The Hanbury Brown and Twiss effect

If we had just 2Nk in the sum, this would be proportional to the energy of each mode times the number of quanta in each mode, summed over all modes. In fact, we have a ‘zero point’ contribution even when Nk = 0. It has exactly the same origin as the 12~ω ground state energy of the simple harmonic oscillator. In this case, the infinite number of modes means that the sum in Eq. (3) is not convergent. Fortunately, this is not what a real experiment measures. To detect light when the number of photons is small we might use a device like a photomultiplier, which harnesses the photoelectric effect to convert a photon into a current pulse, destroying it in the process. Thus it is clear that we should have 2Nk in the sum. We account for this property of the detector by arranging the mode operators inside any quantitiy that we measure in normal order. That