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arXiv:2403.06229 · Physical Review Research

Optimal parametric control of transport across a Josephson junction

Hannah Kleine-Pollmann, Guido Homann, Ludwig Mathey

Published May 27, 2026• 0 citations
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Abstract

We present optimal control strategies for the dc transport across a Josephson junction. Specifically, we consider a junction in which the Josephson coupling is driven parametrically, with either a bichromatic or a trichromatic driving protocol, and optimize the prefactor of the 1 / ω divergence of the imaginary part of the conductivity, which we refer to as the effective Josephson coupling J eff . We demonstrate that for an optimal bichromatic protocol an enhancement of J eff by a factor of 70 can be reached, and for an optimal trichromatic protocol an enhancement by a factor of 135. This is motivated by pump-probe experiments that have demonstrated light-enhanced superconductivity along the c axis of underdoped YBa 2 Cu 3 O 6 + δ (YBCO), where the junction serves as a minimal model for the c -axis coupling of superconducting layers. Therefore, the significant enhancement of superconductivity that we show for multifrequency protocols demonstrates that the advancement of pump-probe technology toward these strategies is highly desirable.

DOI
10.1103/5s3j-scll

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We present optimal control strategies for the dc transport across a Josephson junction. Specifically, we consider a junction in which the Josephson coupling is driven parametrically, with either a bichromatic or a trichromatic driving protocol, and optimize the prefactor of the 1 / ω divergence of the imaginary part of the conductivity, which we refer to as the effective Josephson coupling J eff . We demonstrate that for an optimal bichromatic protocol an enhancement of J eff by a factor of 70 can be reached, and for an optimal trichromatic protocol an enhancement by a factor of 135. This is motivated by pump-probe experiments that have demonstrated light-enhanced superconductivity along the c axis of underdoped YBa 2 Cu 3 O 6 + δ (YBCO), where the junction serves as a minimal model for the c -axis coupling of superconducting layers. Therefore, the significant enhancement of superconductivity that we show for multifrequency protocols demonstrates that the advancement of pump-probe technology toward these strategies is highly desirable.
The combined action of a DC bias and a microwave drive on the transport characteristic of a superconductor-quantum dot-superconductor junction is investigated. To cope with time dependent non-equilibrium effects and interactions in the quantum dot, we develop a general formalism for the dynamics of the density operator based on a particle conserving approach to superconductivity. Without invoking a broken U (1) symmetry, we identify a dynamical phase connected to the coherent transfer of Cooper pairs across the junction. In the weak coupling limit, we show that besides quasiparticle transport, proximity induced superconducting correlations manifest in anomalous pair tunneling involving the transfer of a Cooper pair. The resulting generalized master equation in presence of the microwave drive showcases the characteristic bichromatic response due to the combination of the AC Josephson effect and an AC voltage. Analytical expressions for all harmonics in the driving frequency of both the current and the reduced dot operator are given for arbitrary driving strength. For the net DC current the resulting photon assisted processes give rise to rich current-voltage characteristics. In addition to photon assisted subgap transport we find regions of total current inversion in the stability diagram. There, the junction acts as a pump with the net DC current flowing against the applied DC bias. The first harmonic of the current, being closely related to the nonlinear dynamic susceptibility of the junction, is discussed at finite applied DC bias.
The combined action of a dc bias and a microwave drive on the transport characteristic of a superconductor-quantum dot-superconductor junction is investigated. To cope with time dependent nonequilibrium effects and interactions in the quantum dot, we develop a general formalism for the dynamics of the density operator based on a particle conserving approach to superconductivity. Without invoking a broken U(1) symmetry, we identify a dynamical phase connected to the coherent transfer of Cooper pairs across the junction. In the weak-coupling limit, we show that besides quasiparticle transport, proximity induced superconducting correlations manifest in anomalous pair tunneling involving the transfer of a Cooper pair. The resulting generalized master equation in presence of the microwave drive showcases the characteristic bichromatic response due to the combination of the ac Josephson effect and an ac voltage. Analytical expressions for all harmonics in the driving frequency of both the current and the reduced dot operator are given for arbitrary driving strength. For the net dc current, the resulting photon assisted processes give rise to rich current-voltage characteristics. In addition to photon assisted subgap transport, we find regions of total current inversion in the stability diagram. There, the junction acts as a pump with the net dc current flowing against the applied dc bias. The first harmonic of the current, being closely related to the nonlinear dynamic susceptibility of the junction, is discussed at finite applied dc bias.
