Abstract
Finally, the sixth and last lesson dealt with the conversion of the quantum state of a mechanical resonator into an electromagnetic quantum state, and vice versa. This process is similar to the teleportation of a quantum state discussed in the 2010 lecture. The interest of this type of process is understandable if we realize that microwave frequencies are favourable for quantum signal processing, while optical frequencies are favourable for its propagation. we have treated this quantum conversion by taking up the classical calculation performed in the fourth lesson, but extending it in terms of quantum Langevin equations involving the annihilation operators of two bosonic fields : that of the photons irradiating the electromagnetic oscillator, and that of the phonons irradiating the mechanical oscillator. We then obtain input-output equations for quantum waves, with known boundary conditions for incoming waves. This 140 miCheL devoret boundary condition involves the Bose-Einstein distribution, which enables us to correctly impose the source of thermal and quantum fluctuations for both the electromagnetic and mechanical oscillators. In these equations, a parameter known as the cooperativity plays a crucial role. It is given by the square of the coupling frequency multiplied by the average number of photons in the pump signal and divided by the product of the linewidths of the two resonators.
