Dynamical Coulomb Blockade of Shot Noise

We observe the suppression of the finite frequency shot-noise produced by a voltage biased tunnel junction due to its interaction with a single electromagnetic mode of high impedance. The tunnel junction is embedded in a quarter wavelength resonator containing a dense SQUID array providing it with a characteristic impedance in the kOhms range and a resonant frequency tunable in the 4-6 GHz range. Such high impedance gives rise to a sizeable Coulomb blockade on the tunnel junction (roughly 30% reduction in the differential conductance) and allows an efficient measurement of the spectral density of the current fluctuations at the resonator frequency. The observed blockade of shot-noise is found in agreement with an extension of the dynamical Coulomb blockade theory

Multiplexed Readout of Transmon Qubits with Josephson Bifurcation Amplifiers

Achieving individual qubit readout is a major challenge in the development of scalable superconducting quantum processors. We have implemented the multiplexed readout of a four transmon qubit circuit using non-linear resonators operated as Josephson bifurcation amplifiers. We demonstrate the simultaneous measurement of Rabi oscillations of the four transmons. We find that multiplexed Josephson bifurcation is a high-fidelity readout method, the scalability of which is not limited by the need of a large bandwidth nearly quantum-limited amplifier as is the case with linear readout resonators.Comment: 7 pages, 6 figures, and 31 reference

High-gain weakly nonlinear flux-modulated Josephson parametric amplifier using a SQUID-array

We have developed and measured a high-gain quantum-limited microwave parametric amplifier based on a superconducting lumped LC resonator with the inductor L including an array of 8 superconducting quantum interference devices (SQUIDs). This amplifier is parametrically pumped by modulating the flux threading the SQUIDs at twice the resonator frequency. Around 5 GHz, a maximum gain of 31 dB, a product amplitude-gain x bandwidth above 60 MHz, and a 1 dB compression point of -123 dBm at 20 dB gain are obtained in the non-degenerate mode of operation. Phase sensitive amplification-deamplification is also measured in the degenerate mode and yields a maximum gain of 37 dB. The compression point obtained is 18 dB above what would be obtained with a single SQUID of the same inductance, due to the smaller nonlinearity of the SQUID array.Comment: 7 pages, 4 figures, 23 reference

Fluctuation-Dissipation Relations of a Tunnel Junction Driven by a Quantum Circuit

We derive fluctuation-dissipation relations for a tunnel junction driven by a high impedance microwave resonator, displaying strong quantum fluctuations. We find that the fluctuation-dissipation relations derived for classical forces hold, provided the effect of the circuit's quantum fluctuations is incorporated into a modified non-linear $I(V)$ curve. We also demonstrate that all quantities measured under a coherent time dependent bias can be reconstructed from their dc counterpart with a photo-assisted tunneling relation. We confirm these predictions by implementing the circuit and measuring the dc current through the junction, its high frequency admittance and its current noise at the frequency of the resonator.Comment: Publisehd as Physical Review Letters, 114, 12680

Storage and Retrieval of a Microwave Field in a Spin Ensemble

We report the storage and retrieval of a small microwave field from a superconducting resonator into collective excitations of a spin ensemble. The spins are nitrogen-vacancy centers in a diamond crystal. The storage time of the order of 30 ns is limited by inhomogeneous broadening of the spin ensemble.Comment: 4 pages + supplementary material. Submitted to PR

Dephasing of qubits by transverse low-frequency noise

We analyze the dissipative dynamics of a two-level quantum system subject to low-frequency, e.g. 1/f noise, motivated by recent experiments with superconducting quantum circuits. We show that the effect of transverse linear coupling of the system to low-frequency noise is equivalent to that of quadratic longitudinal coupling. We further find the decay law of quantum coherent oscillations under the influence of both low- and high-frequency fluctuations, in particular, for the case of comparable rates of relaxation and pure dephasing

Circuit QED with a Nonlinear Resonator : ac-Stark Shift and Dephasing

We have performed spectroscopic measurements of a superconducting qubit dispersively coupled to a nonlinear resonator driven by a pump microwave field. Measurements of the qubit frequency shift provide a sensitive probe of the intracavity field, yielding a precise characterization of the resonator nonlinearity. The qubit linewidth has a complex dependence on the pump frequency and amplitude, which is correlated with the gain of the nonlinear resonator operated as a small-signal amplifier. The corresponding dephasing rate is found to be close to the quantum limit in the low-gain limit of the amplifier.Comment: Paper : 4 pages, 3 figures; Supplementary material : 1 page, 1 figur

Quasiparticle decay rate of Josephson charge qubit oscillations

We analyze the decay of Rabi oscillations in a charge qubit consisting of a Cooper pair box connected to a finite-size superconductor by a Josephson junction. We concentrate on the contribution of quasiparticles in the superconductors to the decay rate. Passing of a quasiparticle through the Josephson junction tunes the qubit away from the charge degeneracy, thus spoiling the Rabi oscillations. We find the temperature dependence of the quasiparticle contribution to the decay rate for open and isolated systems. The former case is realized if a normal-state trap is included in the circuit, or if just one vortex resides in the qubit; the decay rate has an activational temperature dependence with the activation energy equal to the superconducting gap $\Delta$. In a superconducting qubit isolated from the environment, the activation energy equals $2\Delta$ if the number of electrons is even, while for an odd number of electrons the decay rate of an excited qubit state remains finite in the limit of zero temperature. We estimate the decay rate for realistic parameters of a qubit.Comment: 8 pages, 3 figures, final version as published in PRB, minor change