Pub Date : 2019-09-10DOI: 10.1093/oso/9780198808350.003.0005
I. Kenyon
Electron energy bands in solids are introduced. Free electron theory for metals is presented: the Fermi gas, Fermi energy and temperature. Electrical and thermal conductivity are interpreted, including the Wiedermann–Franz law. The Hall effect and information it brings about charge carriers is discussed. Plasma oscillations of conduction electrons and the optical properties of metals are examined. Formation of quasi-particles of an electron and its screening cloud are discussed. Electron-electron and electron-phonon scattering and how they affect the mean free path are treated. Then the analysis of crystalline materials using electron Bloch waves is presented. Tight and weak binding cases are examined. Electron band structure is explained including Brillouin zones, electron kinematics and effective mass. Fermi surfaces in crystals are treated. The ARPES technique for exploring dispersion relations is explained.
{"title":"Electrons in solids","authors":"I. Kenyon","doi":"10.1093/oso/9780198808350.003.0005","DOIUrl":"https://doi.org/10.1093/oso/9780198808350.003.0005","url":null,"abstract":"Electron energy bands in solids are introduced. Free electron theory for metals is presented: the Fermi gas, Fermi energy and temperature. Electrical and thermal conductivity are interpreted, including the Wiedermann–Franz law. The Hall effect and information it brings about charge carriers is discussed. Plasma oscillations of conduction electrons and the optical properties of metals are examined. Formation of quasi-particles of an electron and its screening cloud are discussed. Electron-electron and electron-phonon scattering and how they affect the mean free path are treated. Then the analysis of crystalline materials using electron Bloch waves is presented. Tight and weak binding cases are examined. Electron band structure is explained including Brillouin zones, electron kinematics and effective mass. Fermi surfaces in crystals are treated. The ARPES technique for exploring dispersion relations is explained.","PeriodicalId":165376,"journal":{"name":"Quantum 20/20","volume":"85 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132610051","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-09-10DOI: 10.1093/oso/9780198808350.003.0002
I. Kenyon
Eigenstates of the square well potential are calculated and displayed. Barrier penetration and the connection to total internal reflection are explained. α–decay by barrier penetration is calculated and used to explain Geiger–Nuttall plots. Gauss–Hermite solutions to the harmonic oscillator potential are deduced and displayed. Zero point fluctuations are introduced. Hydrogen atom eigenstate wavefunctions for the Coulomb potential are calculated and displayed. Principal, orbital angular momentum and intrinsic angular momentum quantum numbers and their allowed combinations are discussed and interpreted: n, l, ml, s and ms. The Stern–Gerlach experiment and Pauli’s perception that electron spin is half-integral are presented; as are Beth’s experiment and photon spin. Dominance of electric dipole transitions and resulting selection rules discussed. Fine spectral structure and spin-orbit coupling are described. Nuclear spin and resulting hyperfine spectral structure are introduced. Landé factors introduced.
{"title":"Solutions to Schrödinger’s equation","authors":"I. Kenyon","doi":"10.1093/oso/9780198808350.003.0002","DOIUrl":"https://doi.org/10.1093/oso/9780198808350.003.0002","url":null,"abstract":"Eigenstates of the square well potential are calculated and displayed. Barrier penetration and the connection to total internal reflection are explained. α–decay by barrier penetration is calculated and used to explain Geiger–Nuttall plots. Gauss–Hermite solutions to the harmonic oscillator potential are deduced and displayed. Zero point fluctuations are introduced. Hydrogen atom eigenstate wavefunctions for the Coulomb potential are calculated and displayed. Principal, orbital angular momentum and intrinsic angular momentum quantum numbers and their allowed combinations are discussed and interpreted: n, l, ml, s and ms. The Stern–Gerlach experiment and Pauli’s perception that electron spin is half-integral are presented; as are Beth’s experiment and photon spin. Dominance of electric dipole transitions and resulting selection rules discussed. Fine spectral structure and spin-orbit coupling are described. Nuclear spin and resulting hyperfine spectral structure are introduced. Landé factors introduced.","PeriodicalId":165376,"journal":{"name":"Quantum 20/20","volume":"66 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123018241","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-09-10DOI: 10.1093/oso/9780198808350.003.0016
I. Kenyon
The (gaseous) BECs are introduced: clouds of 106−8 alkali metal atoms, usually 87Rb or 23Na, below ~1 μK. The laser cooling and magnetic trapping are described including the evaporation step needed to reach the conditions for condensation. The magnetooptical and Ioffe–Pritchard traps are described. Imaging methods, both destructive and non-destructive are described. Evidence of condensation is presented; and of interference between separated clouds, thus confirming the coherence of the condensates. The measurement of the condensate fraction is recounted. The Gross–Pitaevskii analysis of condensate properties is given in an appendix. How Bragg spectroscopy is used to obtain the dispersion relation for excitations is detailed. Finally the BEC/BCS crossover is introduced and the role therein of Feshbach resonances.
