Mode locking of hole spin coherences in CsPb(Cl, Br)3 perovskite nanocrystals.

The spin physics of perovskite nanocrystals with confined electrons or holes is attracting increasing attention, both for fundamental studies and spintronic applications. Here, stable [Formula: see text] 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 207Pb 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 [Formula: see text] of a nanosecond and a single hole spin coherence time of T2 = 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.

Discretization of the total magnetic field by the nuclear spin bath in fluorine-doped ZnSe.

The coherent spin dynamics of fluorine donor-bound electrons in ZnSe induced by pulsed optical excitation is studied in a perpendicular applied magnetic field. The Larmor precession frequency serves as a measure for the total magnetic field exerted onto the electron spins and, surprisingly, does not increase linearly with the applied field, but shows a step-like behavior with pronounced plateaus, given by multiples of the laser repetition rate. This discretization occurs by a feedback mechanism in which the electron spins polarize the nuclear spins, which in turn generate a local Overhauser field adjusting the total magnetic field accordingly. Varying the optical excitation power, we can control the plateaus, in agreement with our theoretical model. From this model, we trace the observed discretization to the optically induced Stark field, which causes the dynamic nuclear polarization.

Influence of the Nuclear Electric Quadrupolar Interaction on the Coherence Time of Hole and Electron Spins Confined in Semiconductor Quantum Dots.

The real-time spin dynamics and the spin noise spectra are calculated for p and n-charged quantum dots within an anisotropic central spin model extended by additional nuclear electric quadrupolar interactions and augmented by experimental data. Using realistic estimates for the distribution of coupling constants including an anisotropy parameter, we show that the characteristic long time scale is of the same order for electron and hole spins strongly determined by the quadrupolar interactions even though the analytical form of the spin decay differs significantly consistent with our measurements. The low frequency part of the electron spin noise spectrum is approximately 1/3 smaller than those for hole spins as a consequence of the spectral sum rule and the different spectral shapes. This is confirmed by our experimental spectra measured on both types of quantum dot ensembles in the low power limit of the probe laser.

Spin noise spectroscopy beyond thermal equilibrium and linear response.

Per the fluctuation-dissipation theorem, the information obtained from spin fluctuation studies in thermal equilibrium is necessarily constrained by the system's linear response functions. However, by including weak radio frequency magnetic fields, we demonstrate that intrinsic and random spin fluctuations even in strictly unpolarized ensembles can reveal underlying patterns of correlation and coupling beyond linear response, and can be used to study nonequilibrium and even multiphoton coherent spin phenomena. We demonstrate this capability in a classical vapor of (41)K alkali atoms, where spin fluctuations alone directly reveal Rabi splittings, the formation of Mollow triplets and Autler-Townes doublets, ac Zeeman shifts, and even nonlinear multiphoton coherences.

Two-colour spin noise spectroscopy and fluctuation correlations reveal homogeneous linewidths within quantum-dot ensembles.

'Spin noise spectroscopy' is an optical technique for probing electron and hole spin dynamics that is based on detecting their intrinsic fluctuations while in thermal equilibrium. Here we show that fluctuation correlations can be further exploited in multi-probe noise studies to reveal information that in general cannot be accessed by conventional linear optical spectroscopy, such as the underlying homogeneous linewidths of individual constituents within inhomogeneously broadened systems. This is demonstrated in singly charged (In,Ga)As quantum-dot ensembles using two weak probe lasers: When the lasers have similar wavelengths, they probe the same quantum dots in the ensemble and show correlated spin fluctuations. In contrast, mutually detuned probe lasers measure different subsets of quantum dots, giving uncorrelated fluctuations. The noise correlation versus laser detuning directly reveals the quantum dot homogeneous linewidth even in the presence of a strong inhomogeneous broadening. Such noise-based correlation techniques are not limited to semiconductor spin systems, but are applicable to any system with measurable intrinsic fluctuations.

Optical spectroscopy of spin noise.

Spontaneous fluctuations of the magnetization of a spin system in thermodynamic equilibrium (spin noise) manifest themselves as noise in the Faraday rotation of probe light. We show that the correlation properties of this noise over the optical spectrum can provide clear information about the composition of the spin system that is largely inaccessible for conventional linear optics. Such optical spectroscopy of spin noise, e.g., allows us to clearly distinguish between optical transitions associated with different spin subsystems, to resolve optical transitions that are unresolvable in the usual optical spectra, to unambiguously distinguish between homogeneously and inhomogeneously broadened optical bands, and to evaluate the degree of inhomogeneous broadening. These new possibilities are illustrated by theoretical calculations and by experiments on paramagnets with different degrees of inhomogeneous broadening of optical transitions [atomic vapors of 41K and singly charged (In,Ga)As quantum dots].

Optical measurement and modeling of interactions between two hole spins or two electron spins in coupled InAs quantum dots.

Two electron spins in quantum dots coupled through coherent tunneling are generally acknowledged to approximately obey Heisenberg isotropic exchange. This has not been established for two holes. Here we measure the spectra of two holes and of two electrons in two vertically stacked self-assembled InAs quantum dots using optical spectroscopy as a function of electric and magnetic fields. We find that the exchange is approximately isotropic for both systems, but that significant asymmetric contributions, arising from spin-orbit and Zeeman interactions combined with spatial asymmetries, are required to explain large anticrossings and fine-structure energy splittings in the spectra. Asymmetric contributions to the isotropic Hamiltonian for electrons are of the order of a few percent while those for holes are an order of magnitude larger.

