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Revue de Physique Appliquée

Electromagnetic properties of the Dayem bridge

Mogens T. Levinsen

Published Jan 1, 1974• 29 citations
Publisher

Abstract

The first measurements on the Dayem bridge showed that the behaviour in an applied microwave field was quite different from that of the Josephson tunnel junction. Measurements on bridges one magnitude smaller later showed this difference to result from the bridge size. A very simple equivalent circuit was furthermore shown to characterize these small bridges. Analog computer calculations on this circuit will be compared to experimental results. At high temperatures a rounding of steps and supercurrent presumably due to noise is observed. A comparison with the theory of Ambegaokar and Halperin will be presented. At low temperatures a hysteresis develops. This may result from the bridge capacitance which also may give rise to subharmonic steps. However, the magnitude (1 pF) inferred from the hysteresis is too small to account for the subharmonic steps actually observed. In contrast to other types of junctions the bridge is mechanically very robust. We have therefore been interested in the applicability of the bridge. An upper limit to the sensitivity to 10 GHz radiation has been found in terms of NEP to 9 × 10-14 W/√Hz. Furthermore, we have demonstrated that mixing via the Josephson effect is possible. The power dependence of the sum and difference steps is in fair agreement with analog computer calculations on the equivalent circuit. It has been debated whether the bridge radiates at all. By the observation of a cavity induced step we have now established that bridges do radiate.

DOI
10.1051/rphysap:0197400901013500

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The testing of NbN(g) nanobridges with Al direct shunt resistors for use as millimeter-wave Josephson mixers is discussed. The NbN(g)/Al nanobridges have a nearly sinusoidal current-phase relation, high resistance, well-defined gap structure at approximately 4 mV, large I/sub J/ R/sub N/ products of approximately 3 mV, and nonhysteresis I-V curves. By means of the Al direct shunt, the effective noise temperature T/sub N//sup eff/ of the NbN(g) nanobridges, which was calculated by transition-state theory, was reduced to 4.2 K as a result of reducing the self-heating and noise rounding effects. The NbN(g)/Al nanobridges show almost ideal Josephson response to millimeter-wave radiation at 106 GHz. The well-pronounced Josephson steps were observed up to approximately 4 mV. The observed systematic decreasing of the step heights with increasing the RF current can be accounted for by the effect of the thermal noise if an effective noise temperature of T/sub N/=15 K (at i/sub RF/=3) is assumed. The IF peaks in the Josephson mixing were obtained up to the bias voltage of approximately 1.2 mV. The NEP was about 3*10/sup -20/ W/Hz at 4.2 K.

