Circuits based on superconducting nanostructures are among the most promising platforms for quantum computing. Understanding how device geometry governs nonlinear electrodynamics is crucial for implementing superconducting quantum technologies. However, to date, research has largely been limited to superconducting nanostructures with collinearly aligned static and dynamic applied magnetic fields. Here, we analyze the dynamics of Meissner currents and Abrikosov vortices in a superconducting nanocube exposed to combined static and microwave magnetic fields, extending the analysis to a more general excitation geometry. We demonstrate that, in a noncollinear configuration, the magnetization component parallel to the static field develops a dominant second-harmonic response under the microwave driving. This effect is strongly enhanced when Meissner currents saturate at static fields just below the thresholds for successive vortex nucleation. By numerically solving the time-dependent Ginzburg-Landau equations, we show that the response originates from Meissner-current saturation combined with the nonlinear oscillations of normal-phase indentations, yielding an anisotropic second-harmonic signal that is directionally separated from, and not overshadowed by, the first-harmonic component of the dynamic magnetization. These findings are relevant for superconducting devices that require controllable high-frequency nonlinearity.Circuits based on superconducting nanostructures are among the most promising platforms for quantum computing. Understanding how device geometry governs nonlinear electrodynamics is crucial for implementing superconducting quantum technologies. However, to date, research has largely been limited to superconducting nanostructures with collinearly aligned static and dynamic applied magnetic fields. Here, we analyze the dynamics of Meissner currents and Abrikosov vortices in a superconducting nanocube exposed to combined static and microwave magnetic fields, extending the analysis to a more general excitation geometry. We demonstrate that, in a noncollinear configuration, the magnetization component parallel to the static field develops a dominant second-harmonic response under the microwave driving. This effect is strongly enhanced when Meissner currents saturate at static fields just below the thresholds for successive vortex nucleation. By numerically solving the time-dependent Ginzburg-Landau equations, we show that the response originates from Meissner-current saturation combined with the nonlinear oscillations of normal-phase indentations, yielding an anisotropic second-harmonic signal that is directionally separated from, and not overshadowed by, the first-harmonic component of the dynamic magnetization. These findings are relevant for superconducting devices that require controllable high-frequency nonlinearity.

Physical review. B./Physical review. BJun 2, 20260 citations

Driven Vortex Motion in Periodic Channel Potential Embedded in Superconducting Films

A. Al Luhaibi, A. Glatz, Michael Rudolf Vogl +2 more

In this paper, we investigate vortex dynamics in periodically width-modulated superconducting channels by numerically solving the time-dependent Ginzburg-Landau (TDGL) equations. The channels are designed with sinusoidally varying widths characterized by their average width and modulation amplitude. The motion of driven vortices generates an oscillatory electric field with a fundamental frequency, $f_0$ , set by the channel periodicity, together with higher-order harmonics. In contrast to the situation of vortex lattice dynamics in a periodic pinning landscape of circular holes considered by Al Luhaibi et al. [1], we show that the harmonic content of the generated electric field can be effectively controlled through the channel geometry. In particular, appropriately engineered channel profiles strongly suppress higher-order harmonics, yielding an electric-field response that closely approaches a pure sinusoidal waveform. These results demonstrate that geometric modulation offers a viable route to engineering low-harmonicity microwave signals in superconducting devices and may enable cryogenic on-chip waveform generators for controlling superconducting qubits. Such devices could provide a useful building block for scalable transmon-based quantum computing architectures.In this paper, we investigate vortex dynamics in periodically width-modulated superconducting channels by numerically solving the time-dependent Ginzburg-Landau (TDGL) equations. The channels are designed with sinusoidally varying widths characterized by their average width and modulation amplitude. The motion of driven vortices generates an oscillatory electric field with a fundamental frequency, $f_0$, set by the channel periodicity, together with higher-order harmonics. In contrast to the situation of vortex lattice dynamics in a periodic pinning landscape of circular holes considered by Al Luhaibi et al. [1], we show that the harmonic content of the generated electric field can be effectively controlled through the channel geometry. In particular, appropriately engineered channel profiles strongly suppress higher-order harmonics, yielding an electric-field response that closely approaches a pure sinusoidal waveform. These results demonstrate that geometric modulation offers a viable route to engineering low-harmonicity microwave signals in superconducting devices and may enable cryogenic on-chip waveform generators for controlling superconducting qubits. Such devices could provide a useful building block for scalable transmon-based quantum computing architectures.

