We study arrays of planar $\mathrm{Nb}$ Josephson junctions with contacts to intermediate electrodes, which allow measurements of individual junctions and, thus, provide an insight into intricate array dynamics. We observe strong indications for array phase locking, despite a significant interjunction separation. Several unusual phenomena are reported, such as a bistable critical current with reentrant superconductivity upon switching of nearby junctions; and ``incorrect'' Shapiro steps, occurring at mixing frequencies between the external rf radiation and the internal Josephson frequency in nearby junctions. Our results reveal a surprisingly strong and long-range interjunction interaction, which is attributed to nonlocality of planar-junction electrodynamics, caused by the long-range spreading of stray electromagnetic fields. The nonlocality greatly enhances the high-frequency interjunction coupling and enables large-scale synchronization. Therefore, we conclude that planar geometry is advantageous for the realization of coherent Josephson electronics.We study arrays of planar $\mathrm{Nb}$ Josephson junctions with contacts to intermediate electrodes, which allow measurements of individual junctions and, thus, provide an insight into intricate array dynamics. We observe strong indications for array phase locking, despite a significant interjunction separation. Several unusual phenomena are reported, such as a bistable critical current with reentrant superconductivity upon switching of nearby junctions; and ``incorrect'' Shapiro steps, occurring at mixing frequencies between the external rf radiation and the internal Josephson frequency in nearby junctions. Our results reveal a surprisingly strong and long-range interjunction interaction, which is attributed to nonlocality of planar-junction electrodynamics, caused by the long-range spreading of stray electromagnetic fields. The nonlocality greatly enhances the high-frequency interjunction coupling and enables large-scale synchronization. Therefore, we conclude that planar geometry is advantageous for the realization of coherent Josephson electronics.

arXiv:2201.11453Physical Review AppliedJun 16, 202217 citations

Foundations of Josephson Junction Dynamics

I. N. Askerzade, Ali Bozbey, Mehmet Cantürk

Mathematical engineeringJan 1, 20170 citations

Time-Resolved Dynamics of Josephson Junctions

Joseph Weston

Springer thesesJan 1, 20170 citations

Quantum dynamics of frustrated Josephson junction arrays embedded in a transmission line: An effective X X spin chain with long-range interaction

Benedikt J. P. Pernack, M. V. Fistul, Ilya Eremin

We study theoretically a variety of collective quantum phases occurring in frustrated sawtooth chains of Josephson junctions embedded in a dissipationless transmission line. The basic element of a system, i.e., the triangular superconducting cell, contains two 0 and one $\ensuremath{\pi}$ Josephson junctions characterized by ${E}_{J}$ and $\ensuremath{\alpha}{E}_{J}$ Josephson energies, accordingly. In the frustrated regime the low-energy quantum dynamics of a single cell is determined by anticlockwise or clockwise flowing persistent currents (vortex or antivortex). The direct embedding of $\ensuremath{\pi}$ Josephson junctions in a transmission line allows us to establish a short or long-range interaction between (anti)vortices of well-separated cells. By making use of the variational approach, we map the superconducting circuit Hamiltonian to an effective $XX$ spin model with an exchange spin-spin interaction decaying with the distance $x$ as ${x}^{\ensuremath{-}\ensuremath{\beta}}$, and the local ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\ensuremath{\sigma}}}_{x,n}$ terms corresponding to the coherent quantum beats between vortex and antivortex in a single cell. We obtain that, in long arrays such as $N\ensuremath{\gg}{\ensuremath{\ell}}_{0}\ensuremath{\simeq}\sqrt{C/{C}_{0}}$, where $C$ and ${C}_{0}$ are capacitances of a 0 Josephson junction and a transmission line, respectively, the amplitude of quantum beats is strongly suppressed. By means of exact numerical diagonalization, we study the interplay between the coherent quantum beats and the exchange spin-spin interaction leading to the appearance of various collective quantum phases such as the paramagnetic ( $P$ ), compressible superfluid ( $CS$ ), and weakly compressible superfluid ($w\text{\ensuremath{-}}CS$) states.We study theoretically a variety of collective quantum phases occurring in frustrated sawtooth chains of Josephson junctions embedded in a dissipationless transmission line. The basic element of a system, i.e., the triangular superconducting cell, contains two 0 and one $\ensuremath{\pi}$ Josephson junctions characterized by ${E}_{J}$ and $\ensuremath{\alpha}{E}_{J}$ Josephson energies, accordingly. In the frustrated regime the low-energy quantum dynamics of a single cell is determined by anticlockwise or clockwise flowing persistent currents (vortex or antivortex). The direct embedding of $\ensuremath{\pi}$ Josephson junctions in a transmission line allows us to establish a short or long-range interaction between (anti)vortices of well-separated cells. By making use of the variational approach, we map the superconducting circuit Hamiltonian to an effective $XX$ spin model with an exchange spin-spin interaction decaying with the distance $x$ as ${x}^{\ensuremath{-}\ensuremath{\beta}}$, and the local ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\ensuremath{\sigma}}}_{x,n}$ terms corresponding to the coherent quantum beats between vortex and antivortex in a single cell. We obtain that, in long arrays such as $N\ensuremath{\gg}{\ensuremath{\ell}}_{0}\ensuremath{\simeq}\sqrt{C/{C}_{0}}$, where $C$ and ${C}_{0}$ are capacitances of a 0 Josephson junction and a transmission line, respectively, the amplitude of quantum beats is strongly suppressed. By means of exact numerical diagonalization, we study the interplay between the coherent quantum beats and the exchange spin-spin interaction leading to the appearance of various collective quantum phases such as the paramagnetic ($P$), compressible superfluid ($CS$), and weakly compressible superfluid ($w\text{\ensuremath{-}}CS$) states.

