $4\;$T, for example, corresponds to half a revolution of nuclear spins between two laser pulses., Comment: 21 pages, 16 figures

We investigate and compare experimental and numerical excitonic spectra of the yellow series in cuprous oxide Cu$_2$O in the Voigt configuration and thus partially extend the results from Schweiner et al. [Phys. Rev. B 95, 035202 (2017)], who only considered the Faraday configuration. The main difference between the configurations is given by an additional effective electric field in the Voigt configuration, caused by the motion of the exciton through the magnetic field. This Magneto-Stark effect was already postulated by Gross et al. and Thomas et al. in 1961 [Sov. Phys. Solid State 3, 221 (1961); Phys. Rev. 124, 657 (1961)]. Group theoretical considerations show that the field most of all significantly increases the number of allowed lines by decreasing the symmetry of the system. This conclusion is supported by both the experimental and numerical data., Comment: 10 pages, 5 figure, final version

We address spin properties and spin dynamics of carriers and charged excitons in CdSe/CdS colloidal nanoplatelets with thick shells. Magneto-optical studies are performed by time-resolved and polarization-resolved photoluminescence, spin-flip Raman scattering and picosecond pump-probe Faraday rotation in magnetic fields up to 30 T. We show that at low temperatures the nanoplatelets are negatively charged so that their photoluminescence is dominated by radiative recombination of negatively charged excitons (trions). Electron g-factor of 1.68 is measured and heavy-hole g-factor varying with increasing magnetic field from -0.4 to -0.7 is evaluated. Hole g-factors for two-dimensional structures are calculated for various hole confining potentials for cubic- and wurtzite lattice in CdSe core. These calculations are extended for various quantum dots and nanoplatelets based on II-VI semiconductors. We developed a magneto-optical technique for the quantitative evaluation of the nanoplatelets orientation in ensemble.

We study the band-edge exciton fine structure and in particular its bright-dark splitting in colloidal semiconductor nanocrystals by four different optical methods based on fluorescence line narrowing and time-resolved measurements at various temperatures down to 2 K. We demonstrate that all these methods provide consistent splitting values and discuss their advances and limitations. Colloidal CdSe nanoplatelets with thicknesses of 3, 4 and 5 monolayers are chosen for experimental demonstrations. The bright-dark splitting of excitons varies from 3.2 to 6.0 meV and is inversely proportional to the nanoplatelet thickness. Good agreement between experimental and theoretically calculated size dependence of the bright-dark exciton slitting is achieved. The recombination rates of the bright and dark excitons and the bright to dark relaxation rate are measured by time-resolved techniques.

We study the time evolution of the Optical Spin Hall Effect (OSHE), which occurs when exciton-polaritons undergo resonant Rayleigh scattering. The resulting spin pattern in momentum space is quantified by calculating the degree of circular polarization of the momentum space image for each point in time. We find the degree of circular polarization performing oscillations, which can be described within the framework of the pseudospin model by Kavokin et al. (Ref. 1)., Comment: 6 pages, 4 figures

Electron spin dephasing in a singly charged semiconductor quantum dot can partially be suppressed by periodic laser pulsing. We propose a semi-classical approach describing the decoherence of the electron spin polarization governed by the hyperfine interaction with the nuclear spins as well as the probabilistic nature of the photon absorption. We use the steady-state Floquet condition to analytically derive two subclasses of resonance conditions excellently predicting the peak locations in the part of the Overhauser field distribution which is projected in the direction of the external magnetic field. As a consequence of the periodic pulsing, a non-equilibrium distribution develops as a function of time. The numerical simulation of the coupled dynamics reveals the influence of the hyperfine coupling constant distribution onto the evolution of the electron spin polarisation before the next laser pulse. Experimental indications are provided for both subclasses of resonance conditions., Comment: 21 pages, 21 figures

Up to this point streak-cameras have been a powerful tool for temporal characterization of ultrafast light pulses even at the single photon level. However, the low signal-to-noise ratio in the infrared range prevents measurement on weak light sources in the telecom regime. We present an approach to circumvent this problem. The method utilizes an up-conversion process in periodically poled waveguides in Lithium Niobate. We convert single photons from a parametric down-conversion source in order to reach the point of maximum detection efficiency of commercially available streak-cameras. We explore phase-matching configurations to investigate the up-conversion scheme in real-world applications.

A picosecond acoustic pulse can be used to control the lasing emission from semiconductor nanostructures by shifting their electronic transitions. When the active medium, here an ensemble of (In,Ga)As quantum dots, is shifted into or out of resonance with the cavity mode, a large enhancement or suppression of the lasing emission can dynamically be achieved. Most interesting, even in the case when gain medium and cavity mode are in resonance, we observe an enhancement of the lasing due to shaking by coherent phonons. In order to understand the interactions of the non-linearly coupled photon-exciton-phonon subsystems, we develop a semiclassical model and find an excellent agreement between theory and experiment.