Is it possible for a single photon to be non polarized?

Question

As in classical wave theory, the polarized light is light where the waves emitted corresponds to one axis of propagation. My question is if one single photon could be twisted to a point where it corresponded to every axis 360 degrees around. This is more of a what if question or discussion more than anything else.

Answer 1

Not exactly non-polarised, but something called "circularly polarised", which I think fits what you are trying to describe.  Light can be left-handed circularly polarised, or right-handed circularly polarised, and chiral molecules will interact with one of these polarisation is more strongly than with the other.

Answer 2

No, it can not be if your question refers to the state vector  By definition, the photon polarization states are given by the Jones vectors {1,0} and {0,1}.  There is no way that these can be combined to give {0,0}. Now, you could define a state of polarization at angle θ with respect to the reference axis: {cosθ ,sinθ }, and then try defining a new state by integrating over angle, which will yield {0,0}.  However, this is not a single photon state.  I'm not even sure if that last step is legitemate mathematics.  Quantum mechanically one approach is to calculate the expectation value of the electric field for a one-photon state.  The result of that is always zero for such a state, but can be different for two or more photon states. Physically that can be understood by the picture of the electric field oscillating, so that its time average is zero.  So the answer depends on exactly what you mean with the term polarization.

I don't agree with Paul B: circular polarization states are every bit as much polarization states as linear polarization states.  Thus right-hand circulalrly polarized light is polarized.  If you send a bunch of such photons through a regular polarizer, on the average exactly half of them pass through, showing they must even have linear polarization components.

********************

To Dr R:

Passing a photon through a stationary polarizer only puts it into a definite polarization state.  A way to get the photon into a mixed state is by spinning the polarizer, and then the "state" is described by a probablilty of 1/2 for x and y polarization each. The "mean" polarization is not zero unless you mean the average, i.e. expectation value, of the electric field (as I discussed above).  This is because the photon is polarized in both states, and the description does not differentiate between up and down.  The polarization state {1,0} is the same as {-1,0}.  The expectation value of the electric field in any single-photon state (e.g. pure x polarization or pure right-hand circular polarization, or any mixed single-photon state) is always zero, but that does not mean the polarization is zero.

Answer 3

Sort of. In quantum theory, a single photon can be in a "mixed state" where there is 50 percent chance that it will pass through a polarizing filter, regardless of the directon the filter is rotated.