Electron Spin Precession Frequency Research Articles

Quantum Zeno effect and quantum nondemolition spin measurement in a quantum dot–micropillar cavity in the strong coupling regime

We theoretically describe the quantum Zeno effect in a spin-photon interface represented by a charged quantum dot in a micropillar cavity in the strong coupling regime. This simplest model allows for various generalizations for the different systems. We derive a simple expression for the spin measurement rate, which allows one to tune the electron spin precession frequency in an external magnetic field and spin relaxation time. We calculate the spin noise bispectrum, which reveals the qualitative change of the spin dynamics with an increase of the measurement strength and proves the quantum nature of the spin noise. We also calculate the quantum information gain rate and find the conditions when it equals the spin dephasing rate, i.e., reaches the quantum limit.

Universal nuclear focusing of confined electron spins

For spin-based quantum computation in semiconductors, dephasing of electron spins by a fluctuating background of nuclear spins is a main obstacle. Here we show that this nuclear background can be precisely controlled in generic quantum dots by periodically exciting electron spins. We demonstrate this universal phenomenon in many-electron GaAs/AlGaAs quantum dot ensembles using optical pump-probe spectroscopy. A feedback mechanism between the electron spin polarization and the nuclear system focuses the electron spin precession frequency into discrete spin modes. Employing such control of nuclear spin polarization, the electron spin lifetime within individual dots can surpass the limit of nuclear background fluctuations, thus substantially enhancing the spin coherence time. This opens the door to achieve long electron spin coherence times also in lithographically defined many-electron systems that can be controlled in shape, size and position.

Theoretical Modeling of the Nuclear‐Field Induced Tuning of the Electron Spin Precession for Localized Spins

This work is devoted to a theoretical analysis of the effect of nuclear‐induced field (Overhauser field) on the Larmor frequencies of electron spins under the periodic pulsed excitation. To describe the dynamical nuclear spin polarization, we use the model where the optically induced Stark field determines the magnitude and direction of the Overhauser field. The Stark field strongly depends on the detuning between the photon energy of excitation and the optical transition energy in the quantum system. Detailed calculations which show that the precession frequencies of fluorine donor‐bound electron spins in ZnSe deviate from the linear dependence of the Larmor frequencies on the external magnetic field have been performed. A similar effect is observed for the (In,Ga)As/GaAs quantum dots, where it has been shown that the Overhauser field strongly changes the spectrum of the electron spin precession frequencies.

Electron spin noise under the conditions of nuclei-induced frequency focusing

We study theoretically the electron spin noise in quantum dots under non-equilibrium conditions caused by the pumping by a train of circularly polarized optical pulses. In such a situation, the nuclear spins are known to adjust in such a way, that the electron spin precession frequencies become multiples of the pump pulse repetition frequency. This so called phase synchronization effect was uncovered in [Science {\bf 317}, 1896 (2007)] and termed nuclei-induced frequency focusing of electron spin coherence. Using the classical approach to the central spin model we evaluate the nuclear spin distribution function and the electron spin noise spectrum. We show that the electron spin noise spectrum consists of sharp peaks corresponding to the phase synchronization conditions and directly reveal the distribution of the nuclear spins. We discuss the effects of nuclear spin relaxation after the pumping is over and analyze the corresponding evolution of nuclear spin distributions and electron spin noise spectra.

Nonperturbative correlation effects in diluted magnetic semiconductors

The effects of carrier-impurity correlations due to a Kondo-like spin-spin interaction in diluted magnetic semiconductors are investigated. These correlations are not only responsible for a transfer of spins between the carriers and the impurities, but also produce non-perturbative effects in the spin dynamics such as renormalization of the precession frequency of the carrier spins, which can reach values of several percent in CdMnTe quantum wells. In two-dimensional systems, the precession frequency renormalization for a single electron spin with defined wave vector shows logarithmic divergences similar to those also known from the Kondo problem in metals. For smooth electron distributions, however, the divergences disappear due to the integrability of the logarithm. A possible dephasing mechanism caused by the wave-vector dependence of the electron spin precession frequencies is found to be of minor importance compared to the spin transfer from the carrier to the impurity system. In the Markov limit of the theory, a quasi-equilibrium expression for the carrier-impurity correlation energy can be deduced indicating the formation of strongly correlated carrier-impurity states for temperatures in the mK range.

