Question #43627

In a Young's Double Slit Experiment operating in a low photon-flux regime, a detector records photon counts over a fixed time interval $\tau$. The expected number of coherent signal photons detected at a classical interference maximum is $N_s$, while at a classical minimum it is zero. Additionally, a uniform incoherent background light contributes an expected $N_b = 10$ photons to the detector at any position during $\tau$. The photon arrivals follow independent Poisson statistics, where the variance of a count equals its expected value.

An experimenter measures the total photon count $C_{max}$ at a maximum and $C_{min}$ at an adjacent minimum in separate, independent intervals of length $\tau$. The fringes are defined to be 'just resolvable' if the expected value of the difference $\langle C_{max} - C_{min} \rangle$ is exactly equal to the standard deviation of this difference. Determine the required value of $N_s$ to satisfy this resolvability condition.