准一维半导体量子点中电偶极自旋共振的物理机理

半导体量子点中的电子自旋具有较长相干时间以及可扩展性的特点, 在近十几年来引起了人们的广泛兴趣. 人们常常利用电子自旋共振技术来对单个自旋进行操纵. 这样不但需要一个静磁场来使电子产生赛曼劈裂, 同时还需要一个与之垂直的局域振荡磁场. 但是, 在实验上产生足够强且具有固定频率的局域磁场是比较困难的. 后来人们发现, 局域的振荡电场也可以操纵单个电子自旋, 也就是所谓的电偶极自旋共振. 众所周知, 自旋只有自旋磁矩, 不会与电场有任何直接的相互作用. 所以, 电偶极自旋共振的发生必须依赖于某些媒质. 这些媒质包括：量子点材料中的自旋轨道耦合作用, 量子点中的局域磁场梯度, 以及量子点中电子自旋与核自旋的超精细相互作用. 这些媒质能诱导出自旋与电场之间间接的相互作用, 从而外电场操纵单个电子自旋得以实现. 本文总结归纳了目前半导体量子点系统中发生电偶极自旋共振的三种主要物理机理.     

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.     

Anisotropic spin relaxation in graphene

Spin relaxation in graphene is investigated in electrical graphene spin valve devices in the nonlocal geometry. Ferromagnetic electrodes with in-plane magnetizations inject spins parallel to the graphene layer. They are subject to Hanle spin precession under a magnetic field B applied perpendicular to the graphene layer. Fields above 1.5 T force the magnetization direction of the ferromagnetic contacts to align to the field, allowing injection of spins perpendicular to the graphene plane. A comparison of the spin signals at B=0 and B=2 T shows a 20% decrease in spin relaxation time for spins perpendicular to the graphene layer compared to spins parallel to the layer. We analyze the results in terms of the different strengths of the spin-orbit effective fields in the in-plane and out-of-plane directions and discuss the role of the Elliott-Yafet and Dyakonov-Perel mechanisms for spin relaxation.     

Gate control of quantum dot-based electron spin–orbit qubits

We investigate theoretically the coherent spin dynamics of gate control of quantum dot-based electron spin–orbit qubits subjected to a tilted magnetic field under electric-dipole spin resonance (EDSR). Our results reveal that Rabi oscillation of qubit states can be manipulated electrically based on rapid gate control of SOC strength. The Rabi frequency is strongly dependent on the gate-induced electric field, the strength and orientation of the applied magnetic field. There are two major EDSR mechanisms. One arises from electric field-induced spin–orbit hybridization, and the other arises from magnetic field-induced energy-level crossing. The SOC introduced by the gate-induced electric field allows AC electric fields to drive coherent Rabi oscillations between spin-up and -down states. After the crossing of the energy-levels with the magnetic field, the spin-transfer crossing results in Rabi oscillation irrespective of whether or not the external electric field is present. The spin–orbit qubit is transferred into the orbit qubit. Rabi oscillation is anisotropic and periodic with respect to the tilted and in-plane orientation of the magnetic field originating from the interplay of the SOC, orbital, and Zeeman effects. The strong electrically-controlled SOC strength suggests the possibility for scalable applications of gate-controllable spin–orbit qubits.     

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.     

Electric field induced nuclear spin resonance mediated by oscillating electron spin domains in GaAs-based semiconductors

We demonstrate an alternative nuclear spin resonance using a radio frequency (rf) electric field [nuclear electric resonance (NER)] instead of a magnetic field. The NER is based on the electronic control of electron spins forming a domain structure. The rf electric field applied to a gate excites spatial oscillations of the domain walls and thus temporal oscillations of the hyperfine field to nuclear spins. The rf power and burst duration dependence of the NER spectrum provides insight into the interplay between nuclear spins and the oscillating domain walls.     

Detection and manipulation of statistical polarization in small spin ensembles

We report the detection of the square root of N statistical polarization in a small ensemble of electron spin centers in SiO2 by magnetic resonance force microscopy. A novel detection technique was employed that captures the statistical polarization and cycles it between states that are either locked or antilocked to the effective field in the rotating frame. Using field gradients as high as 5 G/nm, we achieved a detection sensitivity equivalent to roughly two electron spins, and observed ultralong spin-lock lifetimes, as long as 20 s. Given a sufficient signal-to-noise ratio, this scheme should be extendable to single electron spin detection.     

Voltage-selective bidirectional polarization and coherent rotation of nuclear spins in quantum dots

We propose and demonstrate that the nuclear spins of the host lattice in GaAs double quantum dots can be polarized in either of two opposite directions, parallel or antiparallel to an external magnetic field. The direction is selected by adjusting the dc voltage. This nuclear polarization manifests itself by repeated controlled electron-nuclear spin scattering in the Pauli spin-blockade state. Polarized nuclei are also controlled by means of nuclear magnetic resonance. This Letter confirms that the nuclear spins in quantum dots are long-lived quantum states with a coherence time of up to 1 ms, and may be a promising resource for quantum-information processing such as quantum memories for electron spin qubits.     

