Re: Has One Circularly Polarized Photon an Angle of Orientation?

"Darwin123" <drosen0000@xxxxxxxxx> wrote in message
news:0363367c-4d94-4e81-9177-4c3f878b613e@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
Usually, descriptions of elementary particles refer to their
spin, which is the intrinsic angular momentum. However, one can
describe an elementary particle in terms of its intrinsic orientation
instead of its spin. That is, an experiment that describes which way
the particle is "pointing." An uncertainty relation shows that one
can't measure the spin and the orientation simultaneously. Yet, one
can construct a complete description of the particle using one or the
other.
With this in mind, I ask the following question about photons.
Does a circularly polarized photon have an orientation. That is,
in a circularly polarized beam of light (either clockwise or
counterclockwise to the direction of propagation) have a direction of
orientation?
I am thinking of particular experiments where this may be
relevant. The absorption of a strong beam of light on a solution of
dye molecules can induce a linear dichroism on the dye molecules. That
is, the electrons in a particular electronic state may be saturated,
so the absorption for linear polarized light in one polarization is
preferentially bleached. What happens when one photon with a circular
polarization is absorbed? Does the dye molecule develop a horizontal
or a vertical orientation to the optical axis of this dichroic
molecule?
These are of course retorical questions. My point is that spin
and orientation are conjugate variables. For every question involving
the quantum mechanical nature of spin, one can ask a question
corresponding to the quantum mechanical nature of orientation. It may
even be useful for some purposes to talk about the "orientation of the
photon" rather than the "spin of a photon."
Textbooks introducing quantum mechanics don't make this point,
and maybe they shouldn't. This may be useful in later courses,
especially when entanglement experiments are discussed. However, I
think it may be useful for teachers and students to realized that the
photon can have an orientation. The photon is just as easily
described as a paper airplane as it is described as a spinning ball
|:-)

[OP may know much of the below, but it's good review and clarification
for OP and other readers anyway - will try to lead to answer of direct
question.]

Polarized light is different in principle from spin for most other
particles, because polarized light has two "degrees of freedom" in it's
classical and equivalent quantum description. IOW, it isn't just going
at the speed of light that makes photons special. The polarization of a
photon has both orientation and "ellipticity." (I'd call the latter
circularity, explained below.) Consider how the E vector sweeps out a
path in the classical description: it forms an ellipse, which of course
has both orientation and "fatness" or shape. In the "degenerate" cases
we have fully linear light, which also has an orientation. Any ellipse
short of a circle has orientation too of course, relative to e.g. the
longer axis. But a pure circle does not and so cannot have a preferred
orientation perpendicular to the ray motion. However it doesn't "point"
either parallel or antiparallel to that motion.

Hence "spin": the E vector can sweep CW approaching [(-) spin] or CCW
[(+) spin]. This carries angular momentum, and is maximal in pure
circular mode and no spin in linear, with intermediate values
(classically!) for sweeps that are elliptical.

The quantum description is equivalent but statistics rears its head.
Different bases can be picked (as interchangeable constructions of each
other), but for discussing "spin" it is convenient to use circular basis
states. A pure (+) spin photon and equivalent basis is often represented
as |R> [attn. different folks use different standards of chirality.] A
bunch of them adds up to classical right-circular polarized light, and
has net angular momentum of n*hbar as shown by old R. Beth experiment
from 1936. Their spin axes point "with" the line of motion. The negative
spin, |L> will add to -n*hbar worth of angular momentum, with axes
antiparallel to the motion.

We can make superpositions using complex amplitudes with proper
normalization as: a|R> + b|L> where |a|^2 + |b|^2 = 1. This creates
elliptical or linear light (if moduli of a and b equal) in the mass. For
the individual photon, we have a chance |a|^2 of being detected "R" and
|b|^2 of being detected "L" per standard projection postulate etc. The
phases between a and b make for different angles in the mixed cases
(just see that complex coefficients makes for two degrees of freedom.) I
like to refer to "circularity" C which is |a|^2 - |b|^2 and shows the
net signed tendency to impart AM, such that net angular momentum S with
n photons is:
S = C*n*hbar

In conventional theory it is impossible to evaluate C for a single
photon, only test for R or L and have chances of hits thereby. However,
I proposed a thought-experiment to bypass that which got lots of play
here years ago and it and related discussions reside on Google (search
"new quantum measurement paradox"). My later version was: send the same
photon over and over through a half-wave plate P1 (flips coefficient a
and b for even one photon) and a second one P2 to re-invert. The many
passes of the photon (restored to original C by P2) should build up
angular momentum in P1 according to the above formula: but in this case
"n" is number of passes of one photon instead of one pass each by n
quantity of photons. The two should be equivalent (indistinguishability
theorem) and so C for the single photon shows as amount of angular
momentum along a grade. Sure, seems impossible but what is the
refutation? It's so far a "paradox" awaiting solution.

An e.g. electron doesn't have this range of possibilities, it has a
"spin axis" which can be oriented in different ways. Yes it's quantized,
but its half-integer spins is logically different from the integer hbar
spin of a photon. The electron axis is more like a true "vector" and not
the same kind of Poincaré sphere which shows the combined orientation
and "fatness" of a photon. So, circular photons only point "forward or
backward" according to spin. Mixed (superposed) photons (e.g. coming out
of linear polarizer) have a mix of chances to be found pointing parallel
or antiparallel to their motion. It is tempting but wrong to imagine the
angle of linear polarization (which is indeed perpendicular to the ray
motion) as being like a spin vector pointing sideways. (The spin axis of
some particles, like hbar/2 electrons, can actually point sideways.)
Hence, something else must be responsible for what you note about chiral
molecules. Yet indeed circular photons have 50% chance of treating a
molecule like a horizontal linear photon would, and 50% chance of
treating it like a vertical LP would (or any other pair of orthogonal
orientations per the interconvertibility of basis states.)


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