Quantum and Classical Amplifier Theory

Ahmad Salmanogli

In this article, a low noise amplifier is quantum mechanically analyzed to study the behavior of the noise figure. The analysis view is changed from the classic to quantum, because using quantum theory produces some degrees of freedom, which may be ignored when a circuit is analyzed using a classical theory. For this reason, the associated Lagrangian is initially derived for the circuit and then using Legendre transformation and canonical quantization procedure the classical and quantum Hamiltonian are derived, respectively. Consequently, the dynamic equation of motion of the circuit is introduced by which all of the circuit measurable observations such as voltage and current fluctuations are calculated. As an interesting point of this study, the low noise amplifier is deliberately supposed as two oscillators connecting to each other sharing the mutual specifications and accordingly the voltage and current are expressed in terms of the oscillators photon number. As a result, one can analyze the critical quantity such as the noise figure in terms of the oscillators photon number and also the photons coupling between oscillators. The latter mentioning term is considered as a factor to engineering the amplifier critical quantities. Additionally, the considered circuit is designed and classically simulated to testify the derived results using the quantum theory.

Stig Stenholm

William George Unruh

The quantum noise in a linear amplifier is shown to be thermal noise. The theory of linear amplifiers is applied first to the simplest, single or double oscillator model of an amplifier, and then to linear model of an amplifier with continuous fields and input and outputs. Finally it is shown that the thermal noise emitted by black holes first demonstrated by Hawking, and of dumb holes (sonic and other analogs to black holes), arises from the same analysis as for linear amplifiers. The amplifier noise of black holes acting as amplifiers on the quantum fields living in the spacetime surrounding the black hole is the radiation discovered by Hawking. For any amplifier, that quantum noise is completely characterized by the attributes of the system regarded as a classical amplifier, and arises out of those classical amplification factors and the commutation relations of quantum mechanics.

Vitaliy V. Shtykov, Sergey M. Smolskiy

Silvano Donati, Guido Giuliani

After pointing out some questionable assumptions of the standard beating theory, we formulate a new semiclassical wave theory of the noise in optical amplifiers. The theory is simple yet rigorous and uses a few quantum statements in a classical signal framework. The amplifier is modeled as a 2/spl times/2 port device, and the amplified spontaneous emission and associated noise are shown to be just the amplified coherent state (or vacuum state) fluctuation of the field entering the idler input. The new theory can treat other closely related detection schemes as well, correctly supplying both mean signal and noise.

Vitaliy V. Shtykov, Sergey M. Smolskiy