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Journal of Applied Physics

Theoretical investigations of microwave-driven Josephson junctions in a large frequency range

B. Mikolajczak, H.‐G. Meyer, P. Seidel

Published Jul 15, 1989• 5 citations
Publisher

Abstract

Based on the Werthamer model [Phys. Rev. 147, 255 (1966)] we investigate the current-voltage characteristic of Josephson tunnel junctions irradiated by a microwave. Within the first harmonic approximation we derive relations for the constant-voltage steps and the corresponding stability conditions. The results are compared with investigations in the frame of the Stewart–McCumber model. [Appl. Phys. 12, 277 (1968); J. Appl. Phys. 39, 3113 (1968)].

DOI
10.1063/1.343547

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Based on the Werthamer model [Phys. Rev. 147, 255 (1966)] we investigate the current-voltage characteristic of Josephson tunnel junctions irradiated by a microwave. Within the first harmonic approximation we derive relations for the constant-voltage steps and the corresponding stability conditions. The results are compared with investigations in the frame of the Stewart–McCumber model. [Appl. Phys. 12, 277 (1968); J. Appl. Phys. 39, 3113 (1968)].
Josephson oscillations in a large series array of Josephson junctions designed as a superconducting microwave transmission line are studied. For descriptions of the Josephson junctions both the Stewart–McCumber model and the Werthamer model are used. The attenuation of the Josephson oscillations in the considered array is composed of two terms rising from the stripline and from the Josephson junctions. The latter one is of increasing significance for lower than usually applied drive frequencies.
We perform both theoretical and experimental investigations on the phase escape of a current-biased Josephson tunnel junction under microwave irradiation. The switching current distributions exhibit abundant nonlinear behaviors depending on the power and frequency of the applied microwave. We present a model to describe the behavior of the primary peak in the switching current distribution, which is confirmed by our experimental results. The obtained features can be used to characterize the damping parameter of Josephson junctions.
Deep theoretical understanding of the electrical response of Josephson junctions is indispensable regarding both recent discoveries of new kinds of superconductivity and technological advances such as superconducting quantum computers. Here, we study the microscopic theory of the dc current-biased I-V characteristics of Josephson tunnel junctions. We derive an analytical formula of the I-V characteristics of generic junctions. We identify subharmonics of the I-V characteristics and their underlying mechanism as the feedback effect of intrinsic ac currents generated by voltage pulses in the past. We apply our theory to analytically solve the Werthamer equation and describe various dc current-biased I-V characteristics as a function of softening of the superconducting gap. Strikingly, we identify voltage staircases of the I-V characteristics in a genuine Josephson junction without ac current bias or qubit dynamics. Our general analytical formalism opens new avenues for a microscopic understanding of I-V characteristics of Josephson junctions that have been limited to phenomenological models so far.
One-third harmonic signals have been generated in the zero voltage state of a Josephson tunnel junction driven with a microwave current in the frequency range 8–20 GHz. The signal was as much as 50 dB above the noise level of the detector with a linewidth of less than 100 Hz. The junction parameters and microwave current were measured in situ in separate experiments. The subharmonic generation occurred for ranges of microwave current and frequency that were in reasonable agreement with the results of digital computer simulations.
We elaborate a theoretical description of large Josephson junctions which is based on Werthamer's microscopic tunneling theory. The model naturally incorporates coupling of electromagnetic radiation to the tunnel currents and, therefore, is particularly suitable for description of the self-coupling effect in Josephson junction. In our numerical calculations we treat the arising integro-differential equation, which describes temporal evolution of the superconducting phase difference coupled to the electromagnetic field, by the Odintsov-Semenov-Zorin algorithm. This allows us to avoid evaluation of the time integrals at each time step while taking into account all the memory effects. To validate the obtained microscopic model of large Josephson junction we focus our attention on the Josephson flux-flow oscillator. The proposed microscopic model of flux-flow oscillator does not involve the phenomenological damping parameter, rather the damping is taken into account naturally in the tunnel current amplitudes calculated at a given temperature. The theoretically calculated current-voltage characteristics is compared to our experimental results obtained for a set of fabricated flux-flow oscillators of different lengths.