Why does number of photons fluctuate? When counting photons (with, e.g., a CCD), there is the so-called ''photon noise'' (important at low photon numbers). What is the explanation in the framework of QED, QFT? Is it the Heisenberg uncertainty principle? Why does the energy of a single photon not fluctuate instead?
Thanks.
 A: In quantum field theory, the notion of particles is not actually fundamental, as the name indicate. Particle states (states with energy eigenvalues) are subject to fluctuations the same as any other variable, in the case of the EM field, the potential $\hat{A}^\mu$ and the electric field $\hat{E}^\mu$. From those, you get the ladder operators by inverting : 
\begin{eqnarray}
\hat{A}^\mu &=& \int d^3k \sqrt{\frac{\hbar}{2\omega_k \varepsilon_0}} (\hat{a}_k u^\mu_k + \hat{a}_k^\dagger u_k^{\mu *})\\
\hat{E}^\mu &=& i \int d^3k \sqrt{\frac{\hbar \omega_k}{2 \varepsilon_0}} (\hat{a}_k u^\mu_k + \hat{a}_k^\dagger u_k^{\mu *})\\
\end{eqnarray}
Which leads you to the number operator, $\hat{N} = \hat{a}^\dagger \hat{a}$, with eigenvectors $\hat{N}_p \vert n_k \rangle = \delta_{np} n_k \vert n_k \rangle$.
You never really have number states, though. For a start, outside of a box, number states are not normalizable. The more realistic notion of a wavepacket of light is a coherent state $\vert \alpha_k \rangle$, where, for a complex number $\alpha$ (and a mode $k$), 
\begin{eqnarray}
\vert \alpha_k \rangle = e^{(\alpha \hat a^\dagger_k - \alpha^* \hat a_k)} \vert 0 \rangle
\end{eqnarray}
It is well localized in both momentum and coordinate space, normalizable and of finite energy. On the other hand, its probability with respect to the number operator is
\begin{eqnarray}
P_n = \vert \langle n_k \vert \alpha_k \rangle \vert^2 = \frac{\vert\alpha\vert^{2n}}{n!} e^{-\vert \alpha \vert^2}
\end{eqnarray}
That is of course just for coherent states, but more generally, as long as your state is not an eigenvalue of the number operator (which is not really possible), it will always be some superposition of several number states.
A: I think that's the basis of quantum mechanics. That photons are emitted in certain chunks of energy called quanta. No matter how small the energy if it's enough to excite even just one electron then a photon can be emitted.
