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.
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.
Abstract This chapter introduces the basic concepts of quantum information processing with superconducting quantum circuits. It starts with a demonstration of how,in these electrodynamic systems, both the superconducting gap and the long-range Coulomb interactions contribute to the existence of collective modesthat have extremely low dissipationand that can be quantized. The chapter also gives in-depth coverage of quantum harmonic oscillators in all their glory from various perspectives. Superconducting qubits are then introduced, starting with the fundamental theory of the Josephson effect and moving on to a presentation of the variety of existing superconducting qubits. Particular attention is given to the dispersive readout of qubits through their interaction with a cavity into which flying modes can be scattered. Finally, the opportunities offered for quantum information processing by employing the cavity as a quantum bus are presented.
The Jaynes–Cummings Model (JCM) has been at the forefront of modern physics as one of the simplest, yet intricately nonlinear, models of light–matter interaction. Focusing on the omnipresence of the JCM across a range of disciplines, this significantly updated and comprehensive review conveys to the reader the fundamental generality of its formalism, looking at a wide range of applications in specific physical systems and across disciplines including atomic physics, quantum optics, solid-state physics and quantum information sciences. An ideal reference for researchers in quantum physics and quantum optics, the book also comprises an accessible introduction for students engaged with non-equilibrium quantum phase transitions, quantum computing and simulation, quantum many-body physics, cavity, circuit and waveguide quantum electrodynamics. Part of IOP Series in Quantum Technology. Key features • Collects JCM physics and applications scattered across literature and different applications. • The exposition guides the reader through a rich and appealing landscape interlacing quantum optics and condensed-matter physics. • All chapters discuss theory and experiment, linked historically to the development of the various directions stemming from JC physics. This is accompanied by a thorough list of references to the key publications. • The presentation is kept concise, while continuous text is interspersed with various illustrations and an economical use of mathematical expressions.
We review recent developments regarding the quantum dynamics and many-body physics with light, in superconducting circuits and Josephson analogues, by analogy with atomic physics. We start with quantum impurity models addressing dissipative and driven systems. Both theorists and experimentalists are making efforts towards the characterization of these non-equilibrium quantum systems. We show how Josephson junction systems can implement the equivalent of the Kondo effect with microwave photons. The Kondo effect can be characterized by a renormalized light frequency and a peak in the Rayleigh elastic transmission of a photon. We also address the physics of hybrid systems comprising mesoscopic quantum dot devices coupled with an electromagnetic resonator. Then, we discuss extensions to Quantum Electrodynamics (QED) Networks allowing one to engineer the Jaynes–Cummings lattice and Rabi lattice models through the presence of superconducting qubits in the cavities. This opens the door to novel many-body physics with light out of equilibrium, in relation with the Mott–superfluid transition observed with ultra-cold atoms in optical lattices. Then, we summarize recent theoretical predictions for realizing topological phases with light. Synthetic gauge fields and spin–orbit couplings have been successfully implemented in quantum materials and with ultra-cold atoms in optical lattices — using time-dependent Floquet perturbations periodic in time, for example — as well as in photonic lattice systems. Finally, we discuss the Josephson effect related to Bose–Hubbard models in ladder and two-dimensional geometries, producing phase coherence and Meissner currents. The Bose–Hubbard model is related to the Jaynes–Cummings lattice model in the large detuning limit between light and matter (the superconducting qubits). In the presence of synthetic gauge fields, we show that Meissner currents subsist in an insulating Mott phase.
Abstract The Jaynes‐Cummings model describes the coupling between photons and a single two‐level atom in a simplified representation of light‐matter interactions. In circuit QED, this model is implemented by combining microwave resonators and superconducting qubits on a microchip with unprecedented experimental control. Arranging qubits and resonators in the form of a lattice realizes a new kind of Hubbard model, the Jaynes‐Cummings‐Hubbard model, in which the elementary excitations are polariton quasi‐particles. Due to the genuine openness of photonic systems, circuit QED lattices offer the possibility to study the intricate interplay of collective behavior, strong correlations and non‐equilibrium physics. Thus, turning circuit QED into an architecture for quantum simulation, i.e., using a well‐controlled system to mimic the intricate quantum behavior of another system too daunting for a theorist to tackle head‐on, is an exciting idea which has served as theorists’ playground for a while and is now also starting to catch on in experiments. This review gives a summary of the most recent theoretical proposals and experimental efforts.
Abstract The quantum coherent behaviors of superconducting devices at macroscopic scales and recent technical advances in fine tunability have brought the conventional cavity quantum electrodynamics (QED) to superconducting circuits. With an ultra‐strong cavity photon–artificial atom coupling and the inherent nonlinearity of the Josephson junctions, the so‐called circuit QED offers new opportunities to explore new realms of physics that have remained a challenge for conventional cavity QED. Circuit QED has even attracted public attention as the leading architecture for quantum computation. In this article, a pedagogical review of recent studies and activities on exotic quantum states that can be attributed to ultra‐strong coupling is provided. A progress report on attempts to seek the smallest unit of the topological matter and its fundamental interaction with light is also provided.
In this PhD thesis, we will present the theoretical and experimental work that led to the realization of a radio-frequency circuit quantum electrodynamics system (RFcQED). In chapter 2, we provide a detailed derivation of the Hamiltonian of circuit QED formulated in the context of the Rabi model, and extract expressions for the cross-Kerr interaction. The resulting requirements for the coupling rate in RFcQED are discussed, one of them being the need to dramatically increase the coupling rate compared to typical circuit QED device. In chapter 3 we cover two experimental approaches to increasing the coupling in a circuit QED system, one making use of a high impedance resonator, the second utilizing a large coupling capacitor. In chapter 4, we combine these two approaches to implement RFcQED. Through strong dispersive coupling, we could measure individual photons in a megahertz resonator, demonstrate quantum control by cooling the resonator to the ground state or preparing Fock states, and finally observe with nanosecond resolution the re-thermalization of these states. In chapter 5 we present QuCAT or Quantum Circuit Analyzer Tool in Python, a software package that can be used for the design of circuit QED systems such as the one presented in this thesis. In chapter 6 we discuss how certain interplays between general relativity and quantum mechanics cannot be described using our current laws of physics. In particular, we show how radio-frequency mechanical oscillators are perfect candidates to perform experiments in this regime. In chapter 7 we present the prospects for coupling such mechanical oscillator to weakly anharmonic superconducting circuits such as the transmon qubit or RFcQED systems.