Quantum Phase-Slip Junction Under Microwave Irradiation

We consider the dynamics of a quantum phase-slip junction (QPSJ) -- a dual Josephson junction -- connected to a microwave source with frequency $\omega_\textrm{mw}$. With respect to an ordinary Josephson junction, a QPSJ can sustain dual Shapiro steps, consisting of well-defined current plateaus at multiple integers of $e \omega_\textrm{mw} / \pi$ in the current-voltage (I-V) characteristic. The experimental observation of these plateaus has been elusive up to now. We argue that thermal as well as quantum fluctuations can smear the I-V characteristic considerably. In order to understand these effects, we study a current-biased QPSJ under microwave irradiation and connected to an inductive and resistive environment. We find that the effect of these fluctuations are governed by the resistance of the environment and by the ratio of the phase-slip energy and the inductive energy. Our results are of interest for experiments aimed at the observation of dual Shapiro steps in QPSJ devices for the definition of a new quantum current standard.Comment: 12 pages, 9 figures, comments and suggestions would be greatly appreciate

Mode engineering with a one-dimensional superconducting metamaterial

We propose a way to control the Josephson energy of a single Josephson junction embedded in one- dimensional superconducting metamaterial: an inhomogeneous superconducting loop, made out of a superconducting nanowire or a chain of Josephson junctions. The Josephson energy is renormalized by the electromagnetic modes propagating along the loop. We study the behaviour of the modes as well as of their frequency spectrum when the capacitance and the inductance along the loop are spatially modulated. We show that, depending on the amplitude of the modulation, the renormalized Josephson energy is either larger or smaller than the one found for a homogeneous loop. Using typical experimental parameters for Josepshon junction chains and superconducting nanowires, we conclude that this mode-engineering can be achieved with currently available metamaterials

Theory of coherent quantum phase-slips in Josephson junction chains with periodic spatial modulations

We study coherent quantum phase-slips which lift the ground state degeneracy in a Josephson junction ring, pierced by a magnetic flux of the magnitude equal to half of a flux quantum. The quantum phase-slip amplitude is sensitive to the normal mode structure of superconducting phase oscillations in the ring (Mooij-Sch\"on modes). These, in turn, are affected by spatial inhomogeneities in the ring. We analyze the case of weak periodic modulations of the system parameters and calculate the corresponding modification of the quantum phase-slip amplitude

Detecting Photon-Photon Interactions in a Superconducting Circuit

A local interaction between photons can be engineered by coupling a nonlinear system to a transmission line. The required high impedance transmission line can be conveniently formed from a chain of Josephson junctions. The nonlinearity is generated by side-coupling this chain to a Cooper pair box. We propose to probe the resulting photon-photon interactions via their effect on the current-voltage characteristic of a voltage-biased Josephson junction connected to the transmission line. Considering the Cooper pair box to be in the weakly anharmonic regime, we find that the dc current through the probe junction yields features around the voltages $2eV=n\hbar\omega_s$, where $\omega_s$ is the plasma frequency of the superconducting circuit. The features at $n\ge 2$ are a direct signature of the photon-photon interaction in the system.Comment: 10 pages, 7 figure

Rabi-like oscillations of an anharmonic oscillator: classical versus quantum interpretation

8 pagesInternational audienceWe have observed Rabi-like oscillations in a current-biased dc SQUID presenting enhanced coherence times compared to our previous realization~\cite{Claudon_PRL04}. This Josephson device behaves as an anharmonic oscillator which can be driven into a coherent superposition of quantum states by resonant microwave flux pulses. Increasing the microwave amplitude, we study the evolution of the Rabi frequency from the 2-level regime to the regime of multilevel dynamics. When up to $3$ levels are involved, the Rabi frequency is a clear signature of quantum behavior. At higher excitation amplitude, classical and quantum predictions for the Rabi frequency converge. This result is discussed in the light of a calculation of the Wigner function. In particular, our analysis shows that pronounced quantum interferences always appear in the course of the Rabi-like oscillations

Superconducting cascade electron refrigerator

The design and operation of an electronic cooler based on a combination of superconducting tunnel junctions is described. The cascade extraction of hot-quasiparticles, which stems from the energy gaps of two different superconductors, allows for a normal metal to be cooled down to about 100 mK starting from a bath temperature of 0.5 K. We discuss the practical implementation, potential performance and limitations of such a device

Measurement scheme of the Berry phase in superconducting circuits

We present a measurement scheme for observing the Berry phase in a flux assisted Cooper pair pump - the Cooper pair sluice. In contrast to the recent experiments, in which the sluice was employed to generate accurate current through a resistance, we consider a device in a superconducting loop. This arrangement introduces a connection between the pumped current and the Berry phase accumulated during the adiabatic pumping cycles. From the adiabaticity criterion, we derive equations for the maximum pumped current and optimize the sluice accordingly. These results apply also to the high accuracy pumping which results in a potential candidate for a metrological current standard. For measuring the pumped current, an additional Josephson junction is installed into the superconducting loop. We show in detail that the switching of this system from superconducting state into normal state as a consequence of an external current pulse through it may be employed to probe the pumped current. The experimental realization of our scheme would be the first observation of the Berry phase in superconducting circuits.Comment: 19 pages, 5 figure

Electronic coolers based on superconducting tunnel junctions: fundamentals and applications

International audienceThermo-electric transport at the nano-scale is a rapidly developing topic, in particular in superconductor-based hybrid devices. In this review paper, we first discuss the fundamental principles of electronic cooling in mesoscopic superconducting hybrid structures, the related limitations and applications. We review recent work performed in Grenoble on the effects of Andreev reflection, photonic heat transport, phonon cooling, as well as on an innovative fabrication technique for powerful coolers