Due to quantum fluctuations, laser fields have an inherent uncertainty Δn in the number of...

Due to quantum fluctuations, laser fields have an inherent uncertainty Δn in the number of photons n contained in the field. For an ideal laser field, this inherent uncertainty is given by

where is the mean number of photons in the field. A signal cannot be extracted from noise unless the mean signal photon number exceeds the uncertainty in photon number . This requirement gives

Thus the minimum optical signal that can be extracted from the inherent quantum noise in an ideal laser field must contain, on average, at least one photon per detector sampling time. Use this relation to estimate the minimum detectable signal power in an ideal laser field of wavelength 1.5 μm using a detector with a detection observation time of 1 μs.