This chapter describes a method to control and measure quantum cavities, achieved using a superconducting phase qubit, a type of electronic atom. The phase qubit has been under intensive development for use as a quantum processing element in a quantum computer. It has recently been used to demonstrate the quantum control and measurement of excitations in resonant cavities, including controlling photons in superconducting microwave resonators, as well as phonons in microwave-frequency mechanical resonators. The discussion here focuses on the quantum control of electromagnetic resonators.
We investigate the controllability of the Jaynes-Cummings dynamics in the resonant and nearly resonant regime. We analyze two different types of control operators acting on the bosonic part, corresponding—in the application to cavity Quantum Electro Dynamics—to an external electric and magnetic field, respectively. For these models, we prove approximate controllability for all values of the coupling constant g∈R, except those in a countable set S* which is explicitly characterized in the statement. The proof relies on a spectral analysis which yields the non-resonance of the spectrum for every g∈R\S*.
We introduce a tomography approach to describe the optical response of a cavity quantum electrodynamics device, beyond the semiclassical image of polarization rotation, by analyzing the polarization density matrix of the reflected photons in the Poincaré sphere. Applying this approach to an electrically-controlled quantum dot-cavity device, we show that a single resonantly-excited quantum dot induces a large optical polarization rotation by
20∘ in latitude and longitude in the Poincaré sphere, with a polarization purity remaining above
84%. The quantum dot resonance fluorescence is shown to contribute to the polarization rotation via its coherent part, whereas its incoherent part contributes to degrading the polarization purity.