{"title":"Gaseous Bose–Einstein condensates","authors":"I. Kenyon","doi":"10.1093/oso/9780198808350.003.0016","DOIUrl":"https://doi.org/10.1093/oso/9780198808350.003.0016","url":null,"abstract":"The (gaseous) BECs are introduced: clouds of 106−8 alkali metal atoms, usually 87Rb or 23Na, below ~1 μK. The laser cooling and magnetic trapping are described including the evaporation step needed to reach the conditions for condensation. The magnetooptical and Ioffe–Pritchard traps are described. Imaging methods, both destructive and non-destructive are described. Evidence of condensation is presented; and of interference between separated clouds, thus confirming the coherence of the condensates. The measurement of the condensate fraction is recounted. The Gross–Pitaevskii analysis of condensate properties is given in an appendix. How Bragg spectroscopy is used to obtain the dispersion relation for excitations is detailed. Finally the BEC/BCS crossover is introduced and the role therein of Feshbach resonances.","PeriodicalId":165376,"journal":{"name":"Quantum 20/20","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129151960","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-09-10DOI: 10.1093/oso/9780198808350.003.0018
I. Kenyon
Particle families (quarks and leptons), their properties and their interactions are introduced. The exchange mechanism and the Yukawa potential are discussed. Natural units are explained. The cross-section for e − + e + → μ− + μ+ is calculated using a first order Feynman diagram. Comparison with data reveals the existence of the Z0-boson and makes a link between electroweak processes. Higher orders diagrams give divergences and their removal by renormalization is described. Neutrino properties are outlined and the determination of the number of light neutrinos related. The weak interaction is discussed: parity and charge parity are seen to be maximally violated in W-boson exchange, but the product is approximately conserved. Handedness is pursued in an appendix using Dirac spinors. The neutrino mass and weak eigenstates differ and this leads to oscillations between weak eigenstates in flight. Measurements of the neutrino flux from the sun revealing this behaviour are described. Weak and strong eigenstates of quarks also differ by a unitary transformation, the CKM matrix. This difference leads to oscillations of certain neutral mesons from particle to antiparticle. This behaviour is explored for neutral K-mesons and for B0 d mesons. CP violation is observed, which is required for the survival of matter in the universe.
介绍了粒子族(夸克和轻子)及其性质和相互作用。讨论了交换机制和汤川势。解释了自然单位。用一阶费曼图计算了e−+ e +→μ -−+ μ - +的截面。与数据的比较揭示了z0玻色子的存在，并在电弱过程之间建立了联系。高阶图给出了散度，并描述了通过重整化去除散度的方法。概述了中微子的性质，并确定了相关的轻中微子的数量。讨论了弱相互作用:在w -玻色子交换中，宇称和电荷宇称被最大程度地违反，但产物是近似守恒的。在附录中使用狄拉克旋量来研究手性。中微子的质量和弱本征态不同，这导致了飞行中弱本征态之间的振荡。对来自太阳的中微子通量的测量揭示了这种行为。夸克的弱本征态和强本征态也因一个统一变换而不同，即CKM矩阵。这种差异导致某些中性介子从粒子到反粒子的振荡。研究了中性k介子和B0 - d介子的这种行为。CP违逆被观察到，这是物质在宇宙中生存所必需的。
{"title":"Particle physics I","authors":"I. Kenyon","doi":"10.1093/oso/9780198808350.003.0018","DOIUrl":"https://doi.org/10.1093/oso/9780198808350.003.0018","url":null,"abstract":"Particle families (quarks and leptons), their properties and their interactions are introduced. The exchange mechanism and the Yukawa potential are discussed. Natural units are explained. The cross-section for e\u0000 − + e\u0000 + → μ− + μ+ is calculated using a first order Feynman diagram. Comparison with data reveals the existence of the Z0-boson and makes a link between electroweak processes. Higher orders diagrams give divergences and their removal by renormalization is described. Neutrino properties are outlined and the determination of the number of light neutrinos related. The weak interaction is discussed: parity and charge parity are seen to be maximally violated in W-boson exchange, but the product is approximately conserved. Handedness is pursued in an appendix using Dirac