SchroedingersLion said:
So if I have a large number of frequencies, I have to experimentally make sure that they all interfere constructively at some point (and thus periodically). However, with the sun, this is not a given. And only if all the waves of different frequencies interfere constructively, I will get a pulse whose duration decreases with increasing bandwidth?
This is a tricky question. Actually it is a common myth, that the temporal duration of a light pulse forms a Fourier pair with its spectrum (or more exactly its power spectral density). In fact, it is not the temporal duration of the light field, but the autocorrelation of the light field that forms the Fourier pair with the power spectral density via the Wiener-Khinchin theorem. Or to put it simply: A broad spectrum means a short coherence time (as this is given by the decay of the autocorrelation function) and vice versa.
Now, for ultrashort pulses, the minimum duration of the pulse that can be achieved is indeed proportional to the coherence time: If all modes present are in phase at some point in time, the coherence time also defines the timescale on which the phases will become very different again, which defines the pulse duration. Now you might wonder, why multiple pulses are coherent with respect to each other, although the coherence time is so short. If you have a really close look at the spectrum, you will find that it is not really continuous, but consists of lots of closely spaced modes, almost like a frequency comb. The envelope of that spectrum will give you the short-time features, while the periodic discrete peaks will give you "revivals" that occur with the pulse repetition rate.
Now, returning to the question, why sunlight does not consist of short pulses: It does - in a sense. The coherence time defines the time scale of phase fluctuations and as such also the time scale of photon number fluctuations. If you have a look at the Bose-Einstein photon number distribution of thermal light, you will find that the fluctuations are huge and that 0 is the most probable photon number. This can be understood quite easily. A good model for thermal light is given by just taking 100 harmonic oscillators with the same amplitude and completely random phase and giving them a phase kick at random at certain time steps, which represent the coherence time. Most of the time all the fields will cancel out (thus, 0 is the most probable photon number), but at some rare times many of the oscillators will align by chance and provide large residual field and high photon numbers for a very short time. This is what sunlight actually looks like: A train of random short bursts of high intensity and long periods of darkness. However as the duration of the bright and dark periods are given by the coherence time and this is in the hundreds of femtosecond range for sunlight, your eyes (and almost all detectors) just see an averaged constant intensity. Sunlight consists of plenty of short pulses. They just come totally at random.
