Direct Visualization of Phase-Locking of Large Josephson Junction Arrays by Surface Electromagnetic Waves

M.A. Galin, F. Rudau, E.A. Borodianskyi, V.V. Kurin, D. Koelle, R. Kleiner, V.M. Krasnov, and A.M. Klushin

Phys. Rev. Applied 14, 024051 – Published 18 August 2020

Abstract

Phase-locking of oscillators leads to super-radiant amplification of the emission power. This is particularly important for development of terahertz sources, which suffer from low emission efficiency. In this work we study large Josephson junction arrays containing several thousand $Nb$ -based junctions. Using low-temperature scanning laser microscopy, we observe that at certain bias conditions two-dimensional standing-wave patterns are formed, manifesting themselves as global synchronization of the arrays. Analysis of standing waves indicates that they are formed by surface plasmon–type electromagnetic waves propagating at the electrode-substrate interface. Thus, we demonstrate that surface waves provide an effective mechanism for long-range coupling and phase-locking of large junction arrays.

Received 3 April 2020
Revised 13 July 2020
Accepted 14 July 2020

DOI:https://doi.org/10.1103/PhysRevApplied.14.024051

Physics Subject Headings (PhySH)

Collective dynamics Plasmonics

Josephson junctions

Cavity resonators Terahertz techniques

Nonlinear DynamicsCondensed Matter, Materials & Applied Physics

Authors & Affiliations

M.A. Galin ^1,2, F. Rudau³, E.A. Borodianskyi⁴, V.V. Kurin ¹, D. Koelle ³, R. Kleiner³, V.M. Krasnov ^4,2,*, and A.M. Klushin ¹

¹Institute for Physics of Microstructures RAS, Nizhny Novgorod 603950, Russia
²Moscow Institute of Physics and Technology, Dolgoprudny 141700, Moscow Province, Russia
³Physikalisches Institut, Center for Quantum Science and LISA+, Universität Tübingen, 72076 Tübingen, Germany
⁴Department of Physics, Stockholm University, AlbaNova University Center, SE-106 91 Stockholm, Sweden

^*vladimir.krasnov@fysik.su.se

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Vol. 14, Iss. 2 — August 2020

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Images

Figure 1
Geometry of the JJ arrays studied. (a) Top view of the linear array. Red dots represent junctions, yellow and green stripes are $Nb$ electrodes sequentially connecting the JJs, and green rectangles at the corners are contact pads. The inset shows a cross section (side view) of the junction area (from Ref. [32]). (b) Top view of the meander array. Contact pads are outside the image area. The vertical wavy lines in (a),(b) indicate a break in the pictures.
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Figure 2
(a) $I$ - $V$ characteristic of the linear array measured during LTSLM imaging. (b) LTSLM images obtained at four bias points, indicated in (a).The sign of $Δ U$ for most of the JJs changes from positive for bias points $A$ and $B$ to negative for bias points $C$ and $D$ . (c) Simulation of the LTSLM response from a single JJ. The blue and red lines represent IVCs with the laser beam off and on, respectively. Heating by the laser beam leads to suppression of the critical current and reduction of the junction resistance due to the semiconducting nature of the $Nb Si$ barrier. This leads to the sign change of the LTSLM response from positive for points $A$ and $B$ to negative for points $C$ and $D$ .
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Figure 3
The transport and radiation measurements of the linear array. (a) $I$ - $V$ characteristics at different temperatures. (b) The IVC at $T = 6$ K (red) and the simultaneously measured detector signal (olive curve). The appearance of the resonant step structure in the IVCs is clearly seen. The detected EM power is correlated with the step structure.
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Figure 4
The transport and radiation measurements of the meandering array. (a) $I$ - $V$ characteristics at different temperatures measured in a $^{3} He$ cryostat with a base temperature 0.8 K (navy) and 3.5 K (red). (b) The IVC at $T = 5$ K (red) and the simultaneously measured detector signal (olive curve).
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Figure 5
LTSLM analysis of the linear JJ array at $T \sim 6$ K. (a) $I$ - $V$ characteristic of the array measured during LTSLM imaging. (b) LTSLM images obtained at four bias points, indicated in (a). The length of scans along $x$ axis is $L_{x} = 0.91$ mm. The scans are stretched about 2 times along the $y$ axis for better viewing. Development of standing-wave correlations is clearly seen in images B, C, and D. (c) LTSLM response (blue lines) along horizontal array lines 2–4 [from bottom to top as indicated in (b), image C] for image C, $I = 2.37$ mA. The data are averaged over the width of a strip. Red lines represent fitting curves obtained by the method of least squares. Antisymmetric modulation in neighboring lines is seen.
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Figure 6
LTSLM analysis of the meandering array at $T \sim 5$ K. (a) $I$ - $V$ characteristic of the array, measured during LTSLM imaging. (b) LTSLM images at different bias points, indicated in (a). The length of scans along the $x$ axis is $L_{x} = 0.91$ mm. The development of a standing-wave pattern is clearly seen. The standing wave is not periodic in the horizontal direction. Dotted lines indicate the start and the end of the track along the length of the meandering line where periodicity of the response is observed.(c) LTSLM responses (blue lines) along the tracks indicated in (b) from the bottom-left corner to the bottom-right corner of the pattern at the bias point $D$ (top) and bias point $C$ (bottom). The data are averaged over the width of a strip. The red line represents fitting curves obtained by the method of least squares. Clear periodicity along the whole meandering length indicates that standing waves are formed by plasmon-type surface waves propagating along $Nb$ electrodes.
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