spinors. The neutrino mass and weak eigenstates differ and this leads to oscillations between weak eigenstates in flight. Measurements of the neutrino flux from the sun revealing this behaviour are described. Weak and strong eigenstates of quarks also differ by a unitary transformation, the CKM matrix. This difference leads to oscillations of certain neutral mesons from particle to antiparticle. This behaviour is explored for neutral K-mesons and for B0\u0000 d mesons. CP violation is observed, which is required for the survival of matter in the universe.","PeriodicalId":165376,"journal":{"name":"Quantum 20/20","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124827721","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-09-10DOI: 10.1093/oso/9780198808350.003.0001
I. Kenyon
Basic experimental evidence is sketched: the black body radiation spectrum, the photoeffect, Compton scattering and electron diffraction; the Bohr model of the atom. Quantum mechanics is reviewed using the Copenhagen interpretation: eigenstates, observables, hermitian operators and expectation values are explained. Wave-particle duality, Schrödinger’s equation, and expressions for particle density and current are described. The uncertainty principle, the collapse of the wavefunction, Schrödinger’s cat and the no-cloning theorem are discussed. Dirac delta functions and the usage of wavepackets are explained. An introduction to state vectors in Hilbert space and the bra-ket notation is given. Abstracts of special relativity and Lorentz invariants follow. Minimal electromagnetic coupling and the gauge transformations are explained.
{"title":"Review of basic quantum physics","authors":"I. Kenyon","doi":"10.1093/oso/9780198808350.003.0001","DOIUrl":"https://doi.org/10.1093/oso/9780198808350.003.0001","url":null,"abstract":"Basic experimental evidence is sketched: the black body radiation spectrum, the photoeffect, Compton scattering and electron diffraction; the Bohr model of the atom. Quantum mechanics is reviewed using the Copenhagen interpretation: eigenstates, observables, hermitian operators and expectation values are explained. Wave-particle duality, Schrödinger’s equation, and expressions for particle density and current are described. The uncertainty principle, the collapse of the wavefunction, Schrödinger’s cat and the no-cloning theorem are discussed. Dirac delta functions and the usage of wavepackets are explained. An introduction to state vectors in Hilbert space and the bra-ket notation is given. Abstracts of special relativity and Lorentz invariants follow. Minimal electromagnetic coupling and the gauge transformations are explained.","PeriodicalId":165376,"journal":{"name":"Quantum 20/20","volume":"34 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124909825","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-09-10DOI: 10.1093/oso/9780198808350.003.0012
I. Kenyon
The model of a cavity-enclosed 2-state atom with transition frequency near resonant with a cavity mode is introduced. For conditions where their coupling dominates the Jaynes–Cummings model is described. Rabi flopping of energy between atom’s excited state and the cavity mode is recounted. Hybrid states and the AC Stark effect are discussed. Experiments with Rydberg atoms revealing the quantum nature of the cavity-atom state are discussed. Then mechanisms for trapping ions are outlined and the use of a single mercury ion as the pendulum of an optical clock is described. This relies on shelving to make non-demolition measurements on the ion. Then the measurement of (g-2) for the electron using an electron in a Penning trap is related. The quantity of interest, is the difference between the cyclotron and spin precession frequencies: its measurement by a different non-demolition technique is detailed. Finally the Purcell effect is presented, by which the lifetime of an atomic state in a cavity can be shortened or lengthened.
