The Cummings-Tavis model as a nonlinear quantum amplifier
D Kouznetsov-Kallistratova, Rommer Alex Ortega Martínez · Quantum and Semiclassical Optics Journal of the European Optical Society Part B · 1995
A system of N identical two-level atoms interacting with the single mode of the boson field is considered in the rotating-wave approximation. The solution of the Schrodinger equation with the initial condition of all atoms excited and the field in the coherent state is discussed. The resulting state is interpreted as an amplified state of the field correlated with the state of the system of atoms. The system of atoms is interpreted as an example of a nonlinear quantum amplifier. The algorithm to calculate the amplitude of the field at the output and its uncertainty is described. The relation of the mean value of the output field to the input one is interpreted as the amplification coefficient. The uncertainty of the output field is interpreted in terms of the noise of the amplifier. The dependencies of the noise on the amplification coefficient are plotted for several values of N. The noise is compared with the noise of an ideal linear amplifier of the same amplification coefficient. Conditions at which the nonlinear amplifier has less noise than the linear amplifier are found. Uncertainties of quadrature components which correspond to the amplitude and phase of the field are calculated. It is shown that only one of them has an uncertainty less than the uncertainty in the case of the ideal linear amplifier. Another definition of the amplification coefficient of the nonlinear quantum amplifier is suggested. The differential amplification coefficient gives the simple lower bound of the noise of the nonlinear amplifier. It prohibits the construction of a nonlinear amplifier with a signal-to-noise ratio better than that of an ideal linear amplifier. General bounds of the minimal noise in nonlinear amplifiers are compared with results for a particular amplifier.