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Optically Detected Magnetic Resonance
In physics, optically detected magnetic resonance (ODMR) is a double resonance technique by which the electron spin state of a crystal defect may be optically pumped for spin initialisation and readout. Like electron paramagnetic resonance (EPR), ODMR makes use of the Zeeman effect in unpaired electrons. The negatively charged nitrogen vacancy centre (NV−) has been the target of considerable interest with regards to performing experiments using ODMR. ODMR of NV−s in diamond has applications in magnetometry and sensing, biomedical imaging, quantum information and the exploration of fundamental physics. NV ODMR The nitrogen vacancy defect in diamond consists of a single substitutional nitrogen atom (replacing one carbon atom) and an adjacent gap, or vacancy, in the lattice where normally a carbon atom would be located. The nitrogen vacancy occurs in three possible charge states: positive (NV+), neutral (NV0) and negative (NV−). As NV− is the only one of these charge stat ...
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Electron Paramagnetic Resonance
Electron paramagnetic resonance (EPR) or electron spin resonance (ESR) spectroscopy is a method for studying materials that have unpaired electrons. The basic concepts of EPR are analogous to those of nuclear magnetic resonance (NMR), but the spins excited are those of the electrons instead of the atomic nuclei. EPR spectroscopy is particularly useful for studying metal complexes and organic radicals. EPR was first observed in Kazan State University by Soviet physicist Yevgeny Zavoisky in 1944, and was developed independently at the same time by Brebis Bleaney at the University of Oxford. Theory Origin of an EPR signal Every electron has a magnetic moment and spin quantum number s = \tfrac , with magnetic components m_\mathrm = + \tfrac or m_\mathrm = - \tfrac . In the presence of an external magnetic field with strength B_\mathrm , the electron's magnetic moment aligns itself either antiparallel ( m_\mathrm = - \tfrac ) or parallel ( m_\mathrm = + \tfrac ) to the fie ...
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Fluorescence
Fluorescence is the emission of light by a substance that has absorbed light or other electromagnetic radiation. It is a form of luminescence. In most cases, the emitted light has a longer wavelength, and therefore a lower photon energy, than the absorbed radiation. A perceptible example of fluorescence occurs when the absorbed radiation is in the ultraviolet region of the electromagnetic spectrum (invisible to the human eye), while the emitted light is in the visible region; this gives the fluorescent substance a distinct color that can only be seen when the substance has been exposed to UV light. Fluorescent materials cease to glow nearly immediately when the radiation source stops, unlike phosphorescent materials, which continue to emit light for some time after. Fluorescence has many practical applications, including mineralogy, gemology, medicine, chemical sensors (fluorescence spectroscopy), fluorescent labelling, dyes, biological detectors, cosmic-ray detection, vacu ...
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Quantum Mechanics
Quantum mechanics is a fundamental theory in physics that provides a description of the physical properties of nature at the scale of atoms and subatomic particles. It is the foundation of all quantum physics including quantum chemistry, quantum field theory, quantum technology, and quantum information science. Classical physics, the collection of theories that existed before the advent of quantum mechanics, describes many aspects of nature at an ordinary (macroscopic) scale, but is not sufficient for describing them at small (atomic and subatomic) scales. Most theories in classical physics can be derived from quantum mechanics as an approximation valid at large (macroscopic) scale. Quantum mechanics differs from classical physics in that energy, momentum, angular momentum, and other quantities of a bound system are restricted to discrete values ( quantization); objects have characteristics of both particles and waves (wave–particle duality); and there are limits to ...
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Carbon-13
Carbon-13 (13C) is a natural, stable isotope of carbon with a nucleus containing six protons and seven neutrons. As one of the environmental isotopes, it makes up about 1.1% of all natural carbon on Earth. Detection by mass spectrometry A mass spectrum of an organic compound will usually contain a small peak of one mass unit greater than the apparent molecular ion peak (M) of the whole molecule. This is known as the M+1 peak and comes from the few molecules that contain a 13C atom in place of a 12C. A molecule containing one carbon atom will be expected to have an M+1 peak of approximately 1.1% of the size of the M peak, as 1.1% of the molecules will have a 13C rather than a 12C. Similarly, a molecule containing two carbon atoms will be expected to have an M+1 peak of approximately 2.2% of the size of the M peak, as there is double the previous likelihood that any molecule will contain a 13C atom. In the above, the mathematics and chemistry have been simplified, however it can ...
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Hyperfine Structure
In atomic physics, hyperfine structure is defined by small shifts in otherwise degenerate energy levels and the resulting splittings in those energy levels of atoms, molecules, and ions, due to electromagnetic multipole interaction between the nucleus and electron clouds. In atoms, hyperfine structure arises from the energy of the nuclear magnetic dipole moment interacting with the magnetic field generated by the electrons and the energy of the nuclear electric quadrupole moment in the electric field gradient due to the distribution of charge within the atom. Molecular hyperfine structure is generally dominated by these two effects, but also includes the energy associated with the interaction between the magnetic moments associated with different magnetic nuclei in a molecule, as well as between the nuclear magnetic moments and the magnetic field generated by the rotation of the molecule. Hyperfine structure contrasts with '' fine structure'', which results from the interaction b ...
