Early quantum optics 1900-1970
Blackbody radiation
Planck 1900: EM wave amplitudes/energies work as
though they were quantized
Photoelectric effect:
Einstein 1905: They are quantized: photons
Quantum electrodynamics
Quantum field theory for E, B
(Feynman etc, 1940’s-1960’s)
Vacuum fluctuations and zero point energy
Quantum optics as a discipline begins with laser
invention (1960)
Quantum uncertainties in number, phase, position of
photons.
New quantum optics 1970-present
Squeezed states to redistribute uncertainties of phase,
numbers of photons
Photon entanglements to test quantum ideas
Quantum cryptography, “teleportation” of photon or single
atom states
Vacuum zero point energy
A vacuum is a collection of simple harmonic oscillators.
E and B are its excitations, and play roles like x, v in SHO.
Energy levels for each mode in a vacuum:
1

E  h  n  
2

Zero point energy represents fluctuations in E, B that are part
of a vacuum.
Casimir effect predicted in 1948:
Two parallel mirrors are brought close to each
other. Only certain frequencies are allowed inside
the cavity(boundary conditions). Pressure from
more vacuum fluctuations outside than inside!
Casimir force is real
Forces on parallel plates observed to within 15 % of
theory!
Sphere-plate version to
within 1% of theory
Vacuum zero point energy
How much of this energy is there in the
universe?
Energy
h
h 8 3

g() 
volume Hz
2
2 c3
New ultraviolet catastrophe! finite volume has
infinite zero point energy.
New ultraviolet catastrophe!
“This problem, also known as the ‘cosmological
constant problem’ because of its obvious
connection with the introduction of a cosmological
constant in Einstein gravitation equations, has
remained unsolved during the twentieth century,
despite considerable efforts for proposing
solutions. It has the status of a paradox, lying just
at the crucial interface between quantum theory
and gravity, and pointing at the necessity of
substantial reformulations in the present theoretical
formalism.” Serge Reynaud et al, 2000
Quantum Optics: Experiment 1 to remember
Double slit illumination: Quantum superposition in singlephoton experiments
Each photon is in a superposition of “through top slit”
and “through bottom slit” states.
Old experiment and debate: can we know which slit the
photon (electron) went through and get interference?
Image formation one photon at a time!
Single photons know how to do ray optics
Experiment 2 to remember
Quantum superposition in single-photon experiment
Delayed choice experiment. Put shutter in (or not)
randomly, but after the time “the photon should have
passed the beamsplitter” (classically).
Analysis after
experiment
When shutter in:
no interference
When shutter out:
fringes
Quantum entanglement of two particles
Momentum-entangled particle pair emission. (e.g electrons)
Suppose pair (a,b) or (a’,b’) momentum must be conserved
(zero total p)
Can we “know which slit” a particle went through by
measuring the directions of particle b, b’?
How photon entanglement is achieved
Nonlinear downconversion in low symmetry
crystal.
UV photon 2 visible photons of same l
(green), or 2 photons of different l (red/blue)
z
Total momentum is conserved (hence y-z momentum of
pair is zero)
Experiment 3 to remember (1998)
Entangled photons created at crystal, go to camera D1 and
D2. D1 can be at point A or B, either f or 2f from the lens.
Lens is 2f from double slit.
z
Entanglement: photon 1 acts as though it were timereversed copy of photon 2, since they have opposite
momentum components !
“Weird” observations
Photons at D1, FT position (A), show the fringes, even
though their partners went through the slits!
z
Moving D1 to imaging position (B) (2f from lens) lets us see
which slit they go through. This makes the 2-slit pattern at
D2 disappear …. even though we classically “they’ve hit D2
before D1”.
review article
General
If we measure (or could measure) in any way “which slit”
they go through, all interference vanishes
“Quantum eraser”: if we absorb or detect photon 1 in
such a way that it cannot possibly give information
about which slit photon 2 went through, then we get
interference patterns for photon 2.
z
So how can we be sure to achieve an interference
pattern on the screen at the left?