Spin noise of localized electrons: Interplay of hopping and hyperfine interaction

The theory of spin fluctuations is developed for an ensemble of localized electrons taking into account both hyperfine interaction of electron and nuclear spins and electron hopping between the sites. The analytical expression for the spin noise spectrum is derived for arbitrary relation between the electron spin precession frequency in the field of the nuclear fluctuation and the hopping rate. An increase in the hopping rate results in the drastic change of the spin noise spectrum. The effect of an external magnetic field is briefly addressed.

Electron spin synchronization induced by optical nuclear magnetic resonance feedback

We predict a new physical mechanism explaining the electron spin precession frequency focusing effect observed recently in singly charged quantum dots exposed to a periodic train of resonant circularly polarized short optical pulses [A. Greilich et al, Science 317, 1896 (2007), Ref. 1]. We show that electron spin precession in an external magnetic field and a field of nuclei creates a Knight field oscillating at the frequency of nuclear spin resonance. This field drives the projection of the nuclear spin onto magnetic field to the value that makes the electron spin precession frequency a multiple of the train cyclic repetition frequency, which is the condition at which the Knight field vanishes.

Effect of pump-probe detuning on the Faraday rotation and ellipticity signals of mode-locked spins in (In,Ga)As/GaAs quantum dots

We have studied the Faraday rotation and ellipticity signals in ensembles of singly charged (In,Ga)As/GaAs quantum dots by pump-probe spectroscopy. For degenerate pump and probe we observe that the Faraday rotation signal amplitude first grows with increasing the time separation between pump and probe before a decay is observed for large temporal separations. The temporal behavior of the ellipticity signal, on the other hand, is regular: its amplitude decays with the separation. By contrast, for detuned pump and probe the Faraday rotation and ellipticty signals both exhibit similar and conventional behavior. The experimental results are well described in the frame of a recently developed microscopic theory [I. A. Yugova, M. M. Glazov, E. L. Ivchenko, and Al. L. Efros, Phys. Rev. B 80, 104436 (2009)]. The comparison between calculations and experimental data allows us to provide insight into the spectral dependence of the electron spin precession frequencies and extract the electron $g$ factor dependence on energy.

Dephasing of optically generated electron spins in semiconductors

Dephasing of optically generated electron spins in the presence of the external magnetic field and electric bias in semiconductor nano-structures has been studied by time- and polarization-resolved spectrometry. The obtained experimental data are presented in dependence of the strength of the magnetic field. The optically generated electron-spin precession frequency and dephasing time and rate are estimated. It is found that both the spin precession frequency and dephasing rate increase linearly with the external magnetic field up to about 9 T. However, the spin dephasing time is within sub- μs and is found to decrease exponentially with the strength of the external magnetic field. The results are discussed by exploring possible mechanisms of spin dephasing in low-dimensional semiconductor structures, where the quantum-confinement persists within the nano-range.

Electron-Spin Precession in Dependence of the Orientation of the External Magnetic Field

Electron-spin dynamics in semiconductor-based heterostructures has been investigated in oblique magnetic fields. Spins are generated optically by a circularly polarized light, and the dynamics of spins in dependence of the orientation (θ) of the magnetic field are studied. The electron-spin precession frequency, polarization amplitude, and decay rate as a function ofθare obtained and the reasons for their dependences are discussed. From the measured data, the values of the longitudinal and transverse components of the electrong-factor are estimated and are found to be in good agreement with those obtained in earlier investigations. The possible mechanisms responsible for the observed effects are also discussed.

Two-dimensional imaging of the spin-orbit effective magnetic field

We report on spatially resolved measurements of the spin-orbit effective magnetic field in a $\mathrm{Ga}\mathrm{As}∕\mathrm{In}\mathrm{Ga}\mathrm{As}$ quantum well. Biased gate electrodes lead to an electric-field distribution in which the quantum-well electrons move according to the local orientation and magnitude of the electric field. This motion induces Rashba and Dresselhaus effective magnetic fields. The projection of the sum of these fields onto an external magnetic field is monitored locally by measuring the electron spin-precession frequency using time-resolved Faraday rotation. A comparison with simulations shows good agreement with the experimental data.

