We present proposals to simulate many-body physics with superconducting circuits. The "body’’ to work with for superconducting circuits is the microwave photon and interaction is induced by the nonlinearity of the Josephson effect. We present two different approaches to simulate Bose-Hubbard physics, one based on a polariton scheme and another with nonlinear resonators. We also present a Dicke-model like simulator for ultrastrongly coupled Josephson junctions to a resonator and show a scheme for implementing long range interactions.
We present proposals to simulate many-body physics with superconducting circuits. The "body’’ to work with for superconducting circuits is the microwave photon and interaction is induced by the nonlinearity of the Josephson effect. We present two different approaches to simulate Bose-Hubbard physics, one based on a polariton scheme and another with nonlinear resonators. We also present a Dicke-model like simulator for ultrastrongly coupled Josephson junctions to a resonator and show a scheme for implementing long range interactions.
Superconducting quantum circuits are a promising approach for realizations of large scale quantum information processing and quantum simulations. The Josephson junction, which forms the basis of superconducting circuits, is the only known nonlinear non-dissipative circuit element, and its inherent nonlinearities have found many different applications. In this thesis I discuss specific implementations of these circuits. I show that strong two-photon nonlinearities can be induced by coupling photons in the microwave domain to Josephson nonlinearities. I then propose a method to simulate a parent Hamiltonian that can potentially be used to observe fractional quantum Hall states of light. I will also explore how superconducting circuits can be used to modify system-bath couplings to emulate a chemical potential for photons. Finally, I consider the limitations of devising a scheme to couple superconducting circuits to trapped ions, and consider the challenges for such hybrid approaches.
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.
In its infancy circuit quantum electrodynamics (cQED) has quickly started reproducing fundamental quantum optical experiments, e.g. observation of vacuum rabi oscillations in frequency and time domain, with unprecedented cooperativity. This was possible because of the large coupling of the quasi one-dimensional microwave field of the superconducting transmission line resonators to the macroscopic dipole moment of superconducting qubits. cQED has matured to a discipline of experimental physics capable of performing fundamental quantum information tasks and is currently on the verge of crossing the border between few- to many body physics [1]. This opens up a exciting realm of completely new physical phenomena. Because of the ubiquitous influence of the electromagnetic environment however the number of microwave photons is not conserved which separates cQED systems from other quantum simulators involving atoms, e.g. cold atoms in optical latices. Instead cQED is ideally suited for exploring quantum many-body physics in the driven dissipative regime where the interplay of constantly injecting microwave photons and the unpreventable loss of microwave photons into the electromagnetic environment generates a whole new class of steady- but not equilibrium states. We propose an array of capacitively coupled superconducting resonators each coupled to an superconducting charge qubit and show that this device can be considered as an simulator for Bose Hubbard physics combined with the high flexibility of network topologies unique to cQED systems[2]. We further investigate the driven dissipative dynamics of this device. We refine this approach and calculate the eigenmodes and nonlinearities of a Josephson junction intersected transmission line resonator[3](c.f. fig.1a). This spectrum of eigenmodes shows the ultrastrong coupling of the Josephson junction to the resonator modes and nonlinearities are attainable that are significant on the single photon limit. We now proceed one step further and and consider the incorporation of multiple Josephson junctions. A novel transfer matrix technique has to be employed to investigate the eigenmode spectrum of the device.
Recent advances in fabricating superconducting circuits have allowed large numbers of microwave resonators and superconducting qubits to be employed in such circuits, but shared quantum entanglement among the photonics states of the resonators has not been attempted. Theorists now present a proposal that uses superconducting circuits to simulate a particular many-body quantum model that until now has been experimentally inaccessible and to create a type of shared quantum entanglement with the simulation.
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.
In the last decade, the field of Quantum Optics has been enriched with a completely new platform: superconducting quantum circuits, also known as circuit-QED. This platform builds on the original designs of superconducting qubits, that is few-level systems made of superconducting islands and Josephson junctions, but adds to it a new ingredient, microwave photons. In this talk I will review circuit-QED with a focus on two complementary lines of research: ultrastrong light-matter coupling and strongly correlated propagating photons. The first topic deals with novel designs of superconducting qubits, engineering their coupling to the microwave radiation field to reach Rabi frequencies that approach the qubit and photon frequencies. In this regime, known as ”ultrastrong coupling”, the rotating wave approximation from Quantum Optics is no longer valid, the vacuum may spontaneously polarize, producing photons that get bound to the qubit, and novel physics is expected to emerge. I will review recent experiments on this topic, together with various theoretical proposals to tame this ultrastrong coupling. The second topic revolves around the notion of ”propagating” photons in these circuits. Most experiments in circuit-QED so far adopted the typical configuration of artificial atoms (qubits) interacting with artificial cavities (LC resonators). This proved useful in order to reach the strong coupling regime, demonstrating Rabi oscillations and developing a variety of protocols for quantum information, tomograhy, entanglement, etc. However, recent experiments have shown that it is possible to also work with propagating photons, replacing the LC resonators with open transmission lines, and studying the scattering properties of those artificial atoms. In this context we have worked on developing new technology to detect and control these photons, engineering single-photon detectors, quantum metamaterials and photonic crystals, or even new nonlinear media based on coupled cavities.