We all know that monochromatic light is always polarised. Non-monochromatic light can obviously also be linearly polarised. However, can non-monochromatic light be elliptically or circularly polarised?
There's some subtleties around the edges of this question, but the short answer is yes.
Non-monochromatic light is made up of some combination (which might be coherent or incoherent) of light of a range of different frequencies. If each component of that combination is circularly polarized, then we say that the combination is circularly polarized.
If the combination is coherent, then it is a linear superposition that forms some form of pulse, in which case the field shape rotates with time; see e.g. this paper for a recent example.
If the combination is incoherent, then it becomes quite hard to say anything about the detailed time dependence of the pulse, which will generally be a mess, but it will tend to rotate in the specified direction.
In either case, to actually make a non-monochromatic circular polarization, you need a quarter-wave plate as usual -- except that the plate will need to add exactly a quarter-wavelength of optical path to each wavelength, which can't be achieved with a plate of constant birefringence $\Delta n$. Instead, what's needed is an achromatic waveplate whose birefringence $\Delta n$ changes with wavelength in precisely the right way; this is mostly doable over limited frequency ranges, but it gets more and more challenging (and expensive) as the bandwidth of interest increases.