Superconducting Josephson junction arrays (JJAs) are prototypical systems consisting of an array of superconducting islands connected by small Josephson junctions which provide an explicit realization of the canonical XY model of condensed matter physics.In this study we show how circuit quantumelectrodynamics (QED) techniques, perfected for implementing high-quality quantum bits, enable the exploration of new high-frequency regimes of JJAs.By making use of extremely low excitation power and heating of the array, we can probe physics of these systems using one single photon on average.
Superconducting Josephson junction arrays (JJAs) are prototypical systems consisting of an array of superconducting islands connected by small Josephson junctions which provide an explicit realization of the canonical XY model of condensed matter physics.In this study we show how circuit quantumelectrodynamics (QED) techniques, perfected for implementing high-quality quantum bits, enable the exploration of new high-frequency regimes of JJAs.By making use of extremely low excitation power and heating of the array, we can probe physics of these systems using one single photon on average.
Superconductivity provides a canonical example of a quantum phase of matter. When superconducting islands are connected by Josephson junctions in a lattice, the low-temperature state of the system can map to the celebrated XY model and its associated universality classes. This has been used to experimentally implement realizations of Mott insulator and Berezinskii-Kosterlitz-Thouless transitions to vortex dynamics analogous to those in type-II superconductors. When an external magnetic field is added, the effective spins of the XY model become frustrated, leading to the formation of topological defects (vortices). Here, we observe the many-body dynamics of such an array, including frustration, via its coupling to a superconducting microwave cavity. We take the design of the transmon qubit, but replace the single junction between two antenna pads with the complete array. This allows us to probe the system at 10 mK with minimal self-heating by using weak coherent states at the single (microwave) photon level to probe the resonance frequency of the cavity. We observe signatures of an ordered vortex lattice at rational flux fillings of the array.
Josephson junction arrays (JJAs) are engineered many-body quantum systems consisting of several superconducting islands connected by thin tunnel barriers - Josephson junctions (JJs). They are of interest both from a fundamental point of view (e.g. addressing questions of macroscopic quantum physics, providing model systems in which to study complex many-body phenomena) and from the prospect of technological applications (e.g. quantum computing, metrology, metamaterials). In this thesis we present various tools and techniques for the theoretical study of JJAs, and then put these tools to use in the modelling of two particular experiments on JJAs. In our presentation of the physics of JJAs, we emphasise phenomena unique to arrays (i.e. not seen in single junction devices such as qubits). We investigate charge transport through the the bilinear array, consisting of two linear chains of JJs, and show that it exhibits both Coulomb drag and depinning. We predict new phenomena arising from the interplay between Coulomb drag and depinning at voltages higher than have so far been experimentally reported. We then turn our attention to recent experiments in which planar JJAs were placed in 3-D microwave cavities, with vortices being injected via an externally applied magnetic eld. We calculate the impedance spectrum using linear response theory, which enables us to see when new vortices enter the system in the form of sharp changes in the resonance frequency.
In this review of our own work, we show the physics and applications of Josephson Junction (JJ) and 2D arrays (JJA) made with this powerful quantum engine.This study is based on more than twenty articles published in more than two decades.In actual days, applications of this device go from the most sensitive sensor to measure magnetic flux, called S.QU.I.D. (from Superconducting Quantum Interference Device) to quantum bits.A unit cell of a JJ, with a cost of about a few hundred dollars allows the availability of a magnetometer with a cost of about one million dollars to a quantum computer with cost of about ten million dollars.The Josephson junction is an old quantum engine for a rising new world with incredible disruptive technological possibilities.The article is organized as follows: in section 1 we give a short introduction to the subject; section 2 describes the physics of the Josephson effect and the engineering of the Josephson junction; in section 3 we show the magnetic, transport and thermal properties of 2D-JJA; and in section 4 we show the relation between JJA and superconducting granular systems, in particular those related to High-Temperature Superconductors (HTS).
A superconducting circuit is one of the prominent candidates for the realization of quantum computation, which is the grand challenge in 21st-century science.The superconducting circuit has several advantages in a high degree of freedom for designing, and its elementary ingredients, such as superconducting qubits, transmission lines, and hybrid structures called the circuit quantum electrodynamics (QED), have been utilized for the application of quantum computers.The superconducting circuit also provides an ideal and useful platform for the study of fundamental physics.In particular, coupling to environments and disorder, which are usually obstacles for the realization of quantum computers, provides fascinating problems on many-body effects, quantum phase transition, localization, and heat transport.In this thesis, we investigate three problems in superconducting circuits.First, we consider a quantum phase transition in the sub-Ohmic spin-boson system, which is realized by a charge qubit coupled to a transmission line, and study quantum critical phenomena in the frequency dependence of microwave scattering off this circuit.By performing the quantum Monte Carlo simulation, we find signatures of the quantum critical behavior as well as the Fermi-liquid-like feature indicated by the generalized Shiba-Korringa relation.We also describe how to construct the sub-Ohmic spin-boson system using superconducting circuits.Second, we study the transmission properties through a Josephson-junction chain.This system is not only useful for application as a superinductor but also suitable to study many-body effects induced by Coulomb interaction and disorder.When the disorder is added to this system, the interplay of Coulomb interaction and disorder makes the Josephson-junction chain undergo a transition into an intriguing glassy insulator: Bose glass.We focus on the deep insulating regime and show that the collective pinning affects the dynamical properties of the Josephson-junction chain in the whole frequency region.Finally, we study heat transport through an assembly consisting of a superconducting qubit sandwiched between superconducting harmonic resonators, which is described by the quantum Rabi model, a typical multi-level system.Using the non-perturbative approximation, we find a two-peak structure of the linear thermal conductance as a function temperature.This characteristic transport behavior comes from the fact that there are multiple levels in the assembly and is expected to be advantageous for the application of quantum heat devices.These studies will provide a concrete foundation for further research on the physics of superconducting circuits.We also expect that the results obtained in this thesis will be observed in the near future.
The continuous improvement of fabrication techniques and high-quality semiconductor-superconductor interfaces allows for an unprecedented tunability of Josephson junction arrays (JJA), making them a promising candidate for analog quantum simulations of many-body phenomena. While most experimental proposals so far focused on quantum simulations of ensembles of two-level systems, the possibility of tuning the current-phase relation beyond the sinusoidal regime paves the way for studying statistical physics models with larger local Hilbert spaces. Here, we investigate a particular JJA architecture that can be mapped into a Z3 clock model. Through matrix-product-states simulations and bosonization analysis, we show that few experimentally accessible control parameters allow for the exploration of the rich phase diagrams of the associated low-energy field theories. Our results expand the horizon for analog quantum simulations with JJAs towards models that can not be efficiently captured with qubit architectures.
Recent experiments on Josephson junction arrays (JJAs) in microwave cavities have opened up a new avenue for investigating the properties of these devices while minimizing the amount of external noise coming from the measurement apparatus itself. These experiments have already shown promise for probing many-body quantum effects in JJAs. In this work, we develop a general theoretical description of such experiments by deriving a quantum phase model for planar JJAs containing quantized vortices. The dynamical susceptibility of this model is calculated for some simple circuits, and signatures of the injection of additional vortices are identified. The effects of decoherence are considered via a Lindblad master equation.