Polynomially scaling spin dynamics simulation algorithm based on adaptive state-space restriction

We report progress with an old problem in magnetic resonance -- that of the exponential scaling of simulation complexity with the number of spins. It is demonstrated below that a polynomially scaling algorithm can be obtained (and accurate simulations performed for over 200 coupled spins) if the dimension of the Liouville state space is reduced by excluding unimportant and unpopulated spin states. We found the class of such states to be surprisingly wide. It actually appears that a majority of states in large spin systems are not essential in magnetic resonance simulations and can safely be dropped from the state space. In restricted state spaces the spin dynamics simulations scale polynomially. In cases of favourable interaction topologies (sparse graphs, e.g. in protein NMR) the asymptotic scaling is linear, opening the way to direct fitting of molecular structures to experimental spectra.     

Stark tuning of donor electron spins in silicon

We report Stark shift measurements for 121Sb donor electron spins in silicon using pulsed electron spin resonance. Interdigitated metal gates on a Sb-implanted 28Si epilayer are used to apply the electric fields. Two quadratic Stark effects are resolved: a decrease of the hyperfine coupling between electron and nuclear spins of the donor and a decrease in electron Zeeman g factor. The hyperfine term prevails at magnetic fields of 0.35 T, while the g factor term is expected to dominate at higher magnetic fields. We discuss the results in the context of the Kane model quantum computer.     

One-Step Implementation of Single Spin Measurement in Spin Star Network

We present an efficient one-step scheme for a single spin measurement based on nuclear magnetic resonance （NMR） techniques. This scheme considerably reduces the time of operation using a spin star network where a target spin and an ancillary spin are coupled to a ring of N spins. As opposed to the proposal in [Phys. Rev. Lett. 97 （2006） 100501] using a cubic lattice crystal to achieve a cubic speedup, the distinct advantage of this scheme is that under ideal conditions it requires the application of only one step to create a system of N correlated spins. In the process of single spin measurement, the total macroscopic magnetization, the individual magnetization and the transfer fidelity are calculated analytically as simple cosine functions of time and the amplitude of irradiation.     

Magnetic structure and magnetic excitations in the two-dimensional spin system of the Cu<Subscript>3</Subscript>B<Subscript>2</Subscript>O<Subscript>6</Subscript> compound

This paper reports on the results of measurements of the magnetic susceptibility, heat capacity, neutron scattering, muon spin relaxation, and electron paramagnetic resonance in Cu₃B₂O₆ for the study of the ground state of the spin system of this compound. The results obtained suggest that, at a temperature of 10 K, the spin subsystem of the crystal, which consists of single spins and clusters of pairs and fours of spins interacting with one another, undergoes a transition to a state representing a superposition of the singlet (for clusters) and magnetically ordered (for single spins) states.     

Real time magnetic field sensing and imaging using a single spin in diamond

The Zeeman splitting of a localized single spin can be used to construct a highly sensitive magnetometer offering almost atomic spatial resolution. While sub-μT sensitivity can be obtained in principle using pulsed techniques and long measurement times, a fast and easy method without laborious data postprocessing is desirable for a scanning-probe approach with high spatial resolution. In order to measure the resonance frequency in real time, we applied a field-frequency lock to the optically detected magnetic resonance signal of a single electron spin in a nanodiamond. We achieved a sampling rate of up to 100 readings per sec with a sensitivity of 6 μT/sqrt[Hz]. Images of the field distribution around a magnetic wire were acquired with ～30 μT resolution and 4096 submicron sized pixels in 10 min. The response of several spins was used to reconstruct the field orientation.     

Spectroscopic imaging from spatially-encoded single-scan multidimensional MRI data

We have recently proposed a protocol for retrieving multidimensional magnetic resonance images within a single scan, based on a spatial encoding of the spin interactions. This methodology relies on progressively dephasing spin coherences throughout a sample; for instance, by sweeping a radiofrequency pulse in the presence of a magnetic field gradient. When spins are suitably refocused by a second (acquisition) field gradient, this yields a time-domain signal reflecting in its magnitude the spatial distribution of spins throughout the sample. It is hereby shown that whereas the absolute value of the resulting signals conveys such imaging information, the hitherto unutilized phase modulation of the signal encodes the chemical shift offsets of the present speciae. Spectroscopically-resolved multidimensional images can thereby be retrieved in this fashion at no additional expense in either experimental complexity, sensitivity or acquisition time--simply by performing an additional analysis of the collected data. The resulting approach to single-scan spectroscopic imaging can also incorporate "RF shimming" compensating abilities, capable of providing high-resolution spectral and high-definition imaging data even under the presence of substantial magnetic field inhomogeneities. The principles of these methodologies as applied to spectroscopic imaging are briefly reviewed and compared against the background of traditional Fourier-based single-scan spectroscopic imaging protocols. Demonstrations of these new multidimensional spectroscopic MRI experiments on simple phantoms are also given.     