In this dissertation, we theoretically demonstrate laser light induced control and cooling over the order parameter of superconducting cuprates. We predict a non-equilibrium state with enhanced robustness against thermal fluctuations when pumped with coherent pulses. This might ultimately increase the critical temperature of the cuprate. In particular, we propose a parametric cooling scheme for a bilayer cuprate modelled phenomenologically as a stack of long intrinsic Josephson junctions. We identify a parameter regime, which according to the switching current distribution allows a reduction of the effective system temperature by approximately 25%. This cooling scheme suppresses the thermal excitation of Josephson vortices. This might lead to an indirect mechanism for controlling topological excitations in the phase of the superconducting order parameter. We further find that the strong driving of the cuprates can lead to parametric instabilities. To investigate the effect strong driving can have on the dissipative dynamics, we derive a FloquetMarkov master equation. We find that strong driving is a measure for probing the bath spectral density of otherwise inaccessible condensed matter systems.
The integration of ferroelectric barriers into high-temperature Josephson junctions offers a pathway to tunable superconducting quantum devices. Here, we demonstrate robust Josephson coupling in YBa2Cu3O7-x (YBCO)/Bi0.5Na0.5TiO3 (BNT)/YBCO trilayer junctions incorporating a 40 nm ferroelectric BNT barrier. Epitaxial trilayers were fabricated by pulsed laser deposition on SrTiO3 substrates and investigated under broadband terahertz (THz) irradiation (0.5-2.5 THz). At 1.5 THz, close to the Josephson plasma resonance, the BNT polarization increased from 33.4 to 46.4 uC/cm2 at 30 K, enhancing superconducting transport. The junctions exhibited a well-defined zero-voltage supercurrent branch, with the critical current Ic(T) remaining nearly constant up to 60 K and reaching 468.2 uA under 1.5 THz excitation, evidencing strong phase coherence. Scanning tunneling spectroscopy revealed an enhanced superconducting gap in YBCO/BNT/YBCO (Delta = 1.3 meV) compared with pure YBCO (Delta = 1.05 meV), while optical conductivity measurements showed a reduction in conductivity and gap with increasing temperature, consistent with BCS theory under THz excitation. Atomic force microscopy and X-ray reflectivity confirmed uniform morphology and sharp interfaces, excluding defect-mediated transport. Magnetic field modulation of Ic(B) exhibited a canonical Fraunhofer interference pattern, and resistance mapping revealed alternating lobes of high and low dissipation, indicating coherent Josephson tunneling. These results establish that Josephson coupling is intrinsic to the YBCO/BNT/YBCO junctions, enabled by the dipolar character and dynamic THz response of the BNT barrier. This study identifies BNT as a viable, tunable barrier material for next-generation high-Tc superconducting quantum devices.
We present a systematic study of the temperature-dependent transport properties of Nb- and Al-based superconductor--insulator--thin superconductor--ferromagnet--superconductor (SIsFS) Josephson junctions. By varying the superconducting material and the thickness of the intermediate superconducting layer, we identify three distinct transport regimes: a tunnel-dominated SIS-like regime, a temperature-driven crossover, and a complex weak-link regime. A unified Usadel-based description connects these regimes through the self-consistent pair potential of the intermediate s-layer. While for Al-based devices an SIS-like transport regime is observed, a self-consistent calculation of the s/F/S proximity electrode, combined with perturbative tunnel coupling to the outer electrode, accounts for Nb devices with different thickness of the superconducting interlayer. The calculation places the 10-nm-interlayer sample in a proximity-supported, strongly suppressed s state, close to the SInFS limit in which the interlayer is effectively driven normal (\textit{n}). A reduced nonlinear long-junction description captures the same limiting physics. The evolution of I_cR_N(T) thereby provides a direct experimental signature of the three transport regimes. Beyond the fundamental interest, the results establish practical design guidelines: Nb junctions with sufficiently thick s interlayers are well suited for high-speed cryogenic memory elements and tunable superconducting parametric amplifiers, while Al junctions are natural candidates for coherent superconducting quantum circuits