arXiv:2407.03928Physical review. B./Physical review. BNov 1, 20242 citations

Correlations and fluctuations in Josephson junction arrays

Wang Wenguo, MANFRED L. RISTIG

Physics Letters AApr 1, 19982 citations

We study arrays of planar

\mathrm{Nb}

Josephson junctions with contacts to intermediate electrodes, which allow measurements of individual junctions and, thus, provide an insight into intricate array dynamics. We observe strong indications for array phase locking, despite a significant interjunction separation. Several unusual phenomena are reported, such as a bistable critical current with reentrant superconductivity upon switching of nearby junctions; and ``incorrect'' Shapiro steps, occurring at mixing frequencies between the external rf radiation and the internal Josephson frequency in nearby junctions. Our results reveal a surprisingly strong and long-range interjunction interaction, which is attributed to nonlocality of planar-junction electrodynamics, caused by the long-range spreading of stray electromagnetic fields. The nonlocality greatly enhances the high-frequency interjunction coupling and enables large-scale synchronization. Therefore, we conclude that planar geometry is advantageous for the realization of coherent Josephson electronics.

{E}_{J}

and $\ensuremath{\alpha}{E}_{J}$ Josephson energies, accordingly. In the frustrated regime the low-energy quantum dynamics of a single cell is determined by anticlockwise or clockwise flowing persistent currents (vortex or antivortex). The direct embedding of $\ensuremath{\pi}$ Josephson junctions in a transmission line allows us to establish a short or long-range interaction between (anti)vortices of well-separated cells. By making use of the variational approach, we map the superconducting circuit Hamiltonian to an effective

XX

spin model with an exchange spin-spin interaction decaying with the distance

x

as ${x}^{\ensuremath{-}\ensuremath{\beta}}$, and the local ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\ensuremath{\sigma}}}_{x,n}$ terms corresponding to the coherent quantum beats between vortex and antivortex in a single cell. We obtain that, in long arrays such as $N\ensuremath{\gg}{\ensuremath{\ell}}_{0}\ensuremath{\simeq}\sqrt{C/{C}_{0}}$, where

C

and

{C}_{0}

are capacitances of a 0 Josephson junction and a transmission line, respectively, the amplitude of quantum beats is strongly suppressed. By means of exact numerical diagonalization, we study the interplay between the coherent quantum beats and the exchange spin-spin interaction leading to the appearance of various collective quantum phases such as the paramagnetic (

P

), compressible superfluid (

CS

), and weakly compressible superfluid ($w\text{\ensuremath{-}}CS$) states.