Researchers are increasingly focused on understanding current precision within hybrid normal-superconducting systems, crucial for advancing quantum technologies and nanoscale electronics. Nahual Sobrino from The Abdus Salam International Center for Theoretical Physics, Fabio Taddei from NEST, Istituto Nanoscienze-CNR and Scuola Normale Superiore, and Rosario Fazio from Dipartimento di Fisica, Universit`a di Napoli “Federico II”, alongside Governale et al., present a detailed analysis of Andreev-mediated transport and current fluctuations in these systems. Their work significantly advances the field by demonstrating how Coulomb interactions renormalise resonant conditions and suppress superconducting coherence, ultimately reducing current precision even with only minor changes to average current levels. This research clarifies the interplay between Coulomb interactions and nonequilibrium fluctuations in determining transport properties, establishing current precision as a reliable measure of interacting Andreev transport and moving beyond simpler, non-interacting models.

Coulomb interactions diminish current precision in hybrid quantum-dot systems

Researchers have demonstrated a significant advancement in understanding current precision within hybrid normal-superconducting quantum-dot systems. This work details how Coulomb interactions, often present in nanoscale devices, modify Andreev-mediated transport and subsequently impact the accuracy with which electric currents can be generated.
Employing a generalized master equation based on real-time diagrammatics and full counting statistics, the study calculates steady-state current, zero-frequency noise, and the rate of entropy production, all within the limit of a large superconducting gap. Findings reveal that these interactions renormalise resonant conditions and suppress superconducting coherence, leading to a notable reduction in current precision, even when average currents remain relatively stable.

The research highlights that these effects become particularly pronounced at higher temperatures, where conventional Coulomb-blockade phenomena are blurred by thermal effects, yet fluctuation properties retain their sensitivity. By analysing thermodynamic uncertainty relations, scientists show that violations of established quantum bounds, observed in non-interacting systems, are progressively diminished and ultimately suppressed as interactions increase.

Conversely, a recently proposed hybrid bound remains consistently satisfied, indicating a fundamental limit to precision even in interacting systems. This investigation clarifies the combined influence of Coulomb interactions and nonequilibrium fluctuations on transport properties in hybrid superconducting devices.

Current precision is established as a robust benchmark for evaluating interacting Andreev transport, extending beyond the limitations of non-interacting models. The ability to control current with high precision is crucial for applications ranging from metrology, where quantum devices aim for uncertainties below 10−8, to the development of nanoscale heat engines requiring both high efficiency and substantial power output.

Furthermore, the study explores both single quantum dot and double quantum dot configurations, capturing the effects of both local and non-local Andreev processes. Through a reduced density-matrix formalism, the researchers treat Coulomb interactions exactly, providing a detailed understanding of how these interactions affect transport resonances and superconducting coherence. This detailed analysis establishes a foundation for designing future hybrid superconducting devices with enhanced current control and improved thermodynamic performance.

Real time diagrammatic approach to calculating current and fluctuations in normal-superconducting systems

A generalized master equation, formulated using real-time diagrammatics and full counting statistics, underpins the study of Andreev-mediated transport and current fluctuations in interacting normal-superconducting dot systems. The research establishes the steady-state current, zero-frequency noise, and rate of entropy production within the limit of a large superconducting gap.

Coulomb interactions are demonstrated to modify Andreev-mediated transport by renormalizing resonant conditions and suppressing superconducting coherence, resulting in a noticeable reduction in current precision even with only minor effects on average currents. The methodology begins with consideration of an interacting central region connected to a superconducting electrode and one or two normal electrodes, as depicted schematically in the work.

The superconducting electrode couples to the central region via both a local tunneling rate, denoted as ΓS, and a nonlocal tunneling rate, ΓC, effectively transferring and splitting electron pairs. Assuming an infinitely large superconducting gap simplifies the analysis, allowing transport processes to be represented as an effective pairing term within the central region’s Hamiltonian.

Normal leads are assumed to be in local thermal equilibrium, described by a Hamiltonian incorporating electron creation and annihilation operators. Tunneling between the leads and the central region is governed by coupling amplitudes, with simplified assumptions made regarding the normal lead couplings to facilitate calculations.

