wave physics phys 2023 tim freegarde. 2 2 beating two different frequencies
TRANSCRIPT
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Wave PhysicsPHYS 2023
Tim Freegarde
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22
Beating
TWO DIFFERENT FREQUENCIES
tttt2
cos2
coscoscos 212121
•
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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
•
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4
Kelvin ship waves
• deep-water waves:
•
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5
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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6
Doppler effect
source
• wave speed• source
speed• observer stationary
• frequency
observer
source
observer
• wave speed
• observer• source
speedstationary
• frequency
•
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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
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• carries momentum
• ‘comes in lumps’ - PHOTONS
• LIGHT…
• ‘scattering force’
• imparts impulse upon absorption/emission
8
Radiation pressure
•
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• carries momentum
• ‘comes in lumps’ - PHOTONS
• LIGHT…
• ~½mg – a few grains of salt
• imparts impulse upon absorption/emission
9
Radiation pressure
•
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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
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• atoms see only particular wavelengths• Doppler effect changes wavelength seen
11
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
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12
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
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13
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
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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
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1515
Michelson interferometer
• interference by division of amplitude
beamsplitter detector
source
δx
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1616
Wave Physics
• for handouts, links and other material, see http://phyweb.phys.soton.ac.uk/quantum/phys2023.htm
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Wave PhysicsPHYS 2023
Tim Freegarde