Recent advances have made it possible to measure electromagnetic signals in the microwave range with added noise of less than one photon per mode. However, the energy of a microwave photon is around 100 000 times lower than that of an optical photon, and its detection therefore requires a circuit cooled to temperatures below 100 mK. On the other hand, it is much easier to control the spatial and temporal wave function of a photon at 5 GHz than at 500 THz. Experiments in mesoscopic physics, and in particular those on superconducting quantum circuits, can now be understood in the same way as those in quantum optics, where the detection of a single photon has been standard for several decades.
The aim of the lecture is to explain the principles of the new amplifiers at the heart of mesoscopic measurements whose precision is limited only by the uncertainty principle. The first part of the lecture will take an in-depth look at the non-linear and out-of-equilibrium effects characterizing active quantum circuits, using the so-called " input-output " formalism. In particular, we will examine parametric amplifiers based on pumping one or more Josephson junctions. The relationships between gain, bandwidth and dynamic range will illustrate the decisive influence of quantum noise on the operation of these amplifiers and on the signal processing they perform. The use of feedback to control the dynamic state of a qubit will be discussed in the final part of this lecture. An example of metrological interest is the measurement of persistent Rabi oscillations, a quantum phenomenon that has been predicted for many years but has yet to be observed.