Incoming links: Hyperfine structure
How an atomic clock works, and its use in the global positioning system (GPS) by EngineerGuy (2012)
Source. Shows how conceptually an atomic clock is based on a feedback loop of two hyperfine structure states of caesium atoms (non-radioactive caesium-133 as clarified by the Wikipedia page). Like a quartz clock, it also relies on the piezoelectricity of quartz, but unlike the quartz clock, the quartz is not shaped like a tuning fork, and has a much larger resonating frequency of about 7 MHz. The feedback is completed by producing photons that resonate at the right frequency to excite the caesium.Inside the HP 5061A Cesium Clock by CuriousMarc (2020)
Source. A similar model was used in the Hafele-Keating experiment to test special relativity on two planes flying in opposite directions. Miniaturization was key.
Contains a disposable tube with 6g of Caesium. You boil it, so when it runs out, you change the tube, 40k USD. Their tube is made by Agilent Technologies, so a replacement since that opened in 1999, and the original machine is from the 60s.
Detection is done with an electron multiplier.
youtu.be/eOti3kKWX-c?t=1166 They compare it with their 100 dollar GPS disciplined oscillator, since GPS satellites have atomic clocks in them.
Quick presentation of the atomic clock at the National Physical Laboratory (2010)
Source. Their super accurate setup first does laser cooling on the caesium atoms.users.physics.ox.ac.uk/~lvovsky/B3/ contain assorted PDFs from between 2015 and 2019
Syllabus reads:
- Multi-electron atoms: central field approximation, electron configurations, shell structure, residual electrostatic interaction, spin orbit coupling (fine structure).
- Spectra and energy levels: Term symbols, selection rules, X-ray notation, Auger transitions.
- Hyperfine structure; effects of magnetic fields on fine and hyperfine structure. Presumably Zeeman effect.
- Two level system in a classical light field: Rabi oscillations and Ramsey fringes, decaying states; Einstein
- A and B coefficients; homogeneous and inhomogeneous broadening of spectral lines; rate equations.
- Optical absorption and gain: population inversion in 3- and 4-level systems; optical gain cross section; saturated absorption and gain.
Professor in 2000s seems to beBut as of 2023 marked emeritus, so who took over?
- en.wikipedia.org/wiki/Paul_Ewart. He actually fought not to be dismissed by age and won!
- www.physics.ox.ac.uk/our-people/ewart
Ewart is actually religious:This dude is pure trouble for Oxford!
- www.youtube.com/watch?v=aulL-Qa65i0 Paul Ewart, Chance, Science and Spirituality by Faraday Institute for Science and Religion. Oh, he is/was actually chairman of that crap
- www.youtube.com/watch?v=PVX2F4XvGYo Chaos and the Character of God by Prof. Paul Ewart
Undated materials Ewart:
- users.physics.ox.ac.uk/~ewart/index.htm
- users.physics.ox.ac.uk/~ewart/Atomic%20Physics%20lecture%20notes%20C%20port.pdf
- slides: users.physics.ox.ac.uk/~ewart/Atomic%20Physics%20Lecture%20PPT%20slides%201_8.pdf. Also under: www2.physics.ox.ac.uk/sites/default/files/2011-10-19/atomic_physics_lectures_1_8_09_pdf_pdf_18283.pdf. The course was previously B1, they just change the IDs randomly from time to time to fit the B1-7 numbering.
Uses the frequency of the hyperfine structure of caesium-133 ground state, i.e spin up vs spin down of its valence electron , to define the second.
International System of Units definition of the second since 1967, because this is what atomic clocks use.
TODO why does this have more energy than the hyperfine split of the hydrogen line given that it is further from the nucleus?
Experiments explained by QED but not by the Dirac equation:
- Lamb shift: by far the most famous one
- hyperfine structure TODO confirm
- anomalous magnetic dipole moment of the electron
A single line in the emission spectrum.
So precise, so discrete, which makes no sense in classical mechanics!
Has been the leading motivation of the development of quantum mechanics, all the way from the:
- Schrödinger equation: major lines predicted, including Zeeman effect, but not finer line splits like fine structure
- Dirac equation: explains fine structure 2p spin split due to electron spin/orbit interactions, but not Lamb shift
- quantum electrodynamics: explains Lamb shift
- hyperfine structure: due to electron/nucleus spin interactions, offers a window into nuclear spin
This notation is cool as it gives the spin quantum number, which is important e.g. when talking about hyperfine structure.
But it is a bit crap that the spin is not given simply as but rather mixes up both the azimuthal quantum number and spin. What is the reason?
Spectroscopic notation by Andre K (2014)
Source. This notation is so confusing! People often don't manage to explain the intuition behind it, why this is an useful notation. When you see Indian university entry exam level memorization classes about this, it makes you want to cry.
The key reason why term symbols matter are Hund's rules, which allow us to predict with some accuracy which electron configurations of those states has more energy than the other.
web.chem.ucsb.edu/~devries/chem218/Term%20symbols.pdf puts it well: electron configuration notation is not specific enough, as each such notation e.g. 1s2 2s2 2p2 contains several options of spins and z angular momentum. And those affect energy.
This is why those symbols are often used when talking about energy differences: they specify more precisely which levels you are talking about.
Basically, each term symbol appears to represent a group of possible electron configurations with a given quantum angular momentum.
We first fix the energy level by saying at which orbital each electron can be (hyperfine structure is ignored). It doesn't even have to be the ground state: we can make some electrons excited at will.
The best thing to learn this is likely to draw out all the possible configurations explicitly, and then understand what is the term symbol for each possible configuration, see e.g. term symbols for carbon ground state.
It also confusing how uppercase letters S, P and D are used, when they do not refer to orbitals s, p and d, but rather to states which have the same angular momentum as individual electrons in those states.
It is also very confusing how extremelly close it looks to spectroscopic notation!
The form of the term symbol is:
The can be understood directly as the degeneracy, how many configurations we have in that state.
Bibliography:
- chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Supplemental_Modules_(Physical_and_Theoretical_Chemistry)/Spectroscopy/Electronic_Spectroscopy/Spin-orbit_Coupling/Atomic_Term_Symbols
- chem.libretexts.org/Courses/Pacific_Union_College/Quantum_Chemistry/08%3A_Multielectron_Atoms/8.08%3A_Term_Symbols_Gives_a_Detailed_Description_of_an_Electron_Configuration The PDF origin: web.chem.ucsb.edu/~devries/chem218/Term%20symbols.pdf
- chem.libretexts.org/Bookshelves/Inorganic_Chemistry/Inorganic_Coordination_Chemistry_(Landskron)/08%3A_Coordination_Chemistry_III_-_Electronic_Spectra/8.01%3A_Quantum_Numbers_of_Multielectron_Atoms
- physics.stackexchange.com/questions/8567/how-do-electron-configuration-microstates-map-to-term-symbols How do electron configuration microstates map to term symbols?