No Arabic abstract
We perform a quantum mechanical analysis of superconducting resonators subject to dielectric loss arising from charged two-level systems. We present numerical and analytical descriptions of the dynamics of energy decay from the resonator within the Jaynes-Cummings model. Our analysis allows us to distinguish the strong and weak coupling regimes of the model and to describe within each regime cases where the two-level system is unsaturated or saturated. We find that the quantum theory agrees with the classical model for weak coupling. However, for strong coupling the quantum theory predicts lower loss than the classical theory in the unsaturated regime. Also, in contrast to the classical theory, the photon number at which saturation occurs in the strong coupling quantum theory is independent of the coupling between the resonator and the two-level system.
The investigation of two-level-state (TLS) loss in dielectric materials and interfaces remains at the forefront of materials research in superconducting quantum circuits. We demonstrate a method of TLS loss extraction of a thin film dielectric by measuring a lumped element resonator fabricated from a superconductor-dielectric-superconductor trilayer. We extract the dielectric loss by formulating a circuit model for a lumped element resonator with TLS loss and then fitting to this model using measurements from a set of three resonator designs: a coplanar waveguide resonator, a lumped element resonator with an interdigitated capacitor, and a lumped element resonator with a parallel plate capacitor that includes the dielectric thin film of interest. Unlike other methods, this allows accurate measurement of materials with TLS loss lower than $10^{-6}$. We demonstrate this method by extracting a TLS loss of $1.02 times 10^{-3}$ for sputtered $mathrm{Al_2O_3}$ using a set of samples fabricated from an $mathrm{Al/Al_2O_3/Al}$ trilayer. We observe a difference of 11$%$ between extracted loss of the trilayer with and without the implementation of this method.
We perform an experimental and numerical study of dielectric loss in superconducting microwave resonators at low temperature. Dielectric loss, due to two-level systems, is a limiting factor in several applications, e.g. superconducting qubits, Josephson parametric amplifiers, microwave kinetic-inductance detectors, and superconducting single-photon detectors. Our devices are made of disordered NbN, which, due to magnetic-field penetration, necessitates 3D finite-element simulation of the Maxwell--London equations at microwave frequencies to accurately model the current density and electric field distribution. From the field distribution, we compute the geometric filling factors of the lossy regions in our resonator structures and fit the experimental data to determine the intrinsic loss tangents of its interfaces and dielectrics. We emphasise that the loss caused by a spin-on-glass resist such as hydrogen silsesquioxane (HSQ), used for ultrahigh lithographic resolution relevant to the fabrication of nanowires, and find that, when used, HSQ is the dominant source of loss, with a loss tangent of $delta^i_{HSQ} = 8 times 10^{-3}$.
Lossy dielectrics are a significant source of decoherence in superconducting quantum circuits. In this report, we model and compare the dielectric loss in bulk and interfacial dielectrics in titanium nitride (TiN) and aluminum (Al) superconducting coplanar waveguide (CPW) resonators. We fabricate isotropically trenched resonators to produce a series of device geometries that accentuate a specific dielectric regions contribution to resonator quality factor. While each dielectric region contributes significantly to loss in TiN devices, the metal-air interface dominates the loss in the Al devices. Furthermore, we evaluate the quality factor of each TiN resonator geometry with and without a post-process hydrofluoric (HF) etch, and find that it reduced losses from the substrate-air interface, thereby improving the quality factor.
We investigate entanglement dynamics of two isolated atoms, each in its own Jaynes-Cummings cavity. We show analytically that initial entanglement has an interesting subsequent time evolution, including the so-called sudden death effect.
We present a propagator formalism to investigate the scattering of photons by a cavity QED system that consists of a single two-level atom dressed by a leaky optical cavity field. We establish a diagrammatic method to construct the propagator analytically. This allows us to determine the quantum state of the scattered photons for an arbitrary incident photon packet. As an application, we explicitly solve the problem of a single-photon packet scattered by an initially excited atom.