The field of cavity quantum electrodynamics (cQED) with quantum conductors has become an extremely active field of research. The milestone year was 2004, when superconducting qubits have been integrated within a microwave cavity in order to reach, for the very first time in the condensed matter context, the strong coupling regime between photons and matter [1,2]. Since then, many other systems have been successfully coupled to microwave cavities, such as quantum wires , carbon nanotubes , quantum dots , etc. Such hybrid systems offer platforms for new kinds of physics, as one can engineer and manipulate the electromagnetic environment at will.
The versatility of the cQED method relies on the fact that it allows to 1) monitor in a non-invasive fashion the electronic states in quantum conductors, both in equilibrium and non-equilibrium situations, 2) to affect and manipulate the electronic transport, 3) to establish long-range correlations between remote quantum conductors and, finally, 4) it opens the pathway to create non-classical states of light by means of electronic transport.
In my talk, I will discuss some of these aspects for various types of quantum conductors. I will focus mainly on two types of systems: one dimensional p-wave (or topological) mesoscopic superconductors, and semiconductor quantum dots. The former system is known to host zero energy end modes known as Majorana fermions, i. e. particles that are their own antiparticle. These exotic objects are robust against local perturbations and, moreover, they obey non-Abelian statistics under braiding operations, thus recommending them as qubits for the implementation of a topological quantum computer. The latter systems have been shown to emulate the nature-given atoms and their electronic level structure but, as opposed to atoms, they can be easily addressed in electronic transport. While seemingly different, these systems can be probed in a similar fashion by utilizing the photons in a cavity. I will show that the cavity photons give direct access to various electronic susceptibilities of these quantum conductors. For the topological superconductor, I will show that both the so called topological phase transition , as well as the presence Majorana fermions (and some of their peculiar properties) , can be inferred from the cavity field. For the case of quantum dots, I will show that one can reveal properties that are invisible in electronic transport (via the conductance), in particular in out-of-equilibrium situations pertaining to a large voltage bias applied over the quantum dot .
Finally, I will also touch upon the photonic statistics emitted by a voltage biased quantum conductor. Specifically, I will describe a voltage biased Josephson junction coupled to two resonators of incommensurate frequencies. Using a density approach to analyze the cavity fields and an input-output description to analyze the emitted photonic fluxes and their correlation functions, I will show that the emitted radiation is non-classical in the sense that the photonic correlators violate some Cauchy-Schwarz inequalities . I will confront the theory with some recent experimental studies where such violations have been measured .
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