^{1,a)}and Faouzi Boussaha

^{1}

### Abstract

We investigated parallel arrays of superconducting tunnel junctions nonevenly distributed in a superconducting Nb/SiO/Nb microstrip transmission line. Such devices are discretized Josephson transmission lines (DJTLs) in which, from theory, magnetic flux quanta (“fluxons”) can travel as solitonic waves when a dc current bias and a dc magnetic field are applied. We observed a reproducible series of resonant branches in each device’s curve, at Josephson submillimeter-wave frequencies (from 240 to 720 GHz) matching the resonances predicted using a transmission line analysis, where the loading of the junctions is fully taken into account. The nonperiodic distribution was optimized to provide rf matching over a large bandwidth (450–650 GHz typically), implying that the plasma resonance of junctions is inductively tuned out over a similar band by the array. A confirmation of this comes from the observation, at frequencies higher than the untuned junctions plasma frequency, of several Josephson phenomena reported in this article: Fiske-like resonances, phase-locking of the resonance to an external 600 GHz microwave source, rf-induced zero crossing, and resonances at fractional harmonics of the rf signal. These experimental results are all compatible with a fluxon-based resonances interpretation, as in the extensively studied long Josephson junctions yet at higher frequencies. As reported elsewhere, we could detect microwave radiation emitted by our devices in the and modes. In light of these unique properties, we propose nonuniform DJTLs as a promising type of Josephson device for submillimeter-wave oscillators and fast fluxon-based electronics.

This work was supported by the Centre National d’Etudes Spatiales (CNES) and the Institut National des Sciences de l’Univers. We acknowledge Y. Delorme, F. Dauplay, C. Chaumont, A. Feret, B. Lecomte, M. Batrung, and J.-M. Krieg for contributions at various stages of this work, and L. Loukitch and J.-G. Caputo for fruitful discussions and for developing a numerical model applicable to our circuits. We thank Gerard Beaudin, Pierre Encrenaz, and Jean-Michel Lamarre for their support.

I. INTRODUCTION

II. CIRCUITS

III. EXPERIMENTAL RESULTS

A. Resonances

B. Submillimeter-wave phase-locking

IV. DISCUSSION

A. Resonance frequencies

B. Tuned plasma frequency

C. Fluxons or linear modes

V. APPLICATIONS

A. Wideband SISmixers

B. FFOs

C. Other applications

### Key Topics

- Josephson junctions
- 72.0
- Mixers
- 26.0
- Niobium
- 24.0
- Josephson effect
- 22.0
- Microwaves
- 18.0

## Figures

(a) Equivalent circuit of a stripline parallel array of Josephson junctions such as shown in Fig. 2, connected to a microwave circuit of source impedance . The components , , and are, respectively, the quasiparticle conductance, tunnel capacitance, and critical current of junction . At first order, the conductance “seen” by microwaves is . The cells characteristic impedances and lengths are optimized to achieve submillimeter-wave broadband coupling (see Fig. 3). When the lengths of all cells tend to it becomes the equivalent circuit of a continuous LJJ. (b) Zoom on a unit-length of stripline array, anywhere. All elements are per unit length: and are, respectively, the self-inductance and the resistance of the superconducting electrodes, is the quasiparticle conductance, is the Josephson current density, and is the capacitance of the unit length in parallel with the tunnel barrier capacitance. Outside Josephson junctions, the only leakage admittance is the stripline capacitance .

(a) Equivalent circuit of a stripline parallel array of Josephson junctions such as shown in Fig. 2, connected to a microwave circuit of source impedance . The components , , and are, respectively, the quasiparticle conductance, tunnel capacitance, and critical current of junction . At first order, the conductance “seen” by microwaves is . The cells characteristic impedances and lengths are optimized to achieve submillimeter-wave broadband coupling (see Fig. 3). When the lengths of all cells tend to it becomes the equivalent circuit of a continuous LJJ. (b) Zoom on a unit-length of stripline array, anywhere. All elements are per unit length: and are, respectively, the self-inductance and the resistance of the superconducting electrodes, is the quasiparticle conductance, is the Josephson current density, and is the capacitance of the unit length in parallel with the tunnel barrier capacitance. Outside Josephson junctions, the only leakage admittance is the stripline capacitance .

(a) Photograph of circuit A (see Table I). (b) View of a five-junction nonuniform array. The micron-size SIS tunnel junctions are parallel connected by their top and bottom Nb electrodes, and insulated by a SiO dielectric layer. The resulting Nb/SiO/Nb structure makes a rf tuning circuit, as well as a parallel array of SQUIDs. The array is connected on one side to an antenna of well known source impedance, and a rf choke filter (not shown) prevents submillimeter-wave leakage via the bias leads. The circuit shown here was designed for operation as a SIS mixer over the band 450–650 GHz and possibly beyond.

(a) Photograph of circuit A (see Table I). (b) View of a five-junction nonuniform array. The micron-size SIS tunnel junctions are parallel connected by their top and bottom Nb electrodes, and insulated by a SiO dielectric layer. The resulting Nb/SiO/Nb structure makes a rf tuning circuit, as well as a parallel array of SQUIDs. The array is connected on one side to an antenna of well known source impedance, and a rf choke filter (not shown) prevents submillimeter-wave leakage via the bias leads. The circuit shown here was designed for operation as a SIS mixer over the band 450–650 GHz and possibly beyond.

Measured curve at 4.2 K of the circuit C, with . Below the gap at , three resonant branches are seen, looking and behaving like ZFSs or FSs commonly reported in LJJs hosting resonant fluxons, usually at much lower frequencies.

Measured curve at 4.2 K of the circuit C, with . Below the gap at , three resonant branches are seen, looking and behaving like ZFSs or FSs commonly reported in LJJs hosting resonant fluxons, usually at much lower frequencies.

curve at 4.2 K of the circuit A, with . The measurements (a), (b) and (c) differ by the magnetic field applied (a few Gauss at most), which not only modulates the state amplitude (as shown in Fig. 4) but also enhances certain resonances. The highest resonance observed is around 700 GHz.

curve at 4.2 K of the circuit A, with . The measurements (a), (b) and (c) differ by the magnetic field applied (a few Gauss at most), which not only modulates the state amplitude (as shown in Fig. 4) but also enhances certain resonances. The highest resonance observed is around 700 GHz.

Measured characteristic at 4.2 K of the parallel-junction array , with (a) [resp. (b) ]. The higher-order ZFSs are enhanced by a small magnetic field (tens of gauss) applied. Additional structures are seen for the highest current density.

Measured characteristic at 4.2 K of the parallel-junction array , with (a) [resp. (b) ]. The higher-order ZFSs are enhanced by a small magnetic field (tens of gauss) applied. Additional structures are seen for the highest current density.

Frequency-locking of the FS for circuit A, to an external microwave signal at . (a)–(c) correspond to three increasing rf amplitudes.

Frequency-locking of the FS for circuit A, to an external microwave signal at . (a)–(c) correspond to three increasing rf amplitudes.

(a) Zoom on the curve showing the phase-locked resonant branch changing shape as the 600 GHz signal power is increased; (b) current’s locking range as a function of rf amplitude. Filled squares and open circles represent two different measurements, with a slightly modified field. One notices a rf amplitude threshold for the locking mechanism.

(a) Zoom on the curve showing the phase-locked resonant branch changing shape as the 600 GHz signal power is increased; (b) current’s locking range as a function of rf amplitude. Filled squares and open circles represent two different measurements, with a slightly modified field. One notices a rf amplitude threshold for the locking mechanism.

Zero-crossing step at 600 GHz for circuit A. For voltage standard, our circuits may present an interest whenever a wide range of frequencies and voltages need to be measured with a single device.

