Magnetic Flux Controls Current Phase in Double Quantum Dot Josephson Junction, Revealing State Transitions

Researchers are increasingly exploring quantum dots as building blocks for future superconducting circuits, and understanding how these components interact is crucial for developing advanced quantum technologies. Yiyan Wang, Cong Li, and Bing Dong from Shanghai Jiaotong University investigate the behaviour of a Josephson junction containing two quantum dots, focusing on how magnetic fields control the flow of current within the system. Their work demonstrates that manipulating magnetic flux allows precise control over the quantum states of the dots, driving transitions between different configurations and ultimately influencing the current phase relationship. This control is particularly significant because the team discovered conditions where increasing magnetic flux can stabilise a specific quantum state, and even induce a peak in the critical current, offering a pathway towards designing more efficient and robust superconducting devices.

The superconducting electrode is discretised into three distinct energy levels, and the tunneling coefficients are modified to create a finite system. This approach allows for detailed examination of the current-phase relationship, fundamentally important for understanding the behaviour of Josephson junctions and their potential applications in quantum technologies. The study focuses on how magnetic flux influences current flow through the double quantum dot system, providing insights into the interplay between superconductivity and quantum dot properties. By carefully controlling energy levels and tunneling characteristics, the researchers aim to achieve a deeper understanding of the mechanisms governing current flow in these nanoscