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Applied Physics Letters

Calculation of the effects of a focused laser beam on the dynamic Josephson tunneling states

Jhy-Jiun Chang

Published Aug 15, 1985• 10 citations
Publisher

Abstract

Perturbative calculations of the voltage response of constant-current biased Josephson tunnel junctions to a focused laser beam have been performed. The dependence of the voltage modification as a function of the laser beam position was calculated. The results were found to be qualitatively different for junctions biased on the first zero-field current step but with either vortex-mode or cavity-mode excitations. Therefore, the recently developed scanning focused laser beam technique operated in this mode can be a simple and effective method for probing the nature of the dynamic Josephson tunneling state.

DOI
10.1063/1.96135

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Perturbative calculations of the voltage response of constant-current biased Josephson tunnel junctions to a focused laser beam have been performed. The dependence of the voltage modification as a function of the laser beam position was calculated. The results were found to be qualitatively different for junctions biased on the first zero-field current step but with either vortex-mode or cavity-mode excitations. Therefore, the recently developed scanning focused laser beam technique operated in this mode can be a simple and effective method for probing the nature of the dynamic Josephson tunneling state.
A perturbation method is used to calculate the change of the total zero-voltage current ΔIc(y0) flowing through a one-dimensional Josephson tunnel junction due to a focused laser beam irradiated at y0. Nonlocal response of the phase difference function φ as well as the local response of the amplitude J to the laser beam are included. In the junction configuration we considered, it is found that the nonlocal effect can, depending upon the external magnetic field, make the spatial dependences of ΔIc(y0) and the current distribution different.
The effect of a focused laser beam on the critical junction current of a one-dimensional Josephson tunnel junction is analyzed for both short and long junctions. The laser heating locally alters the critical current density and London penetration depth, giving rise to a change in the critical current which is proportional to the local current density of the irradiated region. In addition, the relative pair phase is modified in a nonlocal manner which gives rise to an additional contribution to the change in the critical current of the junction. For short junctions, this nonlocal phase modification contributes two parts to the junction critical current. One has the same spatial dependence as that of the current distribution itself, while the other is independent of the position of the laser beam. This latter contribution depends upon the applied magnetic field and is a signature of the nonlocal effect. For a long junction, the nonlocal phase contribution to the change in the junction critical current can give rise to dramatic effects when the applied magnetic field is less than a critical value Hc{H}_{c}Hc​=\ensuremath{\Elzxh}c/(2ed${\ensuremath{\lambda}}_{J}$). In this case the spatial dependence of the laser-induced change in the critical current can be qualitatively different from the unperturbed current distribution.
Using Takanaka's theory of the zero-field dc-current steps of a Josephson tunnel junction, we have studied the effect of the junction QQQ factor on the shape of the current step near the first even-order resonant voltage $V=h\frac{{\ensuremath{\nu}}_{c}}{e}$, where ${\ensuremath{\nu}}_{c}$ is the frequency of the fundamental cavity mode. In addition, we have found that the effect of a magnetic field on the step height can be qualitatively explained by modifying Takanaka's theory to include a magnetic-field-dependent term.
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.
We have investigated theoretically the amplitudes of RF- induced constant voltage steps in two-dimensional Josephson tunnel junctions, using both a first-order approximation and a numerical it- eration procedure to calculate the current density distribution in the junction. We use a planar resonator model to analyze the electromag- netic field in the microwave-driven junction. Integrating the local Jo- sephson current density over the junction area yields the total dc current on a chosen Shapiro step. Numerical calculations of the Sha- piro step amplitudes in two-dimensional resonant junctions show a qualitatively different behavior from that in one-dimensional resonant junctions. Depending on the dominant resonant mode, the microwave power dependence of the step amplitude gives a smooth curve without zeros. This behavior is advantageous for biasing the Josephson junc- tion in its maximum step amplitude. The main difference between the results of the first-order approximation and the full theory is that- using the iteration procedure-the Shapiro steps in resonant junctions become asymmetric with respect to the quasi-particle curve. This is due to consideration of the losses and the internal Josephson currents in the numerical iteration procedure of the full theory.