Electron-nuclear Spin Dynamics Research Articles

Transport-induced suppression of nuclear field fluctuations in multi-quantum-dot systems

Magnetic noise from randomly fluctuating nuclear spin ensembles is the dominating source of decoherence for many multi-quantum-dot multielectron spin qubits. Here we investigate in detail the effect of a DC electric current on the coupled electron-nuclear spin dynamics in double and triple quantum dots tuned to the regime of Pauli spin blockade. We consider both systems with and without significant spin-orbit coupling and find that in all cases the flow of electrons can induce a process of dynamical nuclear spin polarization that effectively suppresses the nuclear polarization gradients over neighboring dots. Since exactly these gradients are the components of the nuclear fields that act harmfully in the qubit subspace, we believe that this presents a straightforward way to extend coherence times in multielectron spin qubits by at least one order of magnitude.

Electron-nuclear spin dynamics of Ga centers in GaAsN dilute nitride semiconductors probed by pump-probe spectroscopy

We propose an experimental procedure to track the evolution of electronic and nuclear spins in Ga2+ centers in GaAsN dilute semiconductors. The method is based on a pump-probe scheme that enables to monitor the time evolution of the three components of the electronic and nuclear spin variables. In contrast to other characterization methods, as nuclear magnetic resonance, this one only needs moderate magnetic fields (\(B\approx 10\) mT), and does not require microwave irradiation. Specifically, we carry out a series of tests for different experimental conditions in order to optimize the procedure for maximum sensitivity in the measurement of the circular degree of polarization. Based on previous experimental results and the theoretical calculations presented here, we estimate that the method could yield a time resolution of about 10ps.

Spin-filtering effect in GaAsN: electron-nuclear spin dynamics of Ga3+ centers

The impact of Ga3+ centers in the spin-filtering effect observed in GaAsN samples is investigated through a model based on the master equation approach. Our results, compared with experimental data, show that, Ga3+ are essential to understanding the behavior of the photoluminescence intensity and degree of circular polarization as functions of a Faraday configuration magnetic field. The model presented here takes into account the interplay of Ga2+ and Ga3+ centers, Zeeman and hyperfine interaction. The various processes that drive the spin-filtering effect, as the spin selective capture of conduction band electrons into Ga centers are also considered here.

Dynamic nuclear polarization with three electrons in a vertical double quantum dot

We report the observation of dynamic nuclear polarization in a vertical double quantum dot, as a result of a hyperfine interaction with three confined electrons. Our data allow us to distinguish three pumping regimes, characterized by different magnitudes and directions of polarization. Corresponding electron-nuclear spin dynamics is understood by considering relevant three-electron states mixed by hyperfine interaction. Also, an extremely long nuclear spin relaxation time is reported.

Electrical current and coupled electron-nuclear spin dynamics in double quantum dots

We examine electronic transport in a spin-blockaded double quantum dot. We show that by tuning the strength of the spin-orbit interaction the current flowing through the double dot exhibits a dip at zero magnetic field or a peak at a magnetic field for which the two-electron energy levels anticross. This behavior is due to the dependence of the singlet-triplet mixing on the field and spin-orbit amplitude. We derive approximate expressions for the current as a function of the amplitudes of the states involved in the transport. We also consider an alternative model that takes into account a finite number of nuclear spins and study the resulting coupled dynamics between electron and nuclear spins. We show that if the spin ensemble is in a thermal state there are regular oscillations in the transient current followed by quasichaotic revivals akin to those seen in a thermal Jaynes-Cummings model.

Effect of magnetic field on the electron-nuclear spin dynamics in quantum dots

We report on the theoretical study of the joint effect of the hyperfine interaction and an external magnetic field on the electron-nuclear spin dynamics in a quantum dot. The study is based on the quantum-mechanical description of the hyperfine interaction of an electron spin with a finite number of nuclear spins in the frame of the graded box model. This approach clearly demonstrates electron-spin depolarization in the nuclear spin fluctuations and its suppression by the external magnetic field and dynamic nuclear spin polarization.

Detection of local electron and nuclear spin dynamics by time-resolved Kerr microscopy

We implement time-resolved Kerr microscopy (TRKM) system with ∼ 1 μ m spatial resolution for observation of coupled electron–nuclear spin dynamics such as dynamic nuclear polarization (DNP) in a local area of the laser spot. From TRKM measurements, Larmor precession of electron spins injected by right ( σ + ) or left ( σ − ) circular polarized pump pulse is detected. The difference of the precession frequencies between σ + and σ − pumping corresponds to the polarization-dependent nuclear magnetic field caused by DNP. This indicates that we successfully detect coupled electron–nuclear spin dynamics in a local area of the laser spot size of ∼ 1.5 × 1.5 μ m 2 . Furthermore, we show the pump and probe power dependences of DNP in high optical intensity region. All-optical NMR is also demonstrated at arbitrary frequencies by controlling acousto-optical modulator.

