Photon Polarization: Linear vs Circular & Time-Dependent States

[wotanub]

So I know that a linearly polarized photon is in a state

[itex]ψ = cos(θ)\left|x\right\rangle + sin(θ)\left|y\right\rangle[/itex]

What if θ depends on time maybe something like [itex]θ\equiv\frac{E_{0}t}{\hbar}[/itex]? The polarization is linear at any time t, it rotates as time passes? Isn't that circular polarization? What's the difference between the states?

This is my attempt at an explanation:

Is it correct to say that the polarizations photons in the state I'm describing rotate as they move through time, and circularly polarized photons (in a time independent state) rotate as they move through space?

I think this would imply that if I put my photons on a polarizer and measure the intensity, it would oscillate with a frequency [itex]ω=\frac{E_{0}}{\hbar}[/itex]

Let me know if this is sound physics.

 

[azntoon]

Yes, your explanation is correct. The linear polarized state you have described is in fact a time-dependent state which rotates through space as time passes. This state will indeed oscillate in intensity when placed on a polarizer due to the changing angle of polarization. This oscillation will occur at a frequency of ω=\frac{E_{0}}{\hbar}. In contrast, circularly polarized photons (in a time independent state) will rotate through space but not change their polarization angle. These photons will not undergo an intensity oscillation when placed on a polarizer.