Wave Physics PHYS 2023 Tim Freegarde

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

Doppler effect frequency wave speed source speed observer stationary

Doppler effect transition involves photon absorption/emission internal electronic states linked to momentum states THE DOPPLER SHIFT REVISITED include kinetic energy photons have slope energy, momentum conserved Dipole-allowed transition Doppler shift appears automatically: superposition phase slips momentum

Beating TWO DIFFERENT FREQUENCIES 5 5

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

Kelvin ship waves deep-water waves:

Superluminal waves generally: the group velocity = speed of energy propagation = speed of information propagation 1 assumes energy is conserved: not true in an absorbing medium not true in an amplifying medium not true in a nonlinear medium 2 assumes wave propagates: no constraint if wave doesn’t propagate from to 3 assumes nearly monochromatic – i.e. that etc. can be neglected if not, wavepacket changes shape as it propagates group velocity dispersion 4 beware of resonators, e.g. atoms in a crystal anomalous group velocities at Brillouin zone edges single frequency  steady-state excitation system has memory

Total internal reflection Snell’s law:

Total internal reflection Snell’s law:

Total internal reflection

Frustrated total internal reflection (tunnelling)

Superluminal waves tunnelling & the evanescent field

Superluminal waves tunnelling & the evanescent field

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

Wave Physics PHYS 2023 Tim Freegarde

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

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

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

Doppler cooling VELOCITY SELECTION ω0 – Δω atoms see only particular wavelengths ω0 Doppler effect changes wavelength seen Doppler cooling (Rb) to ~1mK v = c Δω/ω0 (in our lab) sub-Doppler cooling to ~10μK (evaporative cooling) ~few pK Bose-Einstein condensation Hänsch & Schawlow (1975)

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

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

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

Michelson interferometer δx interference by division of amplitude beamsplitter detector source

Inertial sensing using light Mach-Zehnder interferometer quantum wavefunction split and recombined laser-cooled atoms sense inertial Coriolis acceleration phase depends upon rotation

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

Wave Physics PHYS 2023 Tim Freegarde