Optical control of coherent interactions between electron spins in InGaAs quantum dots.

Coherent interactions between spins in quantum dots are a key requirement for quantum gates. We have performed pump-probe experiments in which pulsed lasers emitting at different photon energies manipulate two distinct subsets of electron spins within an inhomogeneous InGaAs quantum dot ensemble. The spin dynamics are monitored through their precession about an external magnetic field. These measurements demonstrate spin precession phase shifts and modulations of the magnitude of one subset of oriented spins after optical orientation of the second subset. The observations are consistent with results from a model using a Heisenberg-like interaction with µeV strength.

Spin noise of electrons and holes in self-assembled quantum dots.

We measure the frequency spectra of random spin fluctuations, or "spin noise," in ensembles of (In,Ga)As/GaAs quantum dots (QDs) at low temperatures. We employ a spin noise spectrometer based on a sensitive optical Faraday rotation magnetometer that is coupled to a digitizer and field-programmable gate array, to measure and average noise spectra from 0-1 GHz continuously in real time with subnanoradian/sqrt[Hz] sensitivity. Both electron and hole spin fluctuations generate distinct noise peaks, whose shift and broadening with magnetic field directly reveal their g factors and dephasing rates within the ensemble. A large, energy-dependent anisotropy of the in-plane hole g factor is clearly exposed, reflecting systematic variations in the average QD confinement potential.

Long-term hole spin memory in the resonantly amplified spin coherence of InGaAs/GaAs quantum well electrons.

Pulsed optical excitation of the negatively charged trion has been used to generate electron spin coherence in an n-doped (In,Ga)As/GaAs quantum well. The coherence is monitored by resonant spin amplification detected at times exceeding the trion lifetime by 2 orders of magnitude. Still, even then signatures of the hole spin dynamics in the trion complex are imprinted in the signal leading to an unusual batlike shape of the magnetic field dispersion of spin amplification. From this shape information about the spin relaxation of both electrons and holes can be derived.

Spin coherence of holes in GaAs/(Al,Ga)As quantum wells.

Carrier spin coherence in a p-doped GaAs/(Al,Ga)As quantum well with a diluted hole gas is studied by picosecond pump-probe Kerr rotation. For resonant optical excitation of the positively charged exciton the spin precession shows two types of oscillations: Electron spin beats decaying with the charged exciton radiative lifetime of 50 ps, and long-lived hole spin beats with dephasing times up to 650 ps, which decrease with increasing temperature, underlining the importance of hole localization. The mechanism of hole spin coherence generation is discussed.

Nuclei-induced frequency focusing of electron spin coherence.

The hyperfine interaction of an electron with the nuclei is considered as the primary obstacle to coherent control of the electron spin in semiconductor quantum dots. We show, however, that the nuclei in singly charged quantum dots act constructively by focusing the electron spin precession about a magnetic field into well-defined modes synchronized with a laser pulse protocol. In a dot with a synchronized electron, the light-stimulated fluctuations of the hyperfine nuclear field acting on the electron are suppressed. The information about electron spin precession is imprinted in the nuclei and thereby can be stored for tens of minutes in darkness. The frequency focusing drives an electron spin ensemble into dephasing-free subspaces with the potential to realize single frequency precession of the entire ensemble.

Subsecond spin relaxation times in quantum dots at zero applied magnetic field due to a strong electron-nuclear interaction.

A key to ultralong electron spin memory in quantum dots (QDs) at zero magnetic field is the polarization of the nuclei, such that the electron spin is stabilized along the average nuclear magnetic field. We demonstrate that spin-polarized electrons in n-doped (In,Ga)As/GaAs QDs align the nuclear field via the hyperfine interaction. A feedback onto the electrons occurs, leading to stabilization of their polarization due to formation of a nuclear spin polaron [I. A. Merkulov, Phys. Solid State 40, 930 (1998)]. Spin depolarization of both systems is consequently greatly reduced, and spin memory of the coupled electron-nuclear spin system is retained over 0.3 sec at temperature of 2 K.

Mode locking of electron spin coherences in singly charged quantum dots.

The fast dephasing of electron spins in an ensemble of quantum dots is detrimental for applications in quantum information processing. We show here that dephasing can be overcome by using a periodic train of light pulses to synchronize the phases of the precessing spins, and we demonstrate this effect in an ensemble of singly charged (In,Ga)As/GaAs quantum dots. This mode locking leads to constructive interference of contributions to Faraday rotation and presents potential applications based on robust quantum coherence within an ensemble of dots.

Optical control of spin coherence in singly charged (In,Ga)As/GaAs quantum dots.

Electron spin coherence has been generated optically in n-type modulation doped (In,Ga)As/GaAs quantum dots (QDs) which contain on average a single electron per dot. The coherence arises from resonant excitation of the QDs by circularly polarized laser pulses, creating a coherent superposition of an electron and a trion. Time dependent Faraday rotation is used to probe the spin precession of the optically oriented electrons about a transverse magnetic field. The coherence generation can be controlled by pulse intensity, being most efficient for (2n+1)pi pulses.