(How) is a single photon polarized?

[Richard J]

What quantum mechanical property of the photon determines its polarization?
Can a single photon be unpolarized?
Can a single photon be linear polarized?
Can a single photon be circular polarized?
Can a single photon's polarization be changed?

Can classical and quantum mechanical polarization of an electromagnetic wave/photon coexist?


Richard

 

[Nesk]

Photons are bosons and have spin $$\pm$$ 1, corresponding to two different circular polarization modes. One photon has one of these two, and other modes of polarization are achieved by superposition of more photons.

 

[dextercioby]

Actually the spin quantum number of a photon is 1 and +/- 1 is the helicity (helicity quantum numbers).

 

[Richard J]

Does the spin quantum number or the helicity quantum number of the photon correspond to the classical concept of electromagnetic wave polarization?

 

[JDługosz]

The Wikipedia article on Photon Polarization says that the spin corresponds to classical polarization.

 

[Jim Kata]

Ok let me just writ it out it's simplest this way
The free electromagnetic potential is given by:

$$a^\mu (x) = (2\pi )^{ - 3/2} \int {\frac{{d^3 p}} {{\sqrt {2p^0 } }}} \sum\limits_\sigma {\left[ {e^{ip \cdot x} e^\mu ({\mathbf{p}},\sigma )a({\mathbf{p}},\sigma ) + e^{ - p \cdot x} e^{\mu *} ({\mathbf{p}},\sigma )a^\dag ({\mathbf{p}},\sigma )} \right]}$$

Now, $$e^\mu ({\mathbf{p}},\sigma )$$ that represents the direction of the field is called a polarization vector.
$$\sigma$$ the helicity can be thought of as in which direction the polarization vector is rotating clockwise or counterclockwise.

 

[Jim Kata]

This very similar to the classical situation.

Classically for a single monochromatic plane wave, if you pick your coordinates properly, the wave can be written in the general form:

$${\mathbf{A}} = B\cos (kz - \omega t){\mathbf{x}} \pm C\sin (kz - \omega t){\mathbf{y}}$$ where B and C are the polarizations of the wave, elliptical in general, and the $$\pm$$ symbol represents the helicities which just determine the direction of rotation of the polarized wave.