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Diagram For Spin Dynamics
A diagram is a symbolic representation of information using visualization techniques. Diagrams have been used since prehistoric times on walls of caves, but became more prevalent during the Enlightenment. Sometimes, the technique uses a three-dimensional visualization which is then projected onto a two-dimensional surface. The word ''graph'' is sometimes used as a synonym for diagram. Overview The term "diagram" in its commonly used sense can have a general or specific meaning: * ''visual information device'' : Like the term "illustration", "diagram" is used as a collective term standing for the whole class of technical genres, including graphs, technical drawings and tables. * ''specific kind of visual display'' : This is the genre that shows qualitative data with shapes that are connected by lines, arrows, or other visual links. In science the term is used in both ways. For example, Anderson (1997) stated more generally: "diagrams are pictorial, yet abstract, representat ...
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Bohr Magneton
In atomic physics, the Bohr magneton (symbol ) is a physical constant and the natural unit for expressing the magnetic moment of an electron caused by its orbital or spin angular momentum. The Bohr magneton, in SI units is defined as \mu_\mathrm = \frac , And in Gaussian CGS units: \mu_\mathrm = \frac , where * is the elementary charge, * is the reduced Planck constant, * is the electron rest mass, * is the speed of light. History The idea of elementary magnets is due to Walther Ritz (1907) and Pierre Weiss. Already before the Rutherford model of atomic structure, several theorists commented that the magneton should involve the Planck constant ''h''. By postulating that the ratio of electron kinetic energy to orbital frequency should be equal to ''h'', Richard Gans computed a value that was twice as large as the Bohr magneton in September 1911. At the First Solvay Conference in November that year, Paul Langevin obtained a e\hbar/(12m_\mathrm). Langevin assumed that the attracti ...
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G-factor (physics)
A ''g''-factor (also called ''g'' value or dimensionless magnetic moment) is a dimensionless quantity that characterizes the magnetic moment and angular momentum of an atom, a particle or the nucleus. It is essentially a proportionality constant that relates the different observed magnetic moments ''μ'' of a particle to their angular momentum quantum numbers and a unit of magnetic moment (to make it dimensionless), usually the Bohr magneton or nuclear magneton. Definition Dirac particle The spin magnetic moment of a charged, spin-1/2 particle that does not possess any internal structure (a Dirac particle) is given by \boldsymbol \mu = g \mathbf S , where ''μ'' is the spin magnetic moment of the particle, ''g'' is the ''g''-factor of the particle, ''e'' is the elementary charge, ''m'' is the mass of the particle, and S is the spin angular momentum of the particle (with magnitude ''ħ''/2 for Dirac particles). Baryon or nucleus Protons, neutrons, nuclei and other composit ...
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Planck Constant
The Planck constant, or Planck's constant, is a fundamental physical constant of foundational importance in quantum mechanics. The constant gives the relationship between the energy of a photon and its frequency, and by the mass-energy equivalence, the relationship between mass and frequency. Specifically, a photon's energy is equal to its frequency multiplied by the Planck constant. The constant is generally denoted by h. The reduced Planck constant, or Dirac constant, equal to the constant divided by 2 \pi, is denoted by \hbar. In metrology it is used, together with other constants, to define the kilogram, the SI unit of mass. The SI units are defined in such a way that, when the Planck constant is expressed in SI units, it has the exact value The constant was first postulated by Max Planck in 1900 as part of a solution to the ultraviolet catastrophe. At the end of the 19th century, accurate measurements of the spectrum of black body radiation existed, but the distribut ...
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Degenerate Energy Levels
In quantum mechanics, an energy level is degenerate if it corresponds to two or more different measurable states of a quantum system. Conversely, two or more different states of a quantum mechanical system are said to be degenerate if they give the same value of energy upon measurement. The number of different states corresponding to a particular energy level is known as the degree of degeneracy of the level. It is represented mathematically by the Hamiltonian for the system having more than one linearly independent eigenstate with the same energy eigenvalue. When this is the case, energy alone is not enough to characterize what state the system is in, and other quantum numbers are needed to characterize the exact state when distinction is desired. In classical mechanics, this can be understood in terms of different possible trajectories corresponding to the same energy. Degeneracy plays a fundamental role in quantum statistical mechanics. For an -particle system in three dimens ...
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Magnetic Field
A magnetic field is a vector field that describes the magnetic influence on moving electric charges, electric currents, and magnetic materials. A moving charge in a magnetic field experiences a force perpendicular to its own velocity and to the magnetic field. A permanent magnet's magnetic field pulls on ferromagnetic materials such as iron, and attracts or repels other magnets. In addition, a nonuniform magnetic field exerts minuscule forces on "nonmagnetic" materials by three other magnetic effects: paramagnetism, diamagnetism, and antiferromagnetism, although these forces are usually so small they can only be detected by laboratory equipment. Magnetic fields surround magnetized materials, and are created by electric currents such as those used in electromagnets, and by electric fields varying in time. Since both strength and direction of a magnetic field may vary with location, it is described mathematically by a function assigning a vector to each point of space, cal ...
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