The photodetection of weak light signals preliminary amplified in optical light amplifiers is analysed quantum-mechanically. A linear amplifier and a four-wave-mixing amplifier are considered. The parameters of the signal-to-noise ratio are calculated and analysed for light sources with various quantum-statistical properties. The signal-to-noise ratio for the detector photocurrent is studied as a function of the quantum-statistical properties of the signal and idler waves involved in amplification by using the four-wave-mixing scheme. The four-wave-mixing scheme with the idler wave in the coherent or Fock (squeezed, sub-Poisson) state has a higher signal-to-noise ratio compared to the linear preamplification regime.
A quantum state can be described by its quasiprobability functions or by its density matrix. The quasiprobability functions and density matrix for nonclassical fields have been measured by making use of homodyne detection schemes. We suggest direct photodetection of the amplified signal fields for the quasiprobability function measurements. Linear amplification is described in phase space by a convolution of the signal field to the idler field, which normally determines added noise during amplification. Taking the coherent idler field and using the convolution relation, we show that the direct photodetection of the amplified field results in a quasiprobability function for the signal field. In particular, the probability of there being no photons in the amplified field is the scaled
Q function for the signal field.