Shot noise of a quantum dot measured with GHz stub impedance matching

The demand for a fast high-frequency read-out of high impedance devices, such as quantum dots, necessitates impedance matching. Here we use a resonant impedance matching circuit (a stub tuner) realized by on-chip superconducting transmission lines to measure the electronic shot noise of a carbon nanotube quantum dot at a frequency close to 3 GHz in an efficient way. As compared to wide-band detection without impedance matching, the signal to noise ratio can be enhanced by as much as a factor of 800 for a device with an impedance of 100 k$\Omega$. The advantage of the stub resonator concept is the ease with which the response of the circuit can be predicted, designed and fabricated. We further demonstrate that all relevant matching circuit parameters can reliably be deduced from power reflectance measurements and then used to predict the power transmission function from the device through the circuit. The shot noise of the carbon nanotube quantum dot in the Coulomb blockade regime shows an oscillating suppression below the Schottky value of $2eI$, as well an enhancement in specific regions.Comment: 6 pages, 4 figures, supplementar

Josephson junction qubit network with current-controlled interaction

We design and evaluate a scalable charge qubit chain network with controllable current-current coupling of neighbouring qubit loops via local dc-current gates. The network allows construction of general N-qubit gates. The proposed design is in line with current main stream experiments.Comment: 4 pages, 4 figure

Reversing quantum trajectories with analog feedback

We demonstrate the active suppression of transmon qubit dephasing induced by dispersive measurement, using parametric amplification and analog feedback. By real-time processing of the homodyne record, the feedback controller reverts the stochastic quantum phase kick imparted by the measurement on the qubit. The feedback operation matches a model of quantum trajectories with measurement efficiency $\tilde{\eta} \approx 0.5$, consistent with the result obtained by postselection. We overcome the bandwidth limitations of the amplification chain by numerically optimizing the signal processing in the feedback loop and provide a theoretical model explaining the optimization result.Comment: 5 pages, 4 figures, and Supplementary Information (7 figures

Electrolyte gate dependent high-frequency measurement of graphene field-effect transistor for sensing applications

We performed radiofrequency (RF) reflectometry measurements at 2.4 GHz on electrolyte-gated graphene field-effect transistors (GFETs) utilizing a tunable stub-matching circuit for impedance matching. We demonstrate that the gate voltage dependent RF resistivity of graphene can be deduced even in the presence of the electrolyte which is in direct contact with the graphene layer. The RF resistivity is found to be consistent with its DC counterpart in the full gate voltage range. Furthermore, in order to access the potential of high-frequency sensing for applications, we demonstrate time-dependent gating in solution with nanosecond time resolution.Comment: 14 pages, 4 figure

Optimization of sample-chip design for stub-matched radio-frequency reflectometry measurements

A radio-frequency (rf) matching circuit with an in situ tunable varactor diode used for rf reflectometry measurements in semiconductor nanostructures is investigated and used to optimize the sample-specific chip design. The samples are integrated in a 2-4 GHz stub-matching circuit consisting of a waveguide stub shunted to the terminated coplanar waveguide. Several quantum point contacts fabricated on a GaAs/AlGaAs heterostructure with different chip designs are compared. We show that the change of the reflection coefficient for a fixed change in the quantum point contact conductance can be enhanced by a factor of 3 compared to conventional designs by a suitable electrode geometry

Resolving photon number states in a superconducting circuit

Electromagnetic signals are always composed of photons, though in the circuit domain those signals are carried as voltages and currents on wires, and the discreteness of the photon's energy is usually not evident. However, by coupling a superconducting qubit to signals on a microwave transmission line, it is possible to construct an integrated circuit where the presence or absence of even a single photon can have a dramatic effect. This system is called circuit quantum electrodynamics (QED) because it is the circuit equivalent of the atom-photon interaction in cavity QED. Previously, circuit QED devices were shown to reach the resonant strong coupling regime, where a single qubit can absorb and re-emit a single photon many times. Here, we report a circuit QED experiment which achieves the strong dispersive limit, a new regime of cavity QED in which a single photon has a large effect on the qubit or atom without ever being absorbed. The hallmark of this strong dispersive regime is that the qubit transition can be resolved into a separate spectral line for each photon number state of the microwave field. The strength of each line is a measure of the probability to find the corresponding photon number in the cavity. This effect has been used to distinguish between coherent and thermal fields and could be used to create a photon statistics analyzer. Since no photons are absorbed by this process, one should be able to generate non-classical states of light by measurement and perform qubit-photon conditional logic, the basis of a logic bus for a quantum computer.Comment: 6 pages, 4 figures, hi-res version at http://www.eng.yale.edu/rslab/papers/numbersplitting_hires.pd

Characterizing Quantum Microwave Radiation and its Entanglement with Superconducting Qubits using Linear Detectors

Recent progress in the development of superconducting circuits has enabled the realization of interesting sources of nonclassical radiation at microwave frequencies. Here, we discuss field quadrature detection schemes for the experimental characterization of itinerant microwave photon fields and their entanglement correlations with stationary qubits. In particular, we present joint state tomography methods of a radiation field mode and a two-level system. Including the case of finite quantum detection efficiency, we relate measured photon field statistics to generalized quasi-probability distributions and statistical moments for one-channel and two-channel detection. We also present maximum-likelihood methods to reconstruct density matrices from measured field quadrature histograms. Our theoretical investigations are supported by the presentation of experimental data, for which microwave quantum fields beyond the single-photon and Gaussian level have been prepared and reconstructed.Comment: 14 pages, 5 figure

AC induced damping of a fluxon in long Josephson junction

We present a theoretical and experimental study of Josephson vortex (fluxon) moving in the presence of spatially homogeneous dc and ac bias currents. By mapping this problem to the problem of calculating the current-voltage characteristic of a small Josephson junction, we derive the dependence of the average fluxon velocity on the dc bias current. In particular we find that the low frequency ac bias current results in an additional nonlinear damping of fluxon motion. Such ac induced damping crucially depends on the intrinsic damping parameter and increases drastically as this parameter is reduced. We find a good agreement of the analysis with both the direct numerical simulations and the experimentally measured current-voltage characteristics of a long annular Josephson junction with one trapped fluxon.Comment: Physical Review B, in pres