The dynamics of the central region are then determined by its reduced density matrix, evolving according to a generalized master equation. This equation, expressed in the steady-state, relates the matrix elements to generalized transition rates, calculated using a real-time diagrammatic technique to systematically expand the coupling Hamiltonian while preserving interaction dependence.

The study computes these rates to linear order in the coupling strengths, including the normal lead tunneling rate and the local and nonlocal superconducting tunneling rates. To determine stationary current cumulants, full counting statistics are employed, introducing a counting field χ to dress the jump terms and define a χ-dependent rate kernel.

The current and zero-frequency noise are then calculated using this kernel and its derivatives, utilizing a superoperator formalism to streamline the calculations and define relevant operators within a superspace. This approach allows for a robust benchmark of interacting Andreev transport beyond the noninteracting limit, establishing current precision as a key metric.

Andreev transport precision is diminished by Coulomb interactions and thermal fluctuations

Current precision was established as a robust benchmark for interacting Andreev transport, demonstrating the interplay between Coulomb interactions and nonequilibrium fluctuations in hybrid superconducting devices. The study employed a generalized master equation, utilising real-time diagrammatics and full counting statistics to analyse Andreev-mediated transport in normal-superconducting dot systems.

This approach enabled the calculation of steady-state current, zero-frequency noise, and the rate of entropy production within the large superconducting-gap limit. Analyses of single quantum dot systems revealed how Coulomb interactions renormalise resonant conditions and suppress superconducting coherence, leading to a pronounced reduction in current precision even when average currents remain relatively stable.

These effects become particularly significant at higher temperatures, where conventional Coulomb-blockade features are thermally broadened, but fluctuation properties retain their sensitivity. Violations of the quantum bound, observed in non-interacting regimes, were progressively reduced and ultimately suppressed as interaction strength increased.

Furthermore, the recently proposed hybrid bound remained satisfied throughout the investigation, confirming its robustness even with strong interactions. The research extended to double quantum dot systems, capturing both local and nonlocal Andreev processes, and systematically assessed how interactions modify transport resonances and suppress superconducting coherence, impacting current precision. This work clarifies the combined influence of Coulomb interactions and nonequilibrium fluctuations on transport properties in hybrid superconducting devices, establishing current precision as a key metric for evaluating interacting Andreev transport beyond the non-interacting limit.

Coulomb interactions renormalise superconducting transport and suppress thermodynamic uncertainty relations

Andreev-mediated transport in interacting normal-superconducting dot systems exhibits modified resonant conditions and suppressed superconducting coherence due to Coulomb interactions. These interactions significantly reduce current precision, even when average currents remain relatively unaffected, particularly at higher temperatures where conventional Coulomb blockade effects are less pronounced.

Analysis reveals that violations of established thermodynamic uncertainty relations progressively diminish and are ultimately suppressed as interaction strength increases. The research employed a generalized master equation, real-time diagrammatics, and full counting statistics to compute steady-state current, zero-frequency noise, and entropy production in quantum-dot systems with a large superconducting gap.

Treating Coulomb interactions precisely, the study demonstrates that these interactions impact superconducting transport beyond their influence on average currents by renormalizing resonances and reducing coherent contributions. Current precision serves as a robust indicator of interacting Andreev transport, extending beyond the non-interacting limit and providing a quantitative measure of interaction-induced constraints.

While a quantum thermodynamic uncertainty relation is initially violated in the non-interacting regime, a hybrid bound remains consistently satisfied, confirming its robustness for Andreev-dominated transport. The authors acknowledge limitations related to the complexity of modelling strongly correlated systems and the approximations inherent in the reduced density-matrix formalism.

Future work could explore the effects of dissipation and dephasing on current precision, as well as investigate the behaviour of more complex hybrid superconducting devices. These findings establish current precision as a valuable tool for characterizing renormalization and decoherence in hybrid superconducting devices, clarifying the interplay between superconducting coherence, electron interactions, and nonequilibrium fluctuations.