Long-term dynamics of the electron-nuclear spin system of a semiconductor quantum dot

A quasiclassical theoretical description of polarization and relaxation of nuclear spins in a quantum dot with one resident electron is developed for arbitrary mechanisms of electron-spin polarization. The dependence of the electron-nuclear spin dynamics on the correlation time ${\ensuremath{\tau}}_{c}$ of electron-spin precession, with frequency $\ensuremath{\Omega}$, in the nuclear hyperfine field is analyzed. It is demonstrated that the highest nuclear polarization is achieved for a correlation time close to the period of electron-spin precession in the nuclear field. For these and larger correlation times, the indirect hyperfine field, which acts on nuclear spins, also reaches a maximum. This maximum is of the order of the dipole-dipole magnetic field that nuclei create on each other. This value is nonzero even if the average electron polarization vanishes. It is shown that the transition from short correlation time to $\ensuremath{\Omega}{\ensuremath{\tau}}_{c}\ensuremath{\gtrsim}1$ does not affect the general structure of the equation for nuclear-spin temperature and nuclear polarization in the Knight field but changes the values of parameters, which now become functions of $\ensuremath{\Omega}{\ensuremath{\tau}}_{c}$. For correlation times larger than the precession time of nuclei in the electron hyperfine field, it is found that three thermodynamic potentials $(\ensuremath{\chi},\mathbit{\ensuremath{\xi}},\ensuremath{\varsigma})$ characterize the polarized electron-nuclear spin system. The values of these potentials are calculated assuming a sharp transition from short to long correlation times, and the relaxation mechanisms of these potentials are discussed. The relaxation of the nuclear-spin potential is simulated numerically showing that high nuclear polarization decreases relaxation rate.

Coupled electron-nuclear spin dynamics in quantum dots: A graded box model approach

The dynamics of electron and nuclear spin polarization in an ensemble of singly negatively charged quantum dots subject to optical excitation is theoretically studied using a graded box model, in which the electron density is approximated by a sequence of steps. The model is numerically implemented for a limited number of nuclei (up to $N=192$) with spins $I=1/2$ or $I=3/2$. The polarization dynamics is found to depend strongly on the polarized excitation protocol. For excitation by periodic laser pulses, the electron-nuclear spin dynamics evolves coherently and gives rise to a recurrence effect in the electron spin dynamics as well as to a decelerated nuclear polarization. The validity of the model is justified by comparison with experimental data on the electron spin polarization in (In,Ga)As/GaAs quantum dots.

Switched control of electron nuclear spin systems

We study control of electron-nuclear spin dynamics at magnetic field strengths where the Larmor frequency of the nucleus is comparable to the hyperfine coupling strength. The quantization axis for the nuclear spin differs from the static ${B}_{0}$ field direction and depends on the state of the electron spin. The quantization axis can be switched by flipping the state of electron spin, allowing for universal control of nuclear spin states. We show that by performing a sequence of flips (each followed by a suitable delay), we can perform any desired rotation of the nuclear spin, which can also be conditioned on the state of the electron spin. These operations, combined with electron spin rotations, can be used to synthesize any unitary transformation of the coupled electron-nuclear spin system. We discuss how these methods can be used for design of experiments for transfer of polarization from the electron to the nuclear spins.

Control of electron spin decoherence caused by electron–nuclear spin dynamics in a quantum dot

Control of electron spin decoherence in contact with a mesoscopic bath of many interacting nuclear spins in an InAs quantum dot is studied by solving the coupled quantum dynamics. The nuclear spin bath, because of its bifurcated evolution predicated on the electron spin up or down state, measures the which-state information of the electron spin and hence diminishes its coherence. The many-body dynamics of the nuclear spin bath is solved with a pair-correlation approximation. In the relevant timescale, nuclear pair-wise flip–flops, as elementary excitations in the mesoscopic bath, can be mapped into the precession of non-interacting pseudo-spins. Such mapping provides a geometrical picture for understanding the decoherence and for devising control schemes. A close examination of nuclear bath dynamics reveals a wealth of phenomena and new possibilities of controlling the electron spin decoherence. For example, when the electron spin is flipped by a π-pulse at τ, its coherence will partially recover at as a consequence of quantum disentanglement from the mesoscopic bath. In contrast to the re-focusing of inhomogeneously broadened phases by conventional spin-echoes, the disentanglement is realized through shepherding quantum evolution of the bath state via control of the quantum object. A concatenated construction of pulse sequences can eliminate the decoherence with arbitrary accuracy, with the nuclear–nuclear spin interaction strength acting as the controlling small parameter.

Theory of electron spin decoherence by interacting nuclear spins in a quantum dot

We present a quantum solution to the electron spin decoherence by a nuclear pair-correlation method for the electron-nuclear spin dynamics under a strong magnetic field and a temperature high for the nuclear spins but low for the electron. The theory incorporates the hyperfine interaction, the intrinsic (both direct and indirect) nuclear interactions, and the extrinsic nuclear coupling mediated by the hyperfine interaction with the single electron in question. The last is shown to be important in free-induction decay (FID) of the single electron spin coherence. The spin echo eliminates the hyperfine-mediated decoherence but only reduces the decoherence by the intrinsic nuclear interactions. Thus, the decoherence times for single spin FID and ensemble spin echo are significantly different. The decoherence is explained in terms of quantum entanglement, which involves more than the spectral diffusion.