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Applied Physics Letters

One-third (period three) harmonic generation in microwave-driven Josephson tunnel junctions

Jørn Bindslev Hansen, John L. Clarke, J. Mygind, G. A. Ovsyannikov, Henrik Svensmark

Published Dec 22, 1986• 3 citations
Publisher

Abstract

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.

DOI
10.1063/1.97234

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Abstl'act W& l'epol't the obsel'vation of one-thil'd hal'monic .genel'ation in small Josephson tunnel junctions dl'iven with a micl'owave signal in the fl'equency range 8 to 18 GHz.This phenomenon was observed both with the• junction biased in the zero voltage state and• on micl'owave-induced constant-voltage steps in the.CUl'l'ent-voltage chal'acteristic.With high levels of applied microwave power the period-tl'ipled signal was detected on steps up to order 120.''~

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Measurements have been made of the low-frequency spectral density of the voltage noise in current-biased resistively shunted Josephson tunnel junctions under conditions in which the noise mixed-down from frequencies near the Josephson frequency (${\ensuremath{\nu}}_{J}$) to the measurement frequency ($\ensuremath{\ll}{\ensuremath{\nu}}_{J}$) is in the regime $h{\ensuremath{\nu}}_{J}>{k}_{B}T$. In this limit, quantum corrections to the mixed-down noise are important. The spectral densities measured on junctions with current-voltage characteristics close to the Stewart-McCumber model were in excellent agreement with the predicted values, with no fitted parameters. The mixed-down noise for a wide range of bias voltages was used to infer the spectral density of the current noise in the shunt resistor at frequency $\ensuremath{\nu}$. With no fitted parameters, this spectral density at frequencies up to 500 GHz was in excellent agreement with the prediction $(\frac{2h\ensuremath{\nu}}{R})coth(\frac{h\ensuremath{\nu}}{2{k}_{B}T})$. The presence of the zero-point term, $\frac{2h\ensuremath{\nu}}{R}$, at frequencies $h\ensuremath{\nu}>{k}_{B}T$ was clearly demonstrated. The current-voltage characteristics of a junction with ${\ensuremath{\beta}}_{L}\ensuremath{\equiv}\frac{2\ensuremath{\pi}{L}_{s}{I}_{0}}{{\ensuremath{\Phi}}_{0}}\ensuremath{\sim}1$ and ${\ensuremath{\beta}}_{C}\ensuremath{\equiv}\frac{2\ensuremath{\pi}{I}_{0}{R}^{2}C}{{\ensuremath{\Phi}}_{0}}\ensuremath{\ll}1$, where ${I}_{0}$ is the critical current, $C$ is the junction capacitance, and ${L}_{s}$ is the shunt inductance, showed structure at voltages where the Josephson frequency was near a subharmonic of the ${L}_{s}C$ resonant frequency. The additional nonlinearity of the $I\ensuremath{-}V$ characteristic caused mixing down of noise near higher harmonics of the Josephson frequency, thereby greatly enhancing the voltage noise. The measured noise was in good agreement with that predicted by computer simulations.

Physical review. B, Condensed matter•Jul 1, 1982•117 citations
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.
Relaxation oscillations at subharmonics of the Josephson frequency may occur in a resistively shunted superconducting tunnel junction, where the shunt loop has a large inductance. We have studied the variation in the relaxation period with the shunt inductance and resistance, the Josephson critical current, and the bias current. Steps in the current-voltage curve were noted at bias points where the subharmonic number changed. Radiation powers of the order of a nW were coupled out of small, single, tunnel junctions at 10 GHz. Linewidths scaled with the frequency square as compared with those of the Josephson mode oscillations. Wide signals centered around harmonics of the relaxation frequency were due to amplified noise. Injection locking to a fraction of the frequency of a relatively strong signal occurred, while weaker signals were amplified. Gains up to 15 dB were achieved within a fairly large bandwidth, but the noise temperature was high. The importance of parametrically up-converted noise from low idler frequencies is emphasized.
Abstl'act W& l'epol't the obsel'vation of one-thil'd hal'monic .genel'ation in small Josephson tunnel junctions dl'iven with a micl'owave signal in the fl'equency range 8 to 18 GHz.This phenomenon was observed both with the• junction biased in the zero voltage state and• on micl'owave-induced constant-voltage steps in the.CUl'l'ent-voltage chal'acteristic.With high levels of applied microwave power the period-tl'ipled signal was detected on steps up to order 120.''~
The capacitance of a Josephson tunnel junction is an important parameter, which determines its plasma frequency ωp and thus the energy level spacing in the quantum regime. When a microwave signal at the frequency of ω is applied to a current-biased junction in its zero-voltage state, the escape rate from this state is somehow enhanced. The enhancement is expected to go through a pronounced maximum when ωp=ω. Making use of such microwave generated resonant activation in the thermal regime, we have developed a time-resolved measurement scheme for determining the junction capacitance with an uncertainty of less than 2%.
Measurements have been made of the low-frequency spectral density of the voltage noise in current-biased resistively shunted Josephson tunnel junctions under conditions in which the noise mixed-down from frequencies near the Josephson frequency (${\ensuremath{\nu}}_{J}$) to the measurement frequency ($\ensuremath{\ll}{\ensuremath{\nu}}_{J}$) is in the regime $h{\ensuremath{\nu}}_{J}>{k}_{B}T$. In this limit, quantum corrections to the mixed-down noise are important. The spectral densities measured on junctions with current-voltage characteristics close to the Stewart-McCumber model were in excellent agreement with the predicted values, with no fitted parameters. The mixed-down noise for a wide range of bias voltages was used to infer the spectral density of the current noise in the shunt resistor at frequency $\ensuremath{\nu}$. With no fitted parameters, this spectral density at frequencies up to 500 GHz was in excellent agreement with the prediction $(\frac{2h\ensuremath{\nu}}{R})coth(\frac{h\ensuremath{\nu}}{2{k}_{B}T})$. The presence of the zero-point term, $\frac{2h\ensuremath{\nu}}{R}$, at frequencies $h\ensuremath{\nu}>{k}_{B}T$ was clearly demonstrated. The current-voltage characteristics of a junction with ${\ensuremath{\beta}}_{L}\ensuremath{\equiv}\frac{2\ensuremath{\pi}{L}_{s}{I}_{0}}{{\ensuremath{\Phi}}_{0}}\ensuremath{\sim}1$ and ${\ensuremath{\beta}}_{C}\ensuremath{\equiv}\frac{2\ensuremath{\pi}{I}_{0}{R}^{2}C}{{\ensuremath{\Phi}}_{0}}\ensuremath{\ll}1$, where I0{I}_{0}I0​ is the critical current, CCC is the junction capacitance, and Ls{L}_{s}Ls​ is the shunt inductance, showed structure at voltages where the Josephson frequency was near a subharmonic of the LsC{L}_{s}CLs​C resonant frequency. The additional nonlinearity of the $I\ensuremath{-}V$ characteristic caused mixing down of noise near higher harmonics of the Josephson frequency, thereby greatly enhancing the voltage noise. The measured noise was in good agreement with that predicted by computer simulations.