Abstract
The second lesson was devoted to the modeling of a nonlinear quantum system which is in contact with a dissipative reservoir and whose dynamics are excited by a time-dependent source. The simplest example of such a system consists firstly of three harmonic oscillators, both damped and excited by three sources varying sinusoidally with time, and whose frequencies are close to that of their respective oscillators. The non-linearity of the system is minimal and entirely constituted, at Hamiltonian level, in a tri-linear coupling term of the three oscillators. The system must also satisfy a resonance condition : the largest of the excitation frequencies must be the sum of the two smallest frequencies. There are actually two modes of non-linear operation for such a system, which can be described as a non-degenerate three-wave mixer.
In the first mode, the pump frequency, i.e. the system's power supply frequency, corresponds to the highest frequency. This mode gives the device a photon gain greater than unity. In the second mode, on the other hand, the pump frequency corresponds to one of the two lower frequencies, the signals to be processed being applied to the remaining oscillators. In this case, frequency conversion takes place without photon gain. For optimum pump intensity, completely converting the signals from one port to the other, this last mode can also be seen as dynamic cooling, since it simply exchanges the quanta of one oscillator with those of the other. If the former is at a low frequency and the latter at a high enough frequency to remain in the fundamental state, the thermal quanta of the former will be evacuated to the latter, with no heat flow in the opposite direction.
