Circuit QED

Patrice Bertet

Oliver Viehmann, Jan von Delft, Florian Marquardt

We investigate the equilibrium behavior of a superconducting circuit QED system containing a large number of artificial atoms. It is shown that the currently accepted standard description of circuit QED via an effective model fails in an important aspect: it predicts the possibility of a superradiant phase transition, even though a full microscopic treatment reveals that a no-go theorem for such phase transitions known from cavity QED applies to circuit QED systems as well. We generalize the no-go theorem to the case of (artificial) atoms with many energy levels and thus make it more applicable for realistic cavity or circuit QED systems.

Jonas Larson, Th. K. Mavrogordatos

Nathan K. Langford

The new and rapidly growing field of circuit QED offers extremely exciting prospects for learning about and exercising intimate control over quantum systems, providing flexible, engineerable design and strong nonlinearities and interactions in systems consisting of microwave radiation fields and fixed artificial "atoms". These notes aim to provide a non-expert introduction to the field of circuit QED, to give a basic appreciation of the promise and challenges of the field, along with a number of key concepts that will hopefully be useful for the reader who is new to the field and beginning to explore the research literature. They were written as a pedagogical text designed to complement a course delivered to third-year undergraduate students. After a introductory section which discusses why studying circuit QED might be worthwhile and interesting, I introduce the basic theory tools from quantum optics and quantum information which are needed to understand the key elements of circuit QED. I also provide a brief overview of superconductivity, focussing on the concepts which are most relevant to operation in the regimes of interest in circuit QED. I then describe the three main types of superconducting qubits, and finally give a basic introduction to decoherence and mixture and how they relate to quantum behaviour in electronic circuits.

Pierre Meystre

Jonas Larson, Th. K. Mavrogordatos

Chapter 4 is the first preparatory one toward elaboration on quantum many-body physics—it deals with circuit quantum electrodynamics (QED), i.e. systems of coupled Josephson qubits in macro-cavities, which correspond to coupled Jaynes–Cummings (JC) models. The chapter starts with the discussion of the rich physics of Josephson qubits, and then focuses on the (generalized) JC nonlinearity and spectrum revisited in the light of circuit QED. Finally, control and transfer of quantum information in circuit QED is discussed.