Solid-state quantum computation—a new direction for nanotechnology

We review current proposals for six types of solid-state quantum computers. We discuss the general requirements for solid-state quantum computers and describe proposals which employ superconducting junctions, electron orbitals in quantum dots, electron spin resonance, nuclear spins of impurity atoms, and nuclear spins in a crystal lattice. We also describe our proposed nuclear spin quantum computer based on magnetic resonance force microscopy. Finally, we describe our numerical method for modeling quantum transformations with a large number (up to 1000) of qubits.     

Direct observation of the electron spin relaxation induced by nuclei in quantum dots

We have studied the electron spin relaxation in semiconductor InAs/GaAs quantum dots by time-resolved optical spectroscopy. The average spin polarization of the electrons in an ensemble of p-doped quantum dots decays down to 1/3 of its initial value with a characteristic time T(Delta) approximately 500 ps, which is attributed to the hyperfine interaction with randomly oriented nuclear spins. We show that this efficient electron spin relaxation mechanism can be suppressed by an external magnetic field as small as 100 mT.     

Measurement of a heavy-hole hyperfine interaction in InGaAs quantum dots using resonance fluorescence

We measure the strength and the sign of hyperfine interaction of a heavy hole with nuclear spins in single self-assembled quantum dots. Our experiments utilize the locking of a quantum dot resonance to an incident laser frequency to generate nuclear spin polarization. By monitoring the resulting Overhauser shift of optical transitions that are split either by electron or exciton Zeeman energy with respect to the locked transition using resonance fluorescence, we find that the ratio of the heavy-hole and electron hyperfine interactions is -0.09 ± 0.02 in three quantum dots. Since hyperfine interactions constitute the principal decoherence source for spin qubits, we expect our results to be important for efforts aimed at using heavy-hole spins in quantum information processing.     

Self-polarization and dynamical cooling of nuclear spins in double quantum dots

The spin-blockade regime of double quantum dots features coupled dynamics of electron and nuclear spins resulting from the hyperfine interaction. We explain observed nuclear self-polarization via a mechanism based on feedback of the Overhauser shift on electron energy levels, and propose to use the instability toward self-polarization as a vehicle for controlling the nuclear spin distribution. In the dynamics induced by a properly chosen time-dependent magnetic field, nuclear spin fluctuations can be suppressed significantly below the thermal level.     

Intrinsic spin fluctuations reveal the dynamical response function of holes coupled to nuclear spin baths in (In,Ga)As quantum dots

The problem of how single central spins interact with a nuclear spin bath is essential for understanding decoherence and relaxation in many quantum systems, yet is highly nontrivial owing to the many-body couplings involved. Different models yield widely varying time scales and dynamical responses (exponential, power-law, gaussian, etc.). Here we detect the small random fluctuations of central spins in thermal equilibrium [holes in singly charged (In,Ga)As quantum dots] to reveal the time scales and functional form of bath-induced spin relaxation. This spin noise indicates long (400 ns) spin correlation times at a zero magnetic field that increase to ～5 μs as dominant hole-nuclear relaxation channels are suppressed with small (100 G) applied fields. Concomitantly, the noise line shape evolves from Lorentzian to power law, indicating a crossover from exponential to slow [～1/log(t)] dynamics.     

Spin–orbit interaction induced current dip in a single quantum dot coupled to a spin

Experiments on semiconductor quantum dot systems have demonstrated the coupling between electron spins in quantum dots and spins localized in the neighboring area of the dots. Here we show that in a magnetic field the electrical current flowing through a single quantum dot tunnel-coupled to a spin displays a dip at the singlet–triplet anticrossing point which appears due to the spin–orbit interaction. We specify the requirements for which the current dip is formed and examine the properties of the dip for various system parameters, such as energy detuning, spin–orbit interaction strength, and coupling to leads. We suggest a parameter range in which the dip could be probed.     

Optical RKKY interaction between charged semiconductor quantum dots

We show how a spin interaction between electrons localized in neighboring quantum dots can be induced and controlled optically. The coupling is generated via virtual excitation of delocalized excitons and provides an efficient coherent control of the spins. This quantum manipulation can be realized in the adiabatic limit and is robust against decoherence by spontaneous emission. Applications to the realization of quantum gates, scalable quantum computers, and to the control of magnetization in an array of charged dots are proposed.     

