Download Lecture24 - Purdue Physics

PHYS219 Fall semester 2014
Lecture 24: Quantum Optics: Photons
(moving to Chapter 28)
Dimitrios Giannios
Purdue University
Continuous and Quantized
For the remainder of the course, it will become
increasingly important to distinguish between
continuous and quantized items.
Some things seem inherently continuous (like length,
energy, mass) while other entities seem inherently
discrete or quantized (like money, number of people at
a football game, etc.)
In science, the existence of atoms (different chemical
elements) provided first hint that nature is quantized.
• Light is especially interesting because it displays
different behavior in different situations
• Ray optics – lenses & mirrors
• Wave optics – interference & diffraction
• Quantum optics – interaction w. electrons
continuous
quantized
Visible EM Radiation
•
from Maxwell in the 1860s, we know that light is an EM wave.
• in 1888, Hertz showed that EM waves with long wavelengths
could be launched and detected using transmitters and
receivers (the forerunners of today’s communication industry).
• …………but what about visible light? How is it generated?
Consider a few sources of visible light:
• Sun
• Fire
• Oil lamp
• Gas discharge tube
• Heat radiation (blackbody)
‘WHITE’ light - Newton 1666
Consider sunlight – ‘white’ light containing a continuous spectrum of colors
Glass prism
Continuous
spectrum of
colors
“white” light
light is dispersed
Newton’s Result–inconsistency with light from Gas
Discharge Tube - Discrete Wavelengths (late 1800s)
Glass tube, evacuated
and back-filled with gas
Glass prism
light is dispersed
from Gas Discharge Lamp
Use diffraction grating to accurately measure
wavelengths
bright fringes
(bright spots)
incident light
λ1, λ2, λ3, etc
multiple slits
separation between
slits = d
Note: Each λ produces
a different y
y
W >> y
Viewing
screen
Spectral Lines for Common Gases
Wavelengths
accurately
measured
Why are there so
many lines?
Check out http://www.colorado.edu/physics/2000/applets/a2.html
Focus on light emitted from Hydrogen
discharge tube
Balmer’s empirical formula (1884) explains the observed
visible wavelengths from hydrogen gas with high accuracy
n=7 n=6 n=5
n=4
é1
1ù
= R H ê - ú ; n = 3, 4,5...
êë22 n 2 úû
l
1
RH = 1.097 × 107 m-1
n=3
The Photoelectric Effect
Ejection of electrons from a material due to illumination by light
“photons in, electrons out”
What you can measure/control experimentally?
1. Intensity of
Light
2. Frequency (color)
of Light
3. Composition
of Target
e-
5. Electron
Current (Number
of Electrons)
e-
e-
What’s
going on at
interface?
4. Energy of
Ejected Electrons
In diagram, q is
assumed to be
positive (+)
9
Check out the photoelectric simulation
http://phet.colorado.edu/new/simulations/sims.php?sim=Photoelectric_Effect
What was expected
1. As the intensity increases, the
maximum energy of ejected
electrons should also increase.
- Energy (in J) carried by an EM
wave depends on intensity I:
Metal Plate
U=PΔt=(I⨯A)Δt
2. At low enough intensities, there
will be a delay in electron emission.
- Energy (in J) carried by an EM
wave depends on time Δt:
U=PΔt=(I ⨯ A)Δt
3. Electrons should be emitted for
all wavelengths of light.
-The wavelength λ does not appear
in above equations
Hole in mask,
area A
utot
cΔt
Energy U passing
thru hole in time
Δt
Time
aver.
radiation,
intensity I
What was observed
a) Red light
x2
x2
4Io
2Io
Io
No electron
emission - ever!
Metal plate
b) Blue light
Io
Metal plate
x2
x2
Prompt electron emission even
at lowest intensity!
2Io
4Io
Why the Photoelectric Effect was so
Surprising
a) Low frequency water
waves
Large
amplitude,
any λ
?
h
b) High frequency water
waves
?
High frequency,
small λ
h
When does
the
fisherman
leave the
dock?
The Other Problem: Blackbody Radiation
(EM radiation from objects held at temperature T)
Blackbody Radiation:
• Continuous light emission with no well defined
frequencies
• Light spectrum (to first approximation) does not
depend on material that is heated, only on
absolute temperature T
• Classical physics unable to explain shape of
emitted light spectrum
Classical prediction
based on known
properties of EM waves
Intensity
UV visible
IR
6000 K
3000 K
1000 nm 2000 nm
Wavelength,λ
Heat (blackbody) Radiation
See: http://phet.colorado.edu/simulations/sims.php?sim=Blackbody_Spectrum
Planck’s Hypothesis (1900)
To quantitatively explain blackbody radiation spectra, Planck assumes
that a blackbody is made of “atomic oscillators” that emit light which
is quantized in energy, ie
E = n ⨯(hf)
h= 6.626 x 10-34 J s
(Planck’s Constant)
n = integer
f= frequency of light
This simple idea had an impact
similar to the impact of Newton’s
equations in the 1750’s
Einstein (in 1905) hypothesized
Planck’s idea (in 1900) followed up by Einstein (in 1905)
hypothesized that light itself must be thought of as
quantized packets of energy called photons
one
photon
Ephoton = hf
n=6
Light beam
n=9
n=3
Foundation
of
QUANTUM
optics
Why is this quantization hypothesis so
surprising?
Since light is a wave (only way to explain interference and diffraction effects
from the early 1800’s), everyone thought that it’s energy could be varied
continuously by adjusting the wave’s amplitude. This simple idea was
completely contradicted by Planck’s hypothesis.