Linear response theory of Josephson junction arrays in a microwave cavity

Recent experiments on Josephson junction arrays (JJAs) in microwave cavities have opened up a new avenue for investigating the properties of these devices while minimising 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.Comment: 15 pages, 10 figure

Correlated transport through junction arrays in the small Josephson energy limit: incoherent Cooper-pairs and hot electrons

We study correlated transport in a Josephson junction array for small Josephson energies. In this regime transport is dominated by Cooper-pair hopping, although we observe that quasiparticles can not be neglected. We assume that the energy dissipated by a Cooper-pair is absorbed by the intrinsic impedance of the array. This allows us to formulate explicit Cooper-pair hopping rates without adding any parameters to the system. We show that the current is correlated and crucially, these correlations rely fundamentally on the interplay between the Cooper-pairs and equilibrium quasiparticles.Comment: 11 pages, 9 figures - Published Versio

Depinning of disordered bosonic chains

We consider one-dimensional bosonic chains with a repulsive boson-boson interaction that decays exponentially on large length-scales. This model describes transport of Cooper-pairs in a Josepshon junction array, or transport of magnetic flux quanta in quantum-phase-slip ladders, i.e. arrays of superconducting wires in a ladder-configuration that allow for the coherent tunnelling of flux quanta. In the low-frequency, long wave-length regime these chains can be mapped to an effective model of a one-dimensional elastic field in a disordered potential. The onset of transport in these systems, when biased by external voltage, is described by the standard depinning theory of elastic media in disordered pinning potentials. We numerically study the regimes that are of relevance for quantum-phase-slip ladders. These are (i) very short chains and (ii) the regime of weak disorder. For chains shorter than the typical pinning length, i.e., the Larkin length, the chains reach a saturation regime where the depinning voltage does not depend on the decay length of the repulsive interaction. In the regime of weak disorder we find an emergent correlation length-scale that depends on the disorder strength. For arrays shorter than this length the onset of transport is similar to the clean arrays, i.e., is due to the penetration of solitons into the array. We discuss the depinning scenarios for longer arrays in this regime.Comment: 11 pages, 6 figure

Towards understanding two-level-systems in amorphous solids -- Insights from quantum circuits

Amorphous solids show surprisingly universal behaviour at low temperatures. The prevailing wisdom is that this can be explained by the existence of two-state defects within the material. The so-called standard tunneling model has become the established framework to explain these results, yet it still leaves the central question essentially unanswered -- what are these two-level defects? This question has recently taken on a new urgency with the rise of superconducting circuits in quantum computing, circuit quantum electrodynamics, magnetometry, electrometry and metrology. Superconducting circuits made from aluminium or niobium are fundamentally limited by losses due to two-level defects within the amorphous oxide layers encasing them. On the other hand, these circuits also provide a novel and effective method for studying the very defects which limit their operation. We can now go beyond ensemble measurements and probe individual defects -- observing the quantum nature of their dynamics and studying their formation, their behaviour as a function of applied field, strain, temperature and other properties. This article reviews the plethora of recent experimental results in this area and discusses the various theoretical models which have been used to describe the observations. In doing so, it summarises the current approaches to solving this fundamentally important problem in solid-state physics.Comment: 34 pages, 7 figures, 1 tabl

Influence of two-level fluctuators on adiabatic passage techniques

We study the process of Stimulated Raman Adiabatic Passage (STIRAP) under the influence of a non-trivial solid-state environment, particularly the effect of two-level fluctuators (TLFs) as they are frequently present in solid-state devices. When the amplitudes of the driving-pulses used in STIRAP are in resonance with the level spacing of the fluctuators the quality of the protocol, i.e., the transferred population decreases sharply. In general the effect can not be reduced by speeding up the STIRAP process. We also discuss the effect of a structured noise environment on the process of Coherent Tunneling by Adiabatic Passage (CTAP). The effect of a weakly structured environment or TLFs with short coherence times on STIRAP and CTAP can be described by the Bloch-Redfield theory. For a strongly structured environment a higher-dimensional approach must be used, where the TLFs are treated as part of the system.Comment: 8 pages, 8 figure