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Physical Review Letters

Effect of a Transmission Line Resonator on a Small Capacitance Tunnel Junction

Thorsten Holst, D. Esteve, C. Urbina, Michel Devoret

Published Dec 19, 1994• 113 citations
Publisher

Abstract

We have measured the current-voltage characteristic of a small capacitance tunnel junction coupled to a transmission line resonator. We calibrate the resonator using the sharp resonances displayed by the junction in the superconducting state, which corresponds to the pumping of the modes of the resonator by the ac Josephson current. With this calibration, we explain quantitatively the nonlinearity of the junction characteristic in the normal state as being due to the process by which a single electron tunnels by emitting a photon, the basic process of the theory of the effect of the electromagnetic environment on tunneling.

DOI
10.1103/physrevlett.73.3455

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Physical review. B, Condensed matter•Feb 1, 1994•29 citations
We have measured the current-voltage characteristic of a small capacitance tunnel junction coupled to a transmission line resonator. We calibrate the resonator using the sharp resonances displayed by the junction in the superconducting state, which corresponds to the pumping of the modes of the resonator by the ac Josephson current. With this calibration, we explain quantitatively the nonlinearity of the junction characteristic in the normal state as being due to the process by which a single electron tunnels by emitting a photon, the basic process of the theory of the effect of the electromagnetic environment on tunneling.
An equally spaced series of very large and nearly constant-voltage self-induced singularities has been observed in the dc I-V characteristics of a small Josephson tunnel junction strongly coupled to a resonant section of a superconducting transmission line. The system allows extremely high values of the coupling parameter. The current steps are due to subharmonic parametric excitation of the fundamental mode of the resonator loaded by the junction admittance. Using an applied magnetic field to vary the coupling parameter, we traced out half-integer steps as well as the mode steps known from more weakly coupled systems. Based on a single-resonator model, we explain the exceptional size of the steps by the large content of higher harmonics of the Josephson oscillation sustained by the multiple modes of the resonator. The parameters of the junction and the loaded resonator---measured in situ by using the junction as detector---form a consistent set. The dominant system loss originates in the junction but cannot be ascribed to a relevant conductance.
We have measured the current-voltage $(I\ensuremath{-}V)$ characteristics of small-capacitance single Josephson junctions at low temperatures (T=0.02−−0.6K),(T=0.02--0.6\mathrm{K}),(T=0.02−−0.6K), where the strength of the coupling between the single junction and the electromagnetic environment was controlled with one-dimensional arrays of dc superconducting quantum interence devices (SQUIDs). The single-junction $I\ensuremath{-}V$ curve is sensitive to the impedance of the environment, which can be tuned in situ. We have observed Coulomb blockade of Cooper-pair tunneling and even a region of negative differential resistance, where the zero-bias resistance ${R}_{0}^{\ensuremath{'}}$ of the SQUID arrays is much higher than the quantum resistance ${R}_{K}\ensuremath{\equiv}{h/e}^{2}\ensuremath{\approx}26\mathrm{k}\ensuremath{\Omega}.$ The negative differential resistance is evidence of the coherent single-Cooper-pair tunneling within the theory of current-biased single Josephson junctions. Based on this theory, we have calculated the $I\ensuremath{-}V$ curves numerically in order to compare then with the experimental ones at ${R}_{0}^{\ensuremath{'}}\ensuremath{\gg}{R}_{K}.$ The numerical calculation agrees with the experiments qualitatively. We also discuss the ${R}_{0}^{\ensuremath{'}}$ dependence of the single-Josephson-junction $I\ensuremath{-}V$ curve in terms of the superconductor-insulator transition driven by changing the coupling to the environment.
Unexpected partly dramatic temperature dependences were registered for the basic tunnel parameters used to characterize a Josephson junction. Measurements of the magnetic field variation of the microwave-power reflection, i.e., a mapping of the Josephson plasma resonance, enabled determinations of the rf small-voltage resistance RJ, the cosφ amplitude ζ, and the effective junction capacitance C in both Pb-O-Pb and PbTl-O-Pb junctions. The uncertainties in the parameter values are large, particularly in the low temperature values of ζ, for which we confirm earlier estimates of ζ, but as the superconducting transition temperature Tc is approached, ζ increases rapidly and goes through a positive maximum close to +1 before it decreases towards zero at Tc. Also, RJ displays a pronounced maximum in the same temperature interval; it decreases rapidly within a narrow range below the temperature of the maximum before it again increases slowly well below Tc. The location in temperature for the two maxima depends upon the barrier via the critical current density, but seems to be material independent. Well below Tc, the ratios of RJ to the normal-state tunnel resistance are also affected by the barrier transmission. These latter properties seem hard to explain within a model based only on the relaxation of the order parameters in the superconductors. A considerable decrease in C close to Tc can be explained by temperature-dependent surface losses in the junction electrodes. The Q-value associated with these could be determined as a function of temperature. In accordance with previous measurements, the Josephson current IJ is reduced at low temperature in small high-resistance tunnel junctions. Smaller deviations in IJ from theoretical estimates can be explained by strong coupling effects.
We observe a sharp threshold for dynamic phase locking in a high-Q transmission line resonator embedded with a Josephson tunnel junction, and driven with a purely ac, chirped microwave signal. When the drive amplitude is below a critical value, which depends on the chirp rate and is sensitive to the junction critical current I0, the resonator is only excited near its linear resonance frequency. For a larger amplitude, the resonator phase locks to the chirped drive and its amplitude grows until a deterministic maximum is reached. Near threshold, the oscillator evolves smoothly in one of two diverging trajectories, providing a way to discriminate small changes in I0 with a nonswitching detector, with potential applications in quantum state measurement.
The transport properties of a small superconductor--normal-metal--superconducting tunnel junction can be controlled by a gate electrode coupled capacitively to the central island. We evaluate the critical Josephson current Ic{\mathit{I}}_{\mathit{c}}Ic​ through such a system as a function of the gate voltage Vg{\mathit{V}}_{\mathit{g}}Vg​ taking into account parity effects in the superconductors. The dependence Ic{\mathit{I}}_{\mathit{c}}Ic​(Vg{\mathit{V}}_{\mathit{g}}Vg​) shows resonant singularities and has a qualitatively different character for \ensuremath{\Delta}EC{\mathit{E}}_{\mathit{C}}EC​ and \ensuremath{\Delta}>EC{\mathit{E}}_{\mathit{C}}EC​, \ensuremath{\Delta} being the superconducting gap and EC{\mathit{E}}_{\mathit{C}}EC​=e2{\mathit{e}}^{2}e2/2C being the charging energy. Due to the sweeping of the gate voltage, the system can be driven to states which are metastable with respect to a change of the number of electrons on the central island. Since the lifetime of the metastable states can be macroscopically large, one can observe a remarkable bistability of the Josephson current. A weak magnetic field suppresses the interference of the electrons propagating through the central electrode, and, consequently, the magnitude of the critical current.