Ferromagnetism in diluted magnetic semiconductor quantum dot arrays embedded in semiconductors

We present an Anderson-type model Hamiltonian with exchange coupling between the localized spins and the confined holes in the quantum dots to study the ferromagnetism in diluted magnetic semiconductor (DMS) quantum dot arrays embedded in semiconductors. The hybridization between the quantum-confined holes in the quantum dots and the itinerant holes in the semiconductor valence band makes possible hole transfer between the DMS quantum dots, which can induce the long range ferromagnetic order of the localized spins. In addition, it makes the carrier spins both in the quantum dots and in the semiconductors polarized. The spontaneous magnetization of the localized spins and the spin polarization of the holes are calculated using both the Weiss mean field approximation and the self-consistent spin wave approximation, which are developed for the present model.Received: 17 Mars 2003, Published online: 30 January 2004PACS: 75.75. + a Magnetic properties of nanostructures - 75.30.Ds Spin waves - 75.50.Dd Nonmetallic ferromagnetic materials - 75.50.Pp Magnetic semiconductors     

Computing with spins: from classical to quantum computing

This article reviews the use of single electron spins to compute. In classical computing schemes, a binary bit is represented by the bistable spin polarization of a single electron confined in a quantum dot and subjected to a weak magnetic field. The spin orientation can be either parallel or anti-parallel to the field, so that it becomes a binary variable which can encode logic 0 and logic 1. Coherent superposition of these two polarizations can represent a qubit for quantum computing. By engineering the exchange interaction between closely spaced spins in neighboring quantum dots, it is possible to implement either classical or quantum logic gates.     

Electron–Nuclear Spin Dynamics in Semiconductor QDs

This work presents an overview of investigations of the nuclear spin dynamics in nanostructures with negatively charged InGaAs/GaAs quantum dots characterized by strong quadrupole splitting of nuclear spin sublevels. The main method of the investigations is the experimental measurements and the theoretical analysis of the photoluminescence polarization as a function of the transverse magnetic field (effect Hanle). The dependence of the Hanle curve profile on the temporal protocol of optical excitation is examined. Experimental data are analyzed using an original approach based on separate consideration of behavior of the longitudinal and transverse components of the nuclear polarization. The rise and decay times of each component of the nuclear polarization and their dependence on transverse magnetic field strength are determined. To study the role of the Knight field in the dynamic of nuclear polarization, a weak additional magnetic field parallel to the optical axis is used. We have found that, only taking into account the nuclear spin fluctuations, we can accurately describe the measured Hanle curves and evaluate the parameters of the electron–nuclear spin system in the studied quantum dots. A new effect of the resonant optical pumping of nuclear spin polarization in an ensemble of the singly charged (In,Ga)As/GaAs quantum dots subjected to a transverse magnetic field is discussed. Nuclear spin resonances for all isotopes in the quantum dots are detected in that way. In particular, transitions between the states split off from the ±1/2 doublets by the nuclear quadrupole interaction are identified.     

Pairing of spin excitations in lateral quantum dots

We demonstrate the existence of correlated electronic states as paired spin excitations of lateral quantum dots in the integer quantum Hall regime. Starting from the spin-singlet filling-factor nu=2 droplet, by increasing the magnetic field we force the electrons to flip spins and increase the spin polarization. We identify the second spin-flip process as one accompanied by correlated, spin depolarized phases, interpreted as pairs of spin excitons. The correlated states are identified experimentally in few-electron lateral quantum dots using high source-drain voltage spectroscopy.     

Generating entanglement and squeezed states of nuclear spins in quantum dots

We present a scheme for achieving coherent spin squeezing of nuclear spin states in semiconductor quantum dots. The nuclear polarization dependence of the electron spin resonance generates a unitary evolution that drives nuclear spins into a collective entangled state. The polarization dependence of the resonance generates an area-preserving, twisting dynamics that squeezes and stretches the nuclear spin Wigner distribution without the need for nuclear spin flips. Our estimates of squeezing times indicate that the entanglement threshold can be reached in current experiments.     

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.     

Detecting entanglement using a double-quantum-dot turnstile

We propose a scheme based on using the singlet ground state of an electron spin pair in a double-quantum-dot nanostructure as a suitable setup for detecting entanglement between electron spins via the measurement of an optimal entanglement witness. Using time-dependent gate voltages and magnetic fields the entangled spins are separated and coherently rotated in the quantum dots and subsequently detected at spin-polarized quantum point contacts. We analyze the coherent time evolution of the entangled pair and show that by counting coincidences in the four exits an entanglement test can be done. This setup is close to present-day experimental possibilities and can be used to produce pairs of entangled electrons "on demand."     

