Abstract
The sixth lesson was devoted to the parametric amplification process. The starting point is Caves' theorem, which states that a phase-preserving amplifier must necessarily add to the signal a noise intensity - counted with reference to the input - equivalent to half a photon per signal mode. How can this quantum limit be reached? The solution, in the case of the non-degenerate parametric amplifier, is simple : use the minimum number of possible modes, i.e. 2, if we count the mode to be amplified. The signal mode must therefore be supplemented by an image mode, circulating in an auxiliary line. The most elementary model of this type of amplifier consists of two LC circuits coupled by a mutual inductance varying sinusoidally in time with the pump frequency. Each oscillator is coupled to the transmission line used to inject and extract the signal and image modes, which is achieved in practice with a circulator. Based on input-output theory, we have established the diffusion matrix for such a circuit. This matrix has the remarkable property of being symplectic, which in turn translates mathematically into the conservation of information by this active circuit, despite the non-conservation of energy. In practice, the time-varying mutuality is implemented using a Josephson ring modulator, comprising four tunnel junctions forming a loop into which half a quantum of magnetic flux is fed. The Wheatstone-bridge symmetry of the ring modulator favors three-wave mixing terms in the Hamiltonian, over parasitic coupling terms that favor dynamic chaos and hence excess noise. With such a device, we can experimentally observe noise compression in the correlations between the direct signal and the image signal, by measuring them through interference.
The lesson ended with a brief discussion of the 2008-2009 program, which will continue this review of quantum phenomena in microwave superconducting circuits, and focus on non-perturbative aspects.