{"title":"Cavity quantum physics","authors":"I. Kenyon","doi":"10.1093/oso/9780198808350.003.0012","DOIUrl":"https://doi.org/10.1093/oso/9780198808350.003.0012","url":null,"abstract":"The model of a cavity-enclosed 2-state atom with transition frequency near resonant with a cavity mode is introduced. For conditions where their coupling dominates the Jaynes–Cummings model is described. Rabi flopping of energy between atom’s excited state and the cavity mode is recounted. Hybrid states and the AC Stark effect are discussed. Experiments with Rydberg atoms revealing the quantum nature of the cavity-atom state are discussed. Then mechanisms for trapping ions are outlined and the use of a single mercury ion as the pendulum of an optical clock is described. This relies on shelving to make non-demolition measurements on the ion. Then the measurement of (g-2) for the electron using an electron in a Penning trap is related. The quantity of interest, is the difference between the cyclotron and spin precession frequencies: its measurement by a different non-demolition technique is detailed. Finally the Purcell effect is presented, by which the lifetime of an atomic state in a cavity can be shortened or lengthened.","PeriodicalId":165376,"journal":{"name":"Quantum 20/20","volume":"23 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121848656","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-09-10DOI: 10.1093/oso/9780198808350.003.0015
I. Kenyon
Superconductivity and the associated Meissner effect are introduced, indicating that superconductors are perfect diamagnetics. Condensation energy is deduced. The London analysis showing how superconductors exclude flux is presented. The BCS microscopic theory is recapitulated: Cooper pairs of electrons are the constituents of the Bose condensate that carries the non-dissipative current. The binding energy of pairs (energy gap below the Fermi sea) is deduced and related to their size and the critical temperature. Dependence of the energy gap on temperature is shown consistent with BCS theory. The Ginzberg–Landau analysis and the spontaneous symmetry breaking in the condensate phase are recounted. Quantization of trapped magnetic flux is shown to be related to superconductor topology. Type-II superconductors are treated. Finally Josephson effects show unambiguously that the condensate is a macroscopic quantum state. Josephson applications are enumerated, including a new voltage standard, SQUIDs and preliminary versions of qubits (transmons) for quantum computing.
{"title":"Superconductivity","authors":"I. Kenyon","doi":"10.1093/oso/9780198808350.003.0015","DOIUrl":"https://doi.org/10.1093/oso/9780198808350.003.0015","url":null,"abstract":"Superconductivity and the associated Meissner effect are introduced, indicating that superconductors are perfect diamagnetics. Condensation energy is deduced. The London analysis showing how superconductors exclude flux is presented. The BCS microscopic theory is recapitulated: Cooper pairs of electrons are the constituents of the Bose condensate that carries the non-dissipative current. The binding energy of pairs (energy gap below the Fermi sea) is deduced and related to their size and the critical temperature. Dependence of the energy gap on temperature is shown consistent with BCS theory. The Ginzberg–Landau analysis and the spontaneous symmetry breaking in the condensate phase are recounted. Quantization of trapped magnetic flux is shown to be related to superconductor topology. Type-II superconductors are treated. Finally Josephson effects show unambiguously that the condensate is a macroscopic quantum state. Josephson applications are enumerated, including a new voltage standard, SQUIDs and preliminary versions of qubits (transmons) for quantum computing.","PeriodicalId":165376,"journal":{"name":"Quantum 20/20","volume":"4 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126418637","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-02-14DOI: 10.1017/9781108569361.012
I. Kenyon
Heisenberg’s back action and Robertson’s intrinsic uncertainty are presented. von Neumann’s analysis of quantum measurement is recounted. Advanced LIGO is used as an example of quantum measurement: giant Michelson interferometers achieve sensitivity to motion of 1 part in 1021. The discovery at LIGO of gravitational waves is outlined. Then the standard quantum limit is deduced. The use of cavities in the interferometer arms to increase the photon flux is described. The potential for improvement by squeezing the vacuum at the blank input port is discussed. Prospects for speed interferometry are outlined.
{"title":"Quantum measurement","authors":"I. Kenyon","doi":"10.1017/9781108569361.012","DOIUrl":"https://doi.org/10.1017/9781108569361.012","url":null,"abstract":"Heisenberg’s back action and Robertson’s intrinsic uncertainty are presented. von Neumann’s analysis of quantum measurement is recounted. Advanced LIGO is used as an example of quantum measurement: giant Michelson interferometers achieve sensitivity to motion of 1 part in 1021. The discovery at LIGO of gravitational waves is outlined. Then the standard quantum limit is deduced. The use of cavities in the interferometer arms to increase the photon flux is described. The potential for improvement by squeezing the vacuum at the blank input port is discussed. Prospects for speed interferometry are outlined.","PeriodicalId":165376,"journal":{"name":"Quantum 20/20","volume":"134 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-02-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121799313","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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