arXiv:2610.14775Oct 10, 20260 citations

Compact Model and Circuit Behavior of Bistable 2ϕ-Josephson Junctions

Ana Mitrović, Mark F. Bocko

The 2ϕ-Josephson junctions (JJs), characterized by a dominant second harmonic in the current-phase relationship (CPR), are promising devices for low-power, high-density superconducting digital logic. These junctions eliminate the need for on-chip inductors to store magnetic flux and they reduce bias current requirements. In practical implementations, both first and second harmonic components are typically present in the CPR, affecting the junction dynamics and circuit operation. Understanding this behavior is essential for the reliable design of superconducting logic circuits utilizing these junctions, such as half flux quantum (HFQ) circuits. In this article, a compact Verilog-A model for 2ϕ-JJs is presented that captures the nonlinear behavior of the junctions, accounting for both harmonic contributions and their impact on damping. Two parameter sets are derived from experimental data corresponding to junctions with weak ferromagnetic barriers and ferromagnetic insulator barriers. Based on the inferred parameters, models of each junction type are developed. The model is validated against published experimental results and simulated within a D flip flop cell, demonstrating its use for superconducting circuit design and analysis, including evaluation of circuit behavior under nonideal junction conditions. Stability issues and failure mechanisms introduced by a nonzero first harmonic are analyzed, and underlying junction dynamics are examined to explain the reduction in circuit parameter margins.The 2ϕ-Josephson junctions (JJs), characterized by a dominant second harmonic in the current-phase relationship (CPR), are promising devices for low-power, high-density superconducting digital logic. These junctions eliminate the need for on-chip inductors to store magnetic flux and they reduce bias current requirements. In practical implementations, both first and second harmonic components are typically present in the CPR, affecting the junction dynamics and circuit operation. Understanding this behavior is essential for the reliable design of superconducting logic circuits utilizing these junctions, such as half flux quantum (HFQ) circuits. In this article, a compact Verilog-A model for 2ϕ-JJs is presented that captures the nonlinear behavior of the junctions, accounting for both harmonic contributions and their impact on damping. Two parameter sets are derived from experimental data corresponding to junctions with weak ferromagnetic barriers and ferromagnetic insulator barriers. Based on the inferred parameters, models of each junction type are developed. The model is validated against published experimental results and simulated within a D flip flop cell, demonstrating its use for superconducting circuit design and analysis, including evaluation of circuit behavior under nonideal junction conditions. Stability issues and failure mechanisms introduced by a nonzero first harmonic are analyzed, and underlying junction dynamics are examined to explain the reduction in circuit parameter margins.

IEEE Transactions on Electron DevicesNov 10, 20251 citation

Harmonic dual dressing of spin-1/2 systems

G. Bevilacqua, V. Biancalana, T. Zanon-Willette +1 more

Controlled modifications of the magnetic response of a two-level system are produced in dressed systems by one high-frequency, strong, and nonresonant electromagnetic field. This quantum control is greatly enhanced and enriched by a harmonic, commensurable, and orthogonally oriented dual dressing, as discussed here. The secondary field enables a fine tuning of the qubit response, with control parameter amplitude, harmonic content, spatial orientation, and phase relation. Our analysis, mainly based on a perturbative approach with respect to the driving strength, includes also nonperturbative numerical solutions. The Zeeman response becomes anisotropic in a triaxial geometry and includes a nonlinear quadratic contribution. The long-time dynamics is described by an anisotropic effective magnetic field representing the handle for the system full engineering. Through the low-order harmonic mixing, the bichromatic driving generates a synthetic static field modifying the system dynamics. The spin temporal evolution includes a micromotion at harmonics of the driving frequency whose role in the spin detection is examined. Our dressing increases the two-level energy splitting, improving the spin detection sensitivity. In the weak-field direction it compensates the static fields applied in different geometries. The results presented here lay a foundation for additional applications to be harnessed in quantum simulations.Controlled modifications of the magnetic response of a two-level system are produced in dressed systems by one high-frequency, strong, and nonresonant electromagnetic field. This quantum control is greatly enhanced and enriched by a harmonic, commensurable, and orthogonally oriented dual dressing, as discussed here. The secondary field enables a fine tuning of the qubit response, with control parameter amplitude, harmonic content, spatial orientation, and phase relation. Our analysis, mainly based on a perturbative approach with respect to the driving strength, includes also nonperturbative numerical solutions. The Zeeman response becomes anisotropic in a triaxial geometry and includes a nonlinear quadratic contribution. The long-time dynamics is described by an anisotropic effective magnetic field representing the handle for the system full engineering. Through the low-order harmonic mixing, the bichromatic driving generates a synthetic static field modifying the system dynamics. The spin temporal evolution includes a micromotion at harmonics of the driving frequency whose role in the spin detection is examined. Our dressing increases the two-level energy splitting, improving the spin detection sensitivity. In the weak-field direction it compensates the static fields applied in different geometries. The results presented here lay a foundation for additional applications to be harnessed in quantum simulations.

