How many principles does it take to change a light bulb ... into a laser?

Abstract

Quantum optics did not, and could not, flourish without the laser. The present paper is not about the principles of laser construction, still less a history of how the laser was invented. Rather, it addresses the question: what are the fundamental features that distinguish laser light from thermal light? The obvious answer, "laser light is coherent", is, I argue, so vague that it must be put aside at the start, albeit to revisit later. A more specific, quantum theoretic, version, "laser light is in a coherent state", is simply wrong in this context: both laser light and thermal light can equally well be described by coherent states, with amplitudes that vary stochastically in space. Instead, my answer to the titular question is that four principles are needed: high directionality, monochromaticity, high brightness, and stable intensity. Combining the first three of these principles suffices to show, in a quantitative way --- involving, indeed, very large dimensionless quantities (up to $\sim10^{51}$) --- that a laser must be constructed very differently from a light bulb. This quantitative analysis is quite simple, and is easily relatable to "coherence", yet is not to be found in any text-books on quantum optics to my knowledge. The fourth principle is the most subtle and, perhaps surprisingly, is the only one related to coherent states in the quantum optics sense: it implies that the description in terms of coherent states is the only simple description of a laser beam. Interestingly, this leads to the (not, as it turns out, entirely new) prediction that narrowly filtered laser beams are indistinguishable from similarly filtered thermal beams. I hope that other educators find this material useful, it may contain surprises even for researchers who have been in the field longer than I have.