IEEE Transactions on Magnetics•Mar 1, 1991•6 citations
The first measurements on the Dayem bridge showed that the behaviour in an applied microwave field was quite different from that of the Josephson tunnel junction. Measurements on bridges one magnitude smaller later showed this difference to result from the bridge size. A very simple equivalent circuit was furthermore shown to characterize these small bridges. Analog computer calculations on this circuit will be compared to experimental results. At high temperatures a rounding of steps and supercurrent presumably due to noise is observed. A comparison with the theory of Ambegaokar and Halperin will be presented. At low temperatures a hysteresis develops. This may result from the bridge capacitance which also may give rise to subharmonic steps. However, the magnitude (1 pF) inferred from the hysteresis is too small to account for the subharmonic steps actually observed. In contrast to other types of junctions the bridge is mechanically very robust. We have therefore been interested in the applicability of the bridge. An upper limit to the sensitivity to 10 GHz radiation has been found in terms of NEP to 9 × 10-14 W/√Hz. Furthermore, we have demonstrated that mixing via the Josephson effect is possible. The power dependence of the sum and difference steps is in fair agreement with analog computer calculations on the equivalent circuit. It has been debated whether the bridge radiates at all. By the observation of a cavity induced step we have now established that bridges do radiate.
We report X-band microwave measurements on superconducting thin film micro-bridges (Dayem bridges), mounted in a half wavelength cavity with an adjustable coupling to match the bridge properly. Power emission from the bridge of 10-13W in a 10 MHz bandwidth was measured. Current noise fluctuations caused a total voltage line width corresponding to 150-200 MHz, when the voltage across the bridge was swept through the resonance; from this we estimate a total power emission of 1-2·10-12W into this frequency interval. Transmission measurements and comparison with analogue computer calculations have revealed that an equivalent diagram consisting of an inductance in series with the resistively shunted Josephson junction model can account for the experimental results. A conclusion from these measurements is that there is a possibility for amplification in the device. Moreover, the nonlinearity of the device was used in a mixing experiment with the Josephson oscillation as local oscillator.
Experimental investigations on the proximity effect bridge (a Josephson device) at zero voltage and at finite voltages in the µV range are reported. The phase-super current relation at zero voltage was measured using an asymmetric superconducting quantum interferormeter circuit. The data are in agreement with the Josephson supercurrent-phase relation I_S=I_C sinδ with deviation less than 5% of the critical current I_c. The supercurrent density in the measured bridges reached as high as 50-100 µA/µm^2. Using microcircuitry techniques, proximity effect bridges were strongly coupled to superconducting microstrip resonators. Selfinduced steps in the I-V characteristics of bridges coupled to resonators were observed in the GHz region at voltages (frequencies) corresponding to the expected modes of the resonators. Two types of steps were seen depending on whether the resonator impedance on resonance was much higher or much smaller than the bridge resistance. A simple two fluid model of the bridge-resonator circuit was developed and the size and shape of self-induced steps were calculated for a generalized Josephson oscillator relation I_S = I_c(l-q + q sin∫ 2e/hV dt) where q = 1 corresponds to the original Josephson relation and q = 1/2 represents the phase slip regime. At low critical currents (I_c < 10 µA) and low voltages (V < 3µV) the size and shape of experimentally observed self-induced steps agree with the q = 1 model. At higher voltages and/or critical currents the step size increasingly deviates from the q = 1 model towards q = 1/2. These observations are interpreted to indicate a progressive reduction of the amplitude of the oscillating Josephson supercurrent in proximity effect bridges from I_c towards I_c /2 as the critical current and/or voltage are increased.
Microwave superconducting mixers operating at 10–13 GHz utilizing Josephson junctions have been investigated analytically and experimentally. Measurements on mixer sensitivity were carried out at 13 GHz using waveguide-mounted experimental point-contact Josephson junctions at 4.2 K. Results showed sensitivities of −90 dBm/MHz (10−18 W/Hz) which included mismatch losses encountered in the waveguide structure. The Josephson junction mixing mechanism was analyzed on the basis of small-signal modulation of the staircase like dc I-V characteristics. It was shown that a small-signal microwave excitation results in an ac lateral shift of the regions between steps, such that: (a) Optimum Josephson mixing occurs halfway between steps. (b) Mixing occurs between all steps with maximum conversion efficiency between the zero and first step. (c) Predicted low conversion loss and possibly internal gain for a matched mixer. The analytical model was simulated by a digital computer and the behavior of the Josephson mixer predicted for various conditions of excitation. The model chosen for the analysis and the computer simulation is based on the simplest assumptions concerning bulk-formed Josephson junctions. In the laboratory an external local oscillator set 60 MHz below the signal frequency was used to induce the well-known step structure in the dc I-V characteristic of the point-contact Josephson junction. Mixing of the Lo and signal was found to occur between constant voltage steps in agreement with both analysis and computer simulation. The correctness of the model is demonstrated by the agreement between the theory and experiment.
A major factor in the practical utilization of any Josephson device for microwave and higher frequency applications (such as the generation and detection of electromagnetic radiation) is the success with which the junction device can be coupled to an external transmission line. As part of an experimental investigation of the electrodynamics of small arrays of Josephson tunnel junctions, the properties of the coherent radiation emitted both by individual junctions and by coupled junction systems have been studied at frequencies between 2 and 12 GHz. Near 9 GHz, more than 10-9 W of coherent radiation has been detected from a single Pb-Pb oxide-Pb junction coupled via waveguide. The development of thin film devices in which the tunnel junctions form part of a microstrip line have made it feasible to observe directly (in a single device) the radiation emitted both at the fundamental geometrical frequency and at the low order harmonics. The observed temperature dependence of the junction cavity Q indicate the low temperature losses are primarily due to cavity loading of the external transmission line.
The rf-power dependence of the ac-Josephson steps is measured at 720 GHz, using small area Nb tunnel junctions. This frequency is well above the gap frequency of Nb. The junction is placed in a waveguide, and connected to a superconducting stripline, which effectively tunes out the junction capacitance and facilitates the coupling of the radiation to the junction. We observe three Josephson steps, and the first step crosses the zero current axis over a considerable range of rf-power. This indicates the possible application of THz Josephson steps in voltage standards. The data are compared to the theory and we find clear evidence for the predicted intrinsic roll-off of the Josephson current amplitude above the gap frequency.
The testing of NbN(g) nanobridges with Al direct shunt resistors for use as millimeter-wave Josephson mixers is discussed. The NbN(g)/Al nanobridges have a nearly sinusoidal current-phase relation, high resistance, well-defined gap structure at approximately 4 mV, large I/sub J/ R/sub N/ products of approximately 3 mV, and nonhysteresis I-V curves. By means of the Al direct shunt, the effective noise temperature T/sub N//sup eff/ of the NbN(g) nanobridges, which was calculated by transition-state theory, was reduced to 4.2 K as a result of reducing the self-heating and noise rounding effects. The NbN(g)/Al nanobridges show almost ideal Josephson response to millimeter-wave radiation at 106 GHz. The well-pronounced Josephson steps were observed up to approximately 4 mV. The observed systematic decreasing of the step heights with increasing the RF current can be accounted for by the effect of the thermal noise if an effective noise temperature of T/sub N/=15 K (at i/sub RF/=3) is assumed. The IF peaks in the Josephson mixing were obtained up to the bias voltage of approximately 1.2 mV. The NEP was about 3*10/sup -20/ W/Hz at 4.2 K.