Effects of quasiparticle tunneling in a circuit-QED realization of a strongly driven two-level system

We experimentally and theoretically study the frequency shift of a driven cavity coupled to a superconducting charge qubit. In addition to previous studies, we here also consider drive strengths large enough to energetically allow for quasiparticle creation. Quasiparticle tunneling leads to the inclusion of more than two charge states in the dynamics. To explain the observed effects, we develop a master equation for the microwave dressed charge states, including quasiparticle tunneling. A bimodal behavior of the frequency shift as a function of gate voltage can be used for sensitive charge detection. However, at weak drives the charge sensitivity is significantly reduced by non-equilibrium quasiparticles, which induce transitions to a non-sensitive state. Unexpectedly, at high enough drives, quasiparticle tunneling enables a very fast relaxation channel to the sensitive state. In this regime, the charge sensitivity is thus robust against externally injected quasiparticles and the desired dynamics prevail over a broad range of temperatures. We find very good agreement between theory and experiment over a wide range of drive strengths and temperatures.Comment: 25 pages, 7 figure

Near-Field Scanning Microwave Microscopy in the Single Photon Regime

The microwave properties of nano-scale structures are important in a wide variety of applications in quantum technology. Here we describe a low-power cryogenic near-field scanning microwave microscope (NSMM) which maintains nano-scale dielectric contrast down to the single microwave photon regime, up to $10^{9}$ times lower power than in typical NSMMs. We discuss the remaining challenges towards developing nano-scale NSMM for quantum coherent interaction with two-level systems as an enabling tool for the development of quantum technologies in the microwave regime

Coupling of a locally implanted rare-earth ion ensemble to a superconducting micro-resonator

We demonstrate the coupling of rare-earth ions locally implanted in a substrate (Gd$^{3+}$ in Al$_{2}$O$_{3}$) to a superconducting NbN lumped-element micro-resonator. The hybrid device is fabricated by a controlled ion implantation of rare-earth ions in well-defined micron-sized areas, aligned to lithographically defined micro-resonators. The technique does not degrade the internal quality factor of the resonators which remain above $10^{5}$. Using microwave absorption spectroscopy we observe electron-spin resonances in good agreement with numerical modelling and extract corresponding coupling rates of the order of $1$ MHz and spin linewidths of $50 - 65$ MHz.Comment: 4 pages, 2 Figure

Dynamic parity recovery in a strongly driven Cooper-pair box

We study a superconducting charge qubit coupled to an intensive electromagnetic field and probe changes in the resonance frequency of the formed dressed states. At large driving strengths, exceeding the qubit energy-level splitting, this reveals the well known Landau-Zener-Stuckelberg (LZS) interference structure of a longitudinally driven two-level system. For even stronger drives we observe a significant change in the LZS pattern and contrast. We attribute this to photon-assisted quasiparticle tunneling in the qubit. This results in the recovery of the qubit parity, eliminating effects of quasiparticle poisoning and leads to an enhanced interferometric response. The interference pattern becomes robust to quasiparticle poisoning and has a good potential for accurate charge sensing.Comment: 5 pages, 4 figure

Fast tunable high Q-factor superconducting microwave resonators

We present fast tunable superconducting microwave resonators fabricated from planar NbN on a sapphire substrate. The $3\lambda/4$ wavelength resonators are tuning fork shaped and tuned by passing a dc current which controls the kinetic inductance of the tuning fork prongs. The $\lambda/4$ section from the open end operates as an integrated impedance converter which creates a nearly perfect short for microwave currents at the dc terminal coupling points, thus preventing microwave energy leakage through the dc lines. We measure an internal quality factor $Q_{\rm int}>10{^{5}}$ over the entire tuning range. We demonstrate a tuning range of $> 3\%$ and tuning response times as short as 20 ns for the maximum achievable detuning. Due to the quasi-fractal design, the resonators are resilient to magnetic fields of up to 0.5 T

Tunneling through a multigrain system: deducing the sample topology from the nonlinear conductance

We study a current transport through a system of a few grains connected with tunneling links. The exact solution is given for an arbitrarily connected double-grain system with a shared gate in the framework of the orthodox model. The obtained result is generalized for multigrain systems with strongly different tunneling resistances. We analyse the large-scale nonlinear conductance and demonstrate how the sample topology can be unambiguously deduced from the spectroscopy pattern (differential conductance versus gate-bias plot). We present experimental data for a multigrain sample and reconstruct the sample topology. A simple selection rule is formulated to distinguish samples with spectral patterns free from spurious disturbance caused by recharging of some grains nearby. As an example, we demonstrate experimental data with additional peaks in the spectroscopy pattern, which can not be attributed to coupling to additional grains. The described approach can be used to judge the sample topology when it is not guaranteed by fabrication and direct imaging is not possible.Comment: 13 pages (including 8 figures

Two-level systems in superconducting quantum devices due to trapped quasiparticles

A major issue for the implementation of large scale superconducting quantum circuits is the interaction with interfacial two-level system defects (TLS) that leads to qubit relaxation and impedes qubit operation in certain frequency ranges that also drift in time. Another major challenge comes from non-equilibrium quasiparticles (QPs) that result in qubit dephasing and relaxation. In this work we show that such QPs can also serve as a source of TLS. Using spectral and temporal mapping of TLS-induced fluctuations in frequency tunable resonators, we identify a subset of the general TLS population that are highly coherent TLS with a low reconfiguration temperature $\sim$ 300 mK, and a non-uniform density of states. These properties can be understood if these TLS are formed by QPs trapped in shallow subgap states formed by spatial fluctutations of the superconducting order parameter $\Delta$. Magnetic field measurements of one such TLS reveals a link to superconductivity. Our results imply that trapped QPs can induce qubit relaxation.Comment: 7 pages, 4 figures, plus 18 pages, 13 figures supplementa

First-principles modelling of molecular single-electron transistors

We present a first-principles method for calculating the charging energy of a molecular single-electron transistor operating in the Coulomb blockade regime. The properties of the molecule are modeled using density-functional theory, the environment is described by a continuum model, and the interaction between the molecule and the environment are included through the Poisson equation. The model is used to calculate the charge stability diagrams of a benzene and C$_{60}$ molecular single-electron transistor