Zero-crossing step at 600 GHz for circuit A. For voltage standard, our circuits may present an interest whenever a wide range of frequencies and voltages need to be measured with a single device.

In the presence of an external 600 GHz signal, we measured Josephson signatures at 0.45, 0.81, and 1.64 mV in the curve. These voltages correspond to , 2/3, and 4/3 fractional harmonic responses. This is classically explained in LJJs by a plasma frequency greater than the rf frequency, and is a sign that Josephson nonlinearity dominates over other capacitive or dissipative admittances.

In the presence of an external 600 GHz signal, we measured Josephson signatures at 0.45, 0.81, and 1.64 mV in the curve. These voltages correspond to , 2/3, and 4/3 fractional harmonic responses. This is classically explained in LJJs by a plasma frequency greater than the rf frequency, and is a sign that Josephson nonlinearity dominates over other capacitive or dissipative admittances.

(a) Imaginary part of the array impedance (filled triangles), and its resonant poles. When the Josephson inductive element is also considered (open triangles), these poles give the tuned plasma resonances of the device. One notices a shift. (b) Due to the rf losses in the superconducting electrodes, the plasma resonant poles of A and C smear out (filled symbols), providing both arrays with a wideband, near zero (here ) which enhances the Josephson electrodynamics at these high frequencies. Therefore the multipole, filterlike device tuning explains not only the wideband impedance match but also the high sensitivity of the device to Josephson excitations.

(a) Imaginary part of the array impedance (filled triangles), and its resonant poles. When the Josephson inductive element is also considered (open triangles), these poles give the tuned plasma resonances of the device. One notices a shift. (b) Due to the rf losses in the superconducting electrodes, the plasma resonant poles of A and C smear out (filled symbols), providing both arrays with a wideband, near zero (here ) which enhances the Josephson electrodynamics at these high frequencies. Therefore the multipole, filterlike device tuning explains not only the wideband impedance match but also the high sensitivity of the device to Josephson excitations.

(a) Computed rf coupling of the five-junction arrays (triangles) and (squares) with resp. and , to the mixer’s antenna and waveguide. For our particular mixer mount geometry, the complex source impedance feeding the array is for a wide range of frequencies (Ref. 1). Open symbols correspond to a full calculation using the Mattis–Bardeen theory. (b) RF coupling measured at 4.2 K using a Fourier transform spectrometer. The 3 dB bandwidth is about 450–600 GHz, and the dip around 560 GHz is caused by the absorbing 557 GHz water vapor line.

(a) Computed rf coupling of the five-junction arrays (triangles) and (squares) with resp. and , to the mixer’s antenna and waveguide. For our particular mixer mount geometry, the complex source impedance feeding the array is for a wide range of frequencies (Ref. 1). Open symbols correspond to a full calculation using the Mattis–Bardeen theory. (b) RF coupling measured at 4.2 K using a Fourier transform spectrometer. The 3 dB bandwidth is about 450–600 GHz, and the dip around 560 GHz is caused by the absorbing 557 GHz water vapor line.

Measured interference pattern of the stripline parallel-junction array (open circles). The field is applied with an electromagnet, which was calibrated using a cryogenic Hall probe. Superimposed is that of a stripline two-junction SQUID, made with the same process (filled triangles).

Measured interference pattern of the stripline parallel-junction array (open circles). The field is applied with an electromagnet, which was calibrated using a cryogenic Hall probe. Superimposed is that of a stripline two-junction SQUID, made with the same process (filled triangles).

## Tables

Optimized nonuniform DJTL geometry (all dimensions in ).

Optimized nonuniform DJTL geometry (all dimensions in ).

Fabrication of circuits.

Fabrication of circuits.

Wave propagation parameters.

Wave propagation parameters.

Josephson resonance voltages (all values in mV , measured at 4.2 K).

Josephson resonance voltages (all values in mV , measured at 4.2 K).

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