2.2 Polarization of photons
The entire discussion of the preceding subsection has concentrated on the behavior of classi-
cal waves. Einstein’s explanation of the photo-electric effect (1905) demonstrates that light
is actually composed of individual quanta (photons), whose behavior is that of particles. If
the light intensity is sufficiently reduced, it actually becomes possible to study individual
photons, and to access the quantum behavior of the polarization degree of freedom of pho-
tons.^2 The intensity of a beam, such asN, is then given by the number of photons (per
second). Ameasurementwill consist simply in counting the number of photons in a given
beam, and thereby yielding the intensity of that beam.
We now list the key experimental observations which point to the keyingredients of
quantum behavior.
(1)From observing individual photons, it is found that the detectors forx-polarization
and fory-polarization are never triggered simultaneously. Thus, we must conclude that the
entire photon emerging from the birefringent plate either hasx-polarization ory-polarization.
(2)It isimpossibleto predict whether a photon incident on the birefringent plate will
trigger detectorDxor detectorDy(unlessθ= 0,π, as we shall see later). Instead, a photon
will reach detectorDxandDywith certain probabilitiespxandpy. In the limit where the
number of photonsN becomes very large, the probabilities are given by
px = lim
N→∞(Nx/N) = cos^2 θ
py = lim
N→∞(Ny/N) = sin^2 θ (2.4)
The relationN =Nx+Ny, obtained previously for an ideal birefringent plate, translates
then to the conservation of probabilitypx+py= 1.
(3)The rule according to which probabilities combine may be inferred froman experiment
in which the beam of photons is first split and then recombined using two birefringent plates,
depicted in Fig. 3.
We assume that the intensity of the light beam emerging from the polarizer isN. The
first birefringent plate splits the beams intoxandypolarizations, which are recombined by
the second birefringent plate (whose optical axis is opposite to theone of the first plate),
thus reproducing the original beam. From this consideration, it is clear that the intensity
(^2) With present day technology of photo-multipliers and CCD (charge coupling devices), it is possible to
detect individual photons, one by one. Actually, even the human retina is capable of detecting single photons,
though very few of the photons that reach the retina will actually stimulate a molecule of visual pigment
(rhodopsin), producing a perception.