1. Wave Physics PHYS 2023 Tim Freegarde

2. 2 2 Beating TWO DIFFERENT FREQUENCIES

3. 3 Group velocity 2 sinusoidal components: 10 sinusoidal components: spreading of wavepacket this illustration corresponds to the wavepacket evolution of a quantum mechanical particle, described by the Schrödinger equation generally: the group velocity = speed of energy propagation = speed of information propagation

4. 4 Kelvin ship waves deep-water waves:

5. 5 Speed of light Listen again to Melvyn Bragg’s In Our Time: http://www.bbc.co.uk/radio4/history/inourtime/inourtime_20061130.shtml

6. 6 Doppler effect source wave speed source speed observer stationary frequency observersource observer wave speed observer source speed stationary frequency

7. 7 Wave Physics WAVE EQUATIONS & SINUSOIDAL SOLUTIONS wave equations, derivations and solution sinusoidal wave motions complex wave functions WAVE PROPAGATION Huygens’ model of wave propagation interference general wave phenomenaFraunhofer diffractionlongitudinal waves BEHAVIOUR AT INTERFACES continuity conditions boundary conditions SUPERPOSITIONS linearity and superpositions Fourier series and transforms FURTHER TOPICS waves from moving sources operators for waves and oscillations waves in three dimensions http://www.avcanada.ca/albums/displayimage.php?album=topn&cat=3&pos=7 further phenomena and implications

8. carries momentum ‘comes in lumps’ - PHOTONS LIGHT… ‘scattering force’ imparts impulse upon absorption/emission 8 Radiation pressure

9. carries momentum ‘comes in lumps’ - PHOTONS LIGHT… ~½mg – a few grains of salt imparts impulse upon absorption/emission 9 Radiation pressure

10. 10 Radiation pressure absorption emission carries momentum ‘comes in lumps’ - PHOTONS LIGHT… ~½mg – a few grains of salt imparts impulse upon absorption/emission www.ifa.hawaii.edu/faculty/jewitt/tail-HB.html Hale-Bopp (1997) – Malcolm Ellis

11. atoms see only particular wavelengths Doppler effect changes wavelength seen 11 Doppler cooling Hänsch & Schawlow (1975) ω0ω0 ω 0 – Δω v = c Δω/ω 0 VELOCITY SELECTION Doppler cooling (Rb) to ~1mK (in our lab) sub-Doppler cooling to ~10μK (evaporative cooling) ~few pK Bose-Einstein condensation

12. 12 Doppler cooling 10 million atoms 20 μK <1 mm atoms see only particular wavelengths Doppler effect changes wavelength seen VELOCITY SELECTION Doppler cooling (Rb) to ~1mK (in our lab) sub-Doppler cooling to ~10μK

13. 13 Acousto-optic modulation Doppler shift Fraunhofer diffraction condition Bragg diffraction condition transducer crystal energy and momentum are conserved phonon

14. 14 Diffracting atoms E M Rasel et al, Phys Rev Lett 75 2633 (1995) stimulated Raman transitions equivalent to Bragg scattering from moving standing wave

15. 15 Michelson interferometer interference by division of amplitude beamsplitterdetector source δxδx

16. 16 Wave Physics for handouts, links and other material, see http://phyweb.phys.soton.ac.uk/quantum/phys2023.htm

17. Wave Physics PHYS 2023 Tim Freegarde