High-Field Phenomena of Qubits

Electron and nuclear spins are very promising candidates to serve as quantum bits (qubits) for proposed quantum computers, as the spin degrees of freedom are relatively isolated from their surroundings and can be coherently manipulated, e.g., through pulsed electron paramagnetic resonance (EPR) and nuclear magnetic resonance (NMR). For solid-state spin systems, impurities in crystals based on carbon and silicon in various forms have been suggested as qubits, and very long relaxation rates have been observed in such systems. We have investigated a variety of these systems at high magnetic fields in our multifrequency pulsed EPR/ENDOR (electron nuclear double resonance) spectrometer. A high magnetic field leads to large electron spin polarizations at helium temperatures, giving rise to various phenomena that are of interest with respect to quantum computing. For example, it allows the initialization of both the electron spin as well as hyperfine-coupled nuclear spins in a well-defined state by combining millimeter and radio-frequency radiation. It can increase the T ₂ relaxation times by eliminating decoherence due to dipolar interaction and lead to new mechanisms for the coherent electrical readout of electron spins. We will show some examples of these and other effects in Si:P, SiC:N and nitrogen-related centers in diamond.     

Optical pumping of nuclear spin magnetization in GaAs/AlAs quantum wells of variable electron density

We report the use of time-resolved Faraday rotation to induce and probe the polarization of nuclear spins within a set of quantum wells with varying background electron density. The electron density was controlled over a broad range by making use of structures of mixed type-I/type-II GaAs/AlAs quantum wells that spatially separate photoexcited electron–hole pairs. We find that the optically detected nuclear magnetic field decreases quasi-monotonically with increasing electron density. The likely factors responsible for this behavior are increased electron spin-lattice relaxation, increased electron spin delocalization, and dilution of the electron spin polarization.     

Magnetic interaction between coupled quantum dots

We study the magnetic coupling in artificial molecules composed of two and four laterally coupled quantum dots. The electronic ground-state configurations of such systems are determined by applying current spin density functional theory which allows to include effects of magnetic fields. While the ground-state of a two-dot molecule with strong enough inter-dot coupling tends to be antiferromagnetic with respect to the spins of the single dot components, we find that a square lattice of four dots has a ferromagnetic ground state. Received 17 February 1999 and Received in final form 1 June 1999     

Optical spin orientation of a single manganese atom in a quantum dot

The magnetic state of a single magnetic atom (Mn) embedded in an individual semiconductor quantum dot is optically probed using micro-spectroscopy. A high degree of spin polarization can be achieved for an individual Mn atom localized in a quantum dot using quasi-resonant or fully-resonant optical excitation at zero magnetic field. Optically created spin polarized carriers generate an energy splitting of the Mn spin and enable magnetic moment orientation controlled by the photon helicity and energy. The dynamics and the magnetic field dependence of the optical pumping mechanism shows that the spin lifetime of an isolated Mn atom at zero magnetic field is controlled by a magnetic anisotropy induced by the built-in strain in the quantum dots. The Mn spin distribution prepared by optical pumping is fully conserved for a few microseconds. This opens the way to full optical control of the spin state of an individual magnetic atom in a solid state environment.     

单层正三角锯齿型石墨烯量子点的电子结构和磁性

采用基于密度泛函理论的广义梯度近似(GGA),对不同尺寸(N=2—11)的单层正三角锯齿型石墨烯量子点(Z_N -GNDs)的结构进行优化,得到与实验数据较好符合的晶格常数,进一步计算得到不同尺寸下体系的自旋多重度、磁矩、电子态密度以及自旋电子密度.结果表明:所有体系都呈现金属性,在尺寸较小的体系中量子尺寸效应对电子结构的影响比较明显;与单层石墨烯片一样,sp²杂化作用和非键态电子在量子点中仍起到非常重要的作用;费米能级上有自旋向上的电子分布,体系的 关键词： 石墨烯 量子点 电子结构 磁性     

Modulation of magnetic and electrical properties of bilayer graphene quantum dots using rotational stacking faults

Bilayer graphene quantum dots with rotational stacking faults(RSFs) having different rotational angles were studied.Using the first-principles calculation, we determined that these stacking faults could quantitatively modulate the magnetism and the distribution of spin and energy levels in the electronic structures of the dots.In addition, by examining the spatial distribution of unpaired spins and Bader charge analysis, we found that the main source of magnetic moment originated from the edge atoms of the quantum dots.Our research results can potentially provide a new path for producing all-carbon nanodevices with different electrical and magnetic properties.