Optical tailoring of electron spin coherence in quantum dots

We address the precession of an ensemble of electron spins, each confined in a (In, Ga)As/GaAs self-assembled quantum dot. The quantum dot inhomogeneity is directly reflected in the precession of the optically oriented electron spins about an external magnetic field, which is subject to fast dephasing on a nanoseconds time scale. Proper periodic laser excitation allows synchronization of the electron spin precessions with the excitation cycle. The experimental conditions can be tailored such that eventually all (about a million) electron spins that are excited by the laser precess with a single frequency. In this regime the ensemble can be exploited during the single electron spin coherence times being in the microseconds range.     

Enhancement of electron spin coherence by optical preparation of nuclear spins

We study a large ensemble of nuclear spins interacting with a single electron spin in a quantum dot under optical excitation and photon detection. At the two-photon resonance between the two electron-spin states, the detection of light scattering from the intermediate exciton state acts as a weak quantum measurement of the effective magnetic (Overhauser) field due to the nuclear spins. In a coherent population trapping state without light scattering, the nuclear state is projected into an eigenstate of the Overhauser field operator, and electron decoherence due to nuclear spins is suppressed: We show that this limit can be approached by adapting the driving frequencies when a photon is detected. We use a Lindblad equation to describe the driven system under photon emission and detection. Numerically, we find an increase of the electron coherence time from 5 to 500 ns after a preparation time of 10 micros.     

Competition between quantum spin tunneling and Kondo effect

Quantum spin tunneling and Kondo effect are two very different quantum phenomena that produce the same effect on quantized spins, namely, the quenching of their magnetization. However, the nature of this quenching is very different so that quantum spin tunneling and Kondo effect compete with each other. Importantly, both quantum spin tunneling and Kondo effect produce very characteristic features in the spectral function that can be measured by means of single spin scanning tunneling spectroscopy and allows to probe the crossover from one regime to the other. We model this crossover, and the resulting changes in transport, using a non-perturbative treatment of a generalized Anderson model including magnetic anisotropy that leads to quantum spin tunneling. We predict that, at zero magnetic field, integer spins can feature a split-Kondo peak driven by quantum spin tunneling.     

基于金刚石氮-空位色心的精密磁测量

磁是一种重要的物理现象,对其进行精密测量推动了许多科技领域的发展.各类测磁技术,包括霍尔传感器、超导量子干涉仪、自旋磁共振等,都致力于提升空间分辨率和灵敏度.近年来,金刚石中的氮-空位色心广受关注.这一固态单自旋体系具有许多优点,例如易于初始化和读出、可操控、具有较长相干时间等,这使得它不仅在量子信息、量子计算等领域崭露头角,而且在量子精密测量上显现出巨大的应用前景.基于氮-空位色心,利用动力学解耦、关联谱等技术,已实现若干高灵敏度、高分辨率的微观磁共振实验,其中包括纳米尺度乃至单分子、单自旋的核磁共振和电子顺磁共振.氮-空位色心也可以用于微波和射频信号的精密测量.本文对围绕上述主题开展的一系列研究工作进行综述.     

Detection of Magnetic Field Gradient and Single Spin Using Optically Levitated Nano-Particle in Vacuum

Optically levitated nano-particle with spins is a promising system for high-precision measurement and quantum information processing. We theoretically analyze the ratio between the fluctuation of particle's displacement caused by spins in magnetic field and caused by molecular collisions of the residual air. When the ratio is larger than unity, the displacement fluctuation of spins flipping can be remarkably detected. By theoretical analysis and numerical simulation, we propose and validate a scheme for the detection of gradient of the magnetic field by levitating ferromagnetic nano-particle, and also put forward a realizable detection scheme of the single spin by levitating nano-diamond particle with single nitrogen-vacancy(NV) centers.     

Detection of Magnetic Field Gradient and Single Spin Using Optically Levitated Nano-Particle in Vacuum

Optically levitated nano-particle with spins is a promising system for high-precision measurement and quantum information processing. We theoretically analyze the ratio between the fluctuation of particle's displacement caused by spins in magnetic field and caused by molecular collisions of the residual air. When the ratio is larger than unity, the displacement fluctuation of spins flipping can be remarkably detected. By theoretical analysis and numerical simulation, we propose and validate a scheme for the detection of gradient of the magnetic field by levitating ferromagnetic nano-particle, and also put forward a realizable detection scheme of the single spin by levitating nano-diamond particle with single nitrogen-vacancy(NV) centers.