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Physical Review Letters

Classical phase diffusion in small hysteretic Josephson junctions

John M. Martinis, Richard L. Kautz

Published Oct 2, 1989• 141 citations
Publisher

Abstract

The existence of classical phase diffusion in hysteretic junctions is demonstrated by quantitative agreement between experimental and simulated I-V curves. The simulations are based on a circuit that accurately models both the junction and its external shunting impedance at microwave frequencies. We show that the bias current at which the junction switches from the phase diffusion state to the voltage state is sensitive to dissipation at microwave frequencies.

DOI
10.1103/physrevlett.63.1507

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The existence of classical phase diffusion in hysteretic junctions is demonstrated by quantitative agreement between experimental and simulated I-V curves. The simulations are based on a circuit that accurately models both the junction and its external shunting impedance at microwave frequencies. We show that the bias current at which the junction switches from the phase diffusion state to the voltage state is sensitive to dissipation at microwave frequencies.
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We have observed a dissipative phase diffusion branch in arrays of hysteretic high-Tc{T}_{c}Tc​ intrinsic Josephson junctions. By comparing the data with a thermal activation model we extract the impedance seen by the junction in which phase diffusion is occurring. At the plasma frequency this junction is isolated from its environment and it sees its own large (\ensuremath{\sim} k\ensuremath{\Omega}) impedance. Our results suggest that stacks of Josephson junctions may be used for isolation purposes in the development of a solid state quantum computer.
We report an experimental and theoretical study of low-voltage resistive states observed in small tunnel Josephson junctions subject to microwave radiation. The observed features result from Shapiro steps in the current–voltage characteristics and appear when both thermal fluctuations and high frequency dissipation are strong. Without microwave radiation, Josephson junctions have a phase diffusion supercurrent branch characterized by a finite small resistance and hysteretic switching to a higher voltage range under these conditions. When microwave radiation is applied, three different types of resistive states are observed in the current-voltage characteristics. First, a phase diffusion branch steadily evolves and its maximum voltage Vm increases with the microwave power. Another interesting observed feature is a zero-crossing resistive state characterized by a negative resistance. Finally, we find that the low-voltage resistive state can split into numerous hysteretic fine branches resembling incoherent Shapiro-like steps. The appearance of a particular resistive state depends on the interrelations among the Josephson energy EJ, the energy kBT of thermal fluctuations, and the microwave frequency ω. A theoretical analysis based on incoherent multi-photon absorption by a junction biased in the Josephson phase diffusion regime is in good agreement with the experimental observations.
A new phase diffusive regime in a current biased Josephson junction is theoretically explored which originates from embedding the junction in a circuit environment with anomalous dissipation. This is realized by placing parallel to the junction a resistor in series with a capacitor such that electromagnetic fluctuations effectively couple also to the charge of the junction. This leads to rich Josephson dynamics, in particular for the switching of the junction out of a zero voltage state. Modelled as the escape process of a fictitious phase-particle out of a metastable well, a detailed study reveals that anomalous dissipation has a strong impact at low temperatures when quantum tunneling dominates against thermal activation. As a manifestation, a regime is found, where for realistic circuit parameters the quantum escape process is substantially enhanced, followed by a short voltage pulse and re-trapping with high probability. This class of circuits may be leveraged for detecting microwave photons or dissipative quantum annealing processes. In addition, the analysis provides a general framework for engineering dissipative dynamics in nonlinear systems using anomalous environments.
We have studied the current-voltage characteristics of small area tunnel junctions at temperatures below 1 K. The junctions were made in an edge geometry with a Nb base electrode and had areas less than .05 μm2and critical currents in the nA range. Although the measured I-V characteristics resemble those of ordinary hysteretic junctions, the supposed zero-voltage portion of the curve proved to have a finite slope and to deviate from zero voltage. For these junctions it is apparently possible for occasional 2π phase slips to occur without switching to the usual voltage state. This behavior can be explained either by macroscopic quantum tunneling or by a model in which the effective shunt conductance of the junction is frequency dependent.
We report an experimental and theoretical study of the phase diffusion in small Josephson junctions under microwave irradiation. A peculiar enhancement of the phase diffusion by microwaves is observed. The enhancement manifests itself by a pronounced current peak in the current-voltage characteristics. The voltage position V(top) of the peak increases with the power P of microwave radiation as V(top) proportional to sqrt[P], while its current amplitude weakly decreases with P. As the microwave frequency increases, the peak feature evolves into Shapiro steps with a finite slope. Our theoretical analysis, taking into account the enhancement of incoherent superconducting current by multiphoton absorption, is in good agreement with experimental data.