Oscillatory Dyakonov-Perel spin dynamics in two-dimensional electron gases

Optical pump-probe measurements of spin dynamics at temperatures down to $1.5\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ are described for a series of (001)-oriented $\mathrm{Ga}\mathrm{As}∕\mathrm{Al}\mathrm{Ga}\mathrm{As}$ quantum well samples containing high mobility two-dimensional electron gases (2DEGs). For well widths ranging from $5\phantom{\rule{0.3em}{0ex}}\text{to}\phantom{\rule{0.3em}{0ex}}20\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$ and 2DEG sheet densities from $1.75\ifmmode\times\else\texttimes\fi{}{10}^{11}\phantom{\rule{0.3em}{0ex}}\text{to}\phantom{\rule{0.3em}{0ex}}3.5\ifmmode\times\else\texttimes\fi{}{10}^{11}\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}2}$, the evolution of a small injected spin population is found to be a damped oscillation rather than an exponential relaxation, consistent with the quasi-collision-free regime of the Dyakonov-Perel spin dynamics. A Monte Carlo simulation method is used to extract the spin-orbit-induced electron spin precession frequency $\ensuremath{\mid}\ensuremath{\Omega}({k}_{F})\ensuremath{\mid}$ and electron momentum scattering time $\ensuremath{\tau}_{p}{}^{*}$ at the Fermi wave vector. The spin decay time passes through a minimum at a temperature corresponding to the transition from collision-free to collision-dominated regimes and $\ensuremath{\tau}_{p}{}^{*}$ is found to be close to the ensemble momentum scattering time ${\ensuremath{\tau}}_{p}$ obtained from Hall measurements of electron mobility. The values of $\ensuremath{\mid}\ensuremath{\Omega}({k}_{F})\ensuremath{\mid}$ give the Dresselhaus or bulk inversion asymmetry (BIA) coefficient of spin-orbit interaction as a function of electron confinement energy in the quantum wells and show, qualitatively, the behavior expected from $k∙p$ theory.

Gate tunability of stray-field-induced electron spin precession in aGaAs∕InxGa1−xAsquantum well below an interdigitated magnetized Fe grating

Time-resolved Faraday rotation is used to measure the coherent electron spin precession in a $\mathrm{Ga}\mathrm{As}∕{\mathrm{In}}_{x}{\mathrm{Ga}}_{1\ensuremath{-}x}\mathrm{As}$ quantum well below an interdigitated magnetized Fe grating. We show that the electron spin precession frequency can be modified by applying a gate voltage of opposite polarity to neighboring bars. A tunability of the precession frequency of $0.5\phantom{\rule{0.3em}{0ex}}\mathrm{GHz}∕\mathrm{V}$ has been observed. Modulating the gate potential with a gigahertz frequency allows the electron spin precession to be controlled on a nanosecond timescale.

Optoelectronic control of spin dynamics at near-terahertz frequencies in magnetically doped quantum wells

We use time-resolved Kerr rotation to demonstrate the optical and electronic tuning of both the electronic and local moment (Mn) spin dynamics in electrically gated parabolic quantum wells derived from II-VI diluted magnetic semiconductors. By changing either the electrical bias or the laser energy, the electron spin precession frequency is varied from 0.1 to 0.8 THz at a magnetic field of 3 T and at a temperature of 5 K. The corresponding range of the electrically-tuned effective electron g-factor is an order of magnitude larger compared with similar nonmagnetic III-V parabolic quantum wells. Additionally, we demonstrate that such structures allow electrical modulation of local moment dynamics in the solid state, which is manifested as changes in the amplitude and lifetime of the Mn spin precession signal under electrical bias. The large variation of electron and Mn-ion spin dynamics is explained by changes in magnitude of the sp−d exchange overlap.

Effects of terrestrial tides on the LEP beam energy

The circular e +e − collider LEP located near Geneva is used to investigate the properties of the Z boson. The measurements of the Z boson mass and resonance width are of fundamental importance for the standard model of the electroweak interactions. They require a knowledge of the LEP beam energy with a precision of ∼ 20 ppm, which is provided by a measurement of the electron spin precession frequency. To extrapolate beam energy calibrations over a longer period of time, effects causing energy changes have to be taken into account. Among these are the terrestrial tides due to the sun and moon which move the Earth surface up and down. The lateral components of this motion modify the 26.7 km LEP circumference by about 1 mm. This change in length results in variations of the beam energy up to 120 ppm. We present results of measurements on the influence of terrestrial tides on the LEP beam energy that have been performed in 1992 and 1993.

Microwave resonance relaxation properties of the HTSC materials near Tc

The measurements of the joule heat loss relaxation in the form of the power loss relaxation Q( tau ) of the microwave cavity, with a sample excited at the quasi-free electron spin precession frequency (9.5 GHz) and on cooling the sample from room temperature to 77 K, have been reported. It is found that the microwave resonance relaxation absorption (MRRA) spectra near Tc observed for the sample exhibit the SC phase transition based on the temperature DC resistance measurements.