Coherent unpolarized laser light I notice that in semiclassical treatments of laser light absorption by particles, they treat the laser beam as a coherent oscillating electric field over the form $E_0\cos(kx-\omega t)$, sometimes with a factor added in to account for the Gaussian spread of wavelengths. However, my understanding is that most laser beams are unpolarized, so that they are composed of a practically infinite number of photons whose electric field are all oscillating at the same frequency but in different directions. So shouldn't the average of all these oscillating field be $0$ at all times, or at least vary randomly about $0$? How can we pretend that the atom is question is just exposed to a single linear oscillating electric field and expect to get good results?
 A: If you take two beam of light and combine them, they can interfere destructively in one place and constructively in another. They will not interfere destructively everywhere. If you follow the details, it always works out that way.
You can see that it has to work out that way by considering conservation of energy. Total destructive interference would mean two beams with energy combine to a beam with no energy.
A: Another post is discussing why you usually should expect your laser beam to be polarized.
Nevertheless, if you have a laser beam that is randomly polarized that means that your polarization is changing over time rather than that you have multiple light fields interfering with each other. After all, that interference could mean that your beam is vanishing, and we already agreed that it is present. Therefore there must be an electric field oscillating, even if the plane of those oscillations or their phase in relation to the coexisting magnetic field is changing over time.
And finally, atoms when absorbing photons are changing their internal quantum state. The simplest picture of this process assumes that a laser beam is consisting of photons carrying energies equal to the difference between the ground and excited state. This is not the whole story for real atoms. What is also needed to be considered is the "shape" of an excited state in comparison to the ground one. This interaction is governed by the so-called dipole operator which tells you if the act of absorption can occur, i.e. if the ground state can be transformed under this operator into an excited state. This operation takes into account the polarization of your light. For example, if in your system you introduced a special direction (quantization axis) with a magnetic field, you will find that there are atomic transitions that can only happen with circularly polarized light. If no such special direction is introduced, you can assume that the direction of the field oscillations is introducing this special axis, so your atoms will keep interacting with your driving beam.
A: All lasers are polarized .... where did you hear otherwise?
We can never directly observe the superposition of EM waves in the EM field ..... we can only observe a photon when it excites an electron in a CCD or in your eye. It does not matter if the photons are out of phase (net zero E,M) .... the electrons are able to scatter/separate/absorb them.
The idea of waves of light cancelling is old (and misleading)... based on Fresnel Huygens (1818) ... but is still taught today!  For example in the DSE (double slit experiment) all the high school physics formulas do work to calculate the bands ... but fundamentally photons are not cancelling ... it is likely that the virtual fields are cancelling even before the original photon takes flight.