Physical Review AFeb 23, 20226 citations

Local Broadband Gigahertz Spectroscopy via SQUID-on-Tip DC Readout

Senne Vervoort, Lukas Nulens, Julia Baumgarten +5 more

Superconducting microwave circuits are shaped by their local electromagnetic environment, yet standard microwave measurements do not resolve the local fields and device features that govern their behavior. Here, we combine microwave spectroscopy, nanoscale magnetic sensing, and topographic imaging in a single tapping-mode SQUID-on-tip microscope. The nonlinear Josephson response converts local GHz excitations into Shapiro steps, enabling quantitative measurements of microwave frequency signals and their excitation strength using only DC readout. Applied to a superconducting coplanar waveguide resonator, local spectroscopy reproduces the power-dependent resonance and nonlinear bifurcation observed in microwave transmission measurements. Spatially resolved measurements map the microwave response while simultaneously recording topography and static magnetic features, including vortices and Meissner screening currents. Electromagnetic simulations reveal how coupling through the superconducting probe leads limits spatial resolution and guides localized detector designs. Together, these capabilities establish a platform for correlating microwave circuit dynamics with the local structural and magnetic environment of superconducting devices.Superconducting microwave circuits are shaped by their local electromagnetic environment, yet standard microwave measurements do not resolve the local fields and device features that govern their behavior. Here, we combine microwave spectroscopy, nanoscale magnetic sensing, and topographic imaging in a single tapping-mode SQUID-on-tip microscope. The nonlinear Josephson response converts local GHz excitations into Shapiro steps, enabling quantitative measurements of microwave frequency signals and their excitation strength using only DC readout. Applied to a superconducting coplanar waveguide resonator, local spectroscopy reproduces the power-dependent resonance and nonlinear bifurcation observed in microwave transmission measurements. Spatially resolved measurements map the microwave response while simultaneously recording topography and static magnetic features, including vortices and Meissner screening currents. Electromagnetic simulations reveal how coupling through the superconducting probe leads limits spatial resolution and guides localized detector designs. Together, these capabilities establish a platform for correlating microwave circuit dynamics with the local structural and magnetic environment of superconducting devices.

arXiv:2610.35737Oct 26, 20260 citations

Nonequilibrium dynamics reveal remote Aharonov–Bohm sensitivity in superconductors

ARMEN M. GULIAN, Will Benston, V. R. Nikoghosyan

Previous time-dependent Ginzburg–Landau simulations demonstrated that Abrikosov vortex dynamics in superconductors can be influenced by Aharonov–Bohm-type curl-less vector potentials even in simply connected geometries, without closed-loop trajectories enclosing magnetic flux [A. M. Gulian et al., Phys. Lett. A 382 (2018) 1058]. The origin of this effect has remained unexplained. Here we investigate further nonequilibrium effects in which the relation between a curl-less vector potential and an evolving quantum state produces observable consequences. During transient nonequilibrium state evolution, collective quantum systems may develop measurable responses to curl-less gauge fields despite a simply connected final equilibrium configuration with no persistent current. Using superconducting condensates, we formulate protocols based on the gauge-invariant coupling between quantum phase and the curl-less vector potential, analyze their dynamics using time-dependent Ginzburg–Landau theory and interpret rapid phase formation within the Kibble–Zurek picture. The predicted transient supercurrents and voltage signals provide a physical interpretation of nonequilibrium sensitivity to curl-less gauge fields and motivate experimental tests.Previous time-dependent Ginzburg–Landau simulations demonstrated that Abrikosov vortex dynamics in superconductors can be influenced by Aharonov–Bohm-type curl-less vector potentials even in simply connected geometries, without closed-loop trajectories enclosing magnetic flux [A. M. Gulian et al., Phys. Lett. A 382 (2018) 1058]. The origin of this effect has remained unexplained. Here we investigate further nonequilibrium effects in which the relation between a curl-less vector potential and an evolving quantum state produces observable consequences. During transient nonequilibrium state evolution, collective quantum systems may develop measurable responses to curl-less gauge fields despite a simply connected final equilibrium configuration with no persistent current. Using superconducting condensates, we formulate protocols based on the gauge-invariant coupling between quantum phase and the curl-less vector potential, analyze their dynamics using time-dependent Ginzburg–Landau theory and interpret rapid phase formation within the Kibble–Zurek picture. The predicted transient supercurrents and voltage signals provide a physical interpretation of nonequilibrium sensitivity to curl-less gauge fields and motivate experimental tests.

Physics Letters AOct 19, 20260 citations

f_0

, set by the channel periodicity, together with higher-order harmonics. In contrast to the situation of vortex lattice dynamics in a periodic pinning landscape of circular holes considered by Al Luhaibi et al. [1], we show that the harmonic content of the generated electric field can be effectively controlled through the channel geometry. In particular, appropriately engineered channel profiles strongly suppress higher-order harmonics, yielding an electric-field response that closely approaches a pure sinusoidal waveform. These results demonstrate that geometric modulation offers a viable route to engineering low-harmonicity microwave signals in superconducting devices and may enable cryogenic on-chip waveform generators for controlling superconducting qubits. Such devices could provide a useful building block for scalable transmon-based quantum computing architectures.