Download Wave Physics PHYS2023

Wave Physics
PHYS 2023
Tim Freegarde
Wave Physics
general wave phenomena
WAVE EQUATIONS &
SINUSOIDAL SOLUTIONS
wave equations, derivations and solution
sinusoidal wave motions
complex wave functions
Huygens’ model of wave propagation
WAVE PROPAGATION
interference
Fraunhofer diffraction
longitudinal waves
BEHAVIOUR AT
INTERFACES
SUPERPOSITIONS
continuity conditions
boundary conditions
linearity and superpositions
Fourier series and transforms
waves in three dimensions
FURTHER TOPICS
waves from moving sources
operators for waves and oscillations
further phenomena and implications
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http://www.avcanada.ca/albums/displayimage.php?album=topn&cat=3&pos=7
Doppler effect
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frequency
wave speed
source speed
observer
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frequency
wave speed
source speed
observer
stationary
observer
source
stationary
observer
source
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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
• Doppler shift appears
automatically:
DIPOLE-ALLOWED
TRANSITION
• superposition phase slips
momentum
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Beating
TWO DIFFERENT FREQUENCIES
cos 1t  cos 2t  cos
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1  2
  2
t cos 1
t
2
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Group velocity
• generally: the group velocity
= speed of energy propagation
= speed of information propagation
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sinusoidalcomponents:
components:
2 sinusoidal
• spreading of wavepacket
• this illustration corresponds to the wavepacket evolution of a quantum
mechanical particle, described by the Schrödinger equation
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Kelvin ship waves
• deep-water waves:
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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
3 assumes nearly monochromatic – i.e. that
to
etc. can be neglected
• if not, wavepacket changes shape as it propagates
• group velocity dispersion
4 beware of resonators, e.g. atoms
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in a crystal
anomalous group velocities at Brillouin zone edges
single frequency  steady-state excitation
system has memory
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Total internal reflection
• Snell’s law:
1 sin 1  2 sin 2
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Total internal reflection
90
1
• Snell’s law:
1 sin 1  2 sin 2
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Total internal reflection
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Frustrated total internal reflection (tunnelling)
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Superluminal waves
• tunnelling & the evanescent field
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Superluminal waves
• tunnelling & the evanescent field
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Speed of light
• Listen again to Melvyn Bragg’s In Our Time:
http://www.bbc.co.uk/radio4/history/inourtime/inourtime_20061130.shtml
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Wave Physics
PHYS 2023
Tim Freegarde
Radiation pressure
• LIGHT…
• ‘comes in lumps’ - PHOTONS
• carries momentum
• imparts impulse upon absorption/emission
• ‘scattering force’
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Radiation pressure
• LIGHT…
• ‘comes in lumps’ - PHOTONS
• carries momentum
• imparts impulse upon absorption/emission
• ~½mg – a few grains of salt
•
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Radiation pressure
• LIGHT…
• ‘comes in lumps’ - PHOTONS
• carries momentum
• imparts impulse upon absorption/emission
• ~½mg – a few grains of salt
Hale-Bopp (1997) – Malcolm Ellis
www.ifa.hawaii.edu/faculty/jewitt/tail-HB.html
•
emission
absorption
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1
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Doppler cooling
• VELOCITY SELECTION
• atoms see only particular wavelengths
• Doppler effect changes wavelength seen
• Doppler cooling (Rb) to ~1mK
• (in our lab) sub-Doppler cooling to ~10μK
• (evaporative cooling) ~few pK
• Bose-Einstein condensation
•
ω0
ω0 – Δω
v = c Δω/ω0
Hänsch & Schawlow (1975)
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Doppler cooling
• VELOCITY SELECTION
• atoms see only particular wavelengths
• Doppler effect changes wavelength seen
• Doppler cooling (Rb) to ~1mK
• (in our lab) sub-Doppler cooling to ~10μK
•
10 million atoms
20 μK
<1 mm
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Acousto-optic modulation
• Fraunhofer diffraction condition
kd
crystal
a sin i  sin kd   
d
a
i  d
d  i  a
ki
• Bragg diffraction condition
• Doppler shift
phonon
kd  ki  ka
• energy
kd
i
a
transducer
ki
 and momentum k are conserved
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Diffracting atoms
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Ar 
  32  rad
v  850 m.s -1
Ar  0.012 nm
1.25 m
  811 nm
E M Rasel et al, Phys Rev Lett 75 2633 (1995)
• stimulated Raman transitions equivalent to Bragg
scattering from moving standing wave
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Michelson interferometer
• interference by division of amplitude
δx
beamsplitter
detector
source
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Inertial sensing using light
• Mach-Zehnder interferometer
• quantum wavefunction split
and recombined
• laser-cooled atoms sense
inertial Coriolis acceleration
• phase depends upon rotation
•
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Wave Physics
• for handouts, links and other material, see
http://phyweb.phys.soton.ac.uk/quantum/phys2023.htm
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Wave Physics
PHYS 2023
Tim Freegarde