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Transcript of Wave Physics PHYS 2023 Tim Freegarde. 2 Wave Physics WAVE EQUATIONS & SINUSOIDAL SOLUTIONS wave...
Wave PhysicsPHYS 2023
Tim Freegarde
2
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 phenomena
Fraunhofer diffraction
longitudinal waves
BEHAVIOUR AT INTERFACES
continuity conditions
boundary conditions
SUPERPOSITIONSlinearity and superpositions
Fourier series and transforms
FURTHER TOPICSwaves 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
3
Doppler effect
source
• wave speed• source
speed• observer stationary
• frequency
observer
source
observer
• wave speed
• observer• source
speedstationary
• frequency
•
4
Doppler effect
•
momentum
• energy, momentum conserved• Doppler shift appears automatically:
THE DOPPLER SHIFT REVISITED
• superposition phase slips
• transition involves photon absorption/emission
• photons have slope
• include kinetic energy
DIPOLE-ALLOWED TRANSITION
internal electronic states linked to momentum states
55
Beating
TWO DIFFERENT FREQUENCIES
tttt2
cos2
coscoscos 212121
•
6
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
•
7
Kelvin ship waves
• deep-water waves:
•
8
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
• if not, wavepacket changes shape as it propagates
3 assumes nearly monochromatic – i.e. that etc. can be neglected
• 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
9
Total internal reflection
2211 sinsin • Snell’s law:
10
Total internal reflection
2211 sinsin • Snell’s law:
1
90
11
Total internal reflection
12
Frustrated total internal reflection (tunnelling)
13
Superluminal waves
•
• tunnelling & the evanescent field
14
Superluminal waves
•
• tunnelling & the evanescent field
15
Speed of light
• Listen again to Melvyn Bragg’s In Our Time:
http://www.bbc.co.uk/radio4/history/inourtime/inourtime_20061130.shtml
Wave PhysicsPHYS 2023
Tim Freegarde
• carries momentum
• ‘comes in lumps’ - PHOTONS
• LIGHT…
• ‘scattering force’
• imparts impulse upon absorption/emission
17
Radiation pressure
•
• carries momentum
• ‘comes in lumps’ - PHOTONS
• LIGHT…
• ~½mg – a few grains of salt
• imparts impulse upon absorption/emission
18
Radiation pressure
•
19
Radiation pressure
•
absorption
emission
2
1
• 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
• atoms see only particular wavelengths• Doppler effect changes wavelength seen
20
Doppler cooling
•
Hänsch & Schawlow (1975)
ω0ω0 – Δω
v = c Δω/ω0
• VELOCITY SELECTION
• Doppler cooling (Rb) to ~1mK• (in our lab) sub-Doppler cooling to
~10μK• (evaporative cooling) ~few pK• Bose-Einstein condensation
21
Doppler cooling
•
10 million atoms20 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
22
Acousto-optic modulation
dia sinsin
• Doppler shift
• Fraunhofer diffraction condition
• Bragg diffraction condition di
a
id
transducer
crystal
aid
aid kkk
dk
ik
ik
dk
ak
• energy and momentum are conserved
k
phonon
23
Diffracting atoms
E M Rasel et al, Phys Rev Lett 75 2633 (1995)nm811
-1m.s850v
Ar40
nm012.0Ar
rad32
m25.1
• stimulated Raman transitions equivalent to Bragg scattering from moving standing wave
2424
Michelson interferometer
• interference by division of amplitude
beamsplitter detector
source
δx
25
Inertial sensing using light
•
• Mach-Zehnder interferometer• quantum wavefunction split and recombined
• phase depends upon rotation
• laser-cooled atoms sense inertial Coriolis acceleration
2626
Wave Physics
• for handouts, links and other material, see http://phyweb.phys.soton.ac.uk/quantum/phys2023.htm
Wave PhysicsPHYS 2023
Tim Freegarde