This article compares treatments of the Stern-Gerlach experiment across different physical theories, building up to a novel analysis of electron spin measurement in the context of classical Dirac field theory. Modeling the electron as a classical rigid body or point particle, we can explain why the entire electron is always found at just one location on the detector (uniqueness) but we cannot explain why there are only two locations where the electron is ever found (discreteness). Using non-relativistic or relativistic quantum mechanics, we can explain both uniqueness and discreteness. Moving to more fundamental physics, both features can be explained within a quantum theory of the Dirac field. In a classical theory of the Dirac field, the rotating charge of the electron can split into two pieces that each hit the detector at a different location. In this classical context, we can explain a feature of electron spin that is often described as distinctively quantum (discreteness) but we cannot explain another feature that could be explained within any of the other theories (uniqueness).
Polarization transfers from an electron spin to a nuclear spin are essential for various physical tasks, such as dynamic nuclear polarization in nuclear magnetic resonance and quantum state transformations on hybrid electron-nuclear spin systems. We present time-optimal schemes for electron-nuclear polarization transfers which improve on conventional approaches and will have wide applications.
In this article, 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 on nuclear spin states. We show that by performing a sequence of flips (each followed by a suitable delay), we can perform any desired rotation on the nuclear spins, whi…
We propose a protocol that achieves arbitrary N-qubit interactions between nuclear spins and that can measure directly nuclear many-body correlators by appropriately making the nuclear spins interact with a nitrogen vacancy (NV) center electron spin. The method takes advantage of recently introduced dynamical decoupling techniques and demonstrates that action on the electron spin is sufficient to fully exploit nuclear spins as robust quantum registers. Our protocol is general, being applicable to other nuclear spin based platforms with electronic spin defects acting as mediators as the case of…
Electron spin resonance (ESR) is a useful tool to investigate properties of materials in magnetic fields where high spin polarization of target electron spins is required in order to obtain high sensitivity. However, the smaller magnetic fields becomes, the more difficult high polarization is passively obtained by thermalization. Here, we propose to employ a superconducting flux qubit (FQ) to polarize electron spins actively. We have to overcome a large energy difference between the FQ and electron spins for efficient energy transfer among them. For this purpose, we adopt a spin-lock technique…
Rabi nutations of a single electron spin in a single defect center have been detected. The coherent evolution of the spin quantum state is followed via optical detection of the spin state. Coherence times up to several microseconds at room temperature have been measured. Optical readout of the spin states leads to decoherence, equivalent to the so-called Zeno effect. Quantum beats between electron spin transitions in a single spin Hahn echo experiment are observed. A closer analysis reveals that beats also result from the hyperfine coupling of the electron spin to a single 14N nuclear spin. Th…
Electron spin echo envelope modulation (ESEEM) has been observed for the first time from a coupled hetero-spin pair of electron and nucleus in liquid solution. Previously, modulation effects in spin echo experiments have only been described in liquid solutions for a coupled pair of homonuclear spins in NMR or a pair of resonant electron spins in EPR. We observe low-frequency ESEEM (26 and 52 kHz) due to a new mechanism present for any electron spin with S>1/2 that is hyperfine coupled to a nuclear spin. In our case these are electron spin (S=3/2) and nuclear spin (I=1) in the endohedral fuller…
A simple real-space model for the free-electron wavefunction with spin is proposed, based on coherent vortices on the scale of h/mc, rotating at mc^2/h. This reproduces the proper values for electron spin and magnetic moment. Transformation to a moving reference frame turns this into a wave with the de Broglie wavelength. The mapping of the real two-dimensional vector phasor to the complex plane satisfies the Schrodinger equation. This suggests a fundamental role for spin in quantum mechanics.
We consider the problem of correct measurement of a quantum entanglement in the two-body electron-electron scattering. An expression is derived for a spin correlation tensor of a pure two-electron state. A geometrical measure of a quantum entanglement as the distance between two forms of this tensor in entangled and separable cases is presented. We prove that this measure satisfies properties of a valid entanglement measure: nonnegativity, discriminance, normalization, non-growth under local operations and classical communication. This measure is calculated for a problem of electron-electron s…
Recently, magnetic field sensors based on an electron spin of a nitrogen vacancy (NV) center in diamond have been studied both from an experimental and theoretical point of view. This system provides a nanoscale magnetometer, and it is possible to detect a precession of a single spin. In this paper, we propose a sensor consisting of an electron spin and a nuclear spin in diamond. Although the electron spin has a reasonable interaction strength with magnetic field, the coherence time of the spin is relatively short. On the other hand, the nuclear spin has a longer life time while the spin has a…
We show that two particles interacting via spin exchange exhibit topological features found in one-dimensional single particle lattice models. This is accomplished by absorbing all of the spatial degrees of freedom of the lattices into the spin degrees of freedom of the two particles. Comparing the spin system with the Su-Schrieffer-Heeger model, we show the existence of topologically protected edge spin states and establish the bulk-edge correspondence. Modifying the spin system with a chiral symmetry breaking term results in it resembling the Rice-Mele model and can therefore act as a Thoule…
We experimentally demonstrate the use of a single electronic spin to measure the quantum dynamics of distant individual nuclear spins from within a surrounding spin bath. Our technique exploits coherent control of the electron spin, allowing us to isolate and monitor nuclear spins weakly coupled to the electron spin. Specifically, we detect the evolution of distant individual carbon-13 nuclear spins coupled to single nitrogen vacancy centers in a diamond lattice with hyperfine couplings down to a factor of 8 below the electronic spin bare dephasing rate. Potential applications to nanoscale mag…
Relaxation of conduction electron spins in a semiconductor owing to the hyperfine interaction with spin-1/2 nuclei, in zero applied magnetic field, is investigated. We calculate the electron spin relaxation time scales, in order to evaluate the importance of this relaxation mechanism. Master equations for the electron spin density matrix are derived and solved. Polarized nuclear spins can be used to polarize the electrons in spintronic devices.
Electron and nuclear spins associated with point defects in insulators are promising systems for solid state quantum technology. While the electron spin usually is used for readout and addressing, nuclear spins are exquisite quantum bits and memory systems. With these systems single-shot readout of nearby nuclear spins as well as entanglement aided by the electron spin has been shown. While the electron spin in this example is essential for readout it usually limits nuclear spin coherence. This has set of the quest for defects with spin-free ground states. Here, we isolate a hitherto unidentif…
We present experimental observations and a study of quantum dynamics of strongly interacting electronic spins, at room temperature in the solid state. In a diamond substrate, a single nitrogen vacancy (NV) center coherently interacts with two adjacent S = 1/2 dark electron spins. We quantify NV-electron and electron-electron couplings via detailed spectroscopy, with good agreement to a model of strongly interacting spins. The electron-electron coupling enables an observation of coherent flip-flop dynamics between electronic spins in the solid state, which occur conditionally on the state of th…
Quantum hydrodynamic (QHD) model of charged spin-1/2 particles contains physical quantities defined for all particles of a species including particles with spin-up and with spin-down. Different population of states with different spin direction is included in the spin density (magnetization). In this paper we derive a QHD model, which separately describes spin-up electrons and spin-down electrons. Hence we consider electrons with different projection of spin on the preferable direction as two different species of particles. We show that numbers of particles with different spin direction do not…
We consider the decoherence of a single localized electron spin due to its coupling to the lattice nuclear spin bath in a semiconductor quantum computer architecture. In the presence of an external magnetic field and at low temperatures, the dominant decoherence mechanism is the spectral diffusion of the electron spin resonance frequency due to the temporally fluctuating random magnetic field associated with the dipolar interaction induced flip-flops of nuclear spin pairs. The electron spin dephasing due to this random magnetic field depends intricately on the quantum dynamics of the nuclear s…
We report a pulsed EPR study of the phase relaxation of electron spins bound to phosphorus donors in isotopically purified 29^Si and natural abundance Si single crystals measured at 8 K.
We theoretically study the decoherence and the dynamical decoupling control of nitrogen-vacancy center electron spins in high-purity diamond, where the hyperfine interaction with $^{13}$C nuclear spins is the dominating decoherence mechanism. The decoherence is formulated as the entanglement between the electron spin and the nuclear spins, which is induced by nuclear spin bath evolution conditioned on the electron spin state. The nuclear spin bath evolution is driven by elementary processes such as single spin precession and pairwise flip-flops. The importance of different elementary processes…
A nanodevice capable of separating spins of two electrons confined in a quantum dot formed in a gated semiconductor nanowire is proposed. Two electrons confined initially in a single quantum dot in the singlet state are transformed into the system of two electrons confined in two spatially separated quantum dots with opposite spins. In order to separate the electrons' spins we exploit transitions between the singlet and the triplet state which are induced by resonantly oscillating Rashba spin-obit coupling strength. The proposed device is all electrically controlled and the electron spin separ…
The separate and combined influences of the spin-orbit and electron-electron interactions on the electron magnetization in quantum rings have been studied theoretically on the basis of the spin-density-functional theory and the Kohn-Sham equation used for the calculation of electron states in two-dimensional parabolic quantum rings containing from two to six electrons. The magnetization of electrons in a quantum ring is calculated at zero temperature. The revealed abrupt changes in the ring magnetization are associated with the crossing of electron states that occurs if the spin-orbit and/or e…
We propose an approach to entangle spins of electrons floating on liquid helium by coherently manipulating their spin-orbit interactions. The configuration consists of single electrons, confined individually on liquid helium by the microelectrodes, moving along the surface as the harmonic oscillators. It has been known that the spin of an electron could be coupled to its orbit (i.e., the vibrational motion) by properly applying a magnetic field. Based on this single electron spin-orbit coupling, here we show that a Jaynes-Cummings (JC) type interaction between the spin of an electron and the o…
The Dirac equation is used to describe oblique spin-conserving and spin-flip reflections of relativistic electrons from a one-dimensional potential barrier in a vacuum. When an electron hits the barrier from an oblique direction, its spin-up and spin-down states have different energies due to the spin-orbit interaction and the fact that the system has a structural inversion asymmetry. When the electron is reflected in an elastic spin-conserving process, incoming and outgoing angles are the same. If an elastic reflection is a spin-flip process, the outgoing angle is different from the incoming …
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 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 int…
The effects on the spin state of an electron in a time independent electric field are examined. The probability of spin flipping is calculated, and other effects are studied using the minimally coupled Dirac equation.
In this paper, we introduce a deterministic approach of quantum mechanics for particles with spin 1 2 moving in one dimension. We present a Lagrangian of a spinning particle ($s ={1 \over 2} $), and deduce the expression of the conjugate momentum related to the velocity of the particle.
We experimentally isolate, characterize and coherently control up to six individual nuclear spins that are weakly coupled to an electron spin in diamond. Our method employs multi-pulse sequences on the electron spin that resonantly amplify the interaction with a selected nuclear spin and at the same time dynamically suppress decoherence caused by the rest of the spin bath. We are able to address nuclear spins with interaction strengths that are an order of magnitude smaller than the electron spin dephasing rate. Our results provide a route towards tomography with single-nuclear-spin sensitivit…
The propagation of an electron beam in the presence of transverse magnetic fields possessing integer topological charges is presented. The spin--magnetic interaction introduces a nonuniform spin precession of the electrons that gains a space-variant geometrical phase in the transverse plane proportional to the field's topological charge, whose handedness depends on the input electron's spin state. A combination of our proposed device with an electron orbital angular momentum sorter can be utilized as a spin-filter of electron beams in a mid-energy range. We examine these two different configur…
Effective electric and magnetic polarizabilities of pointlike spin-1/2 particles possesing an anomalous magnetic moment are calculated with the transformation of an initial Hamiltonian to the Foldy-Wouthuysen representation. Polarizabilities of spin-1/2 and spin-1 particles are compared.
We give an argument that a broad class of geometric models of spinning relativistic particles with Casimir mass and spin being separately fixed parameters, have indeterminate worldline (while other spinning particles have definite worldline). This paradox suggests that for a consistent description of spinning particles something more general than a worldline concept should be used. As a particular case, we study at the Lagrangian level the Cauchy problem for a spinor particle and then, at the constrained Hamiltonian level, we generalize our result to other particles.
We study the low-temperature dynamics of a shallow donor, e.g., $^{31}$P, impurity electron spin in silicon, interacting with the bath of nuclear spins of the $^{29}$Si isotope. For small applied magnetic fields, the electron spin relaxation is controlled by the steady state distribution of the nuclear spins. We calculate the relaxation times $T_1$ and $T_2$ as functions of the external magnetic field, and conclude that nuclear spins play an important role in the donor electron spin decoherence in Si:P at low magnetic fields.
Plasma physics give an example of physical system of particles with the long range interaction. At small velocity of particles we can consider the plasma approximately as a system of particles with the Coulomb interaction. The Coulomb interaction is isotropic. Systems of spinning neutral particles have long-range anisotropic interparticle interaction. So, they can reveal more reach properties than plasma. Furthermore for studying of systems of spinning particles we can develop kinetic and hydrodynamic methods analogous to used for the plasma. We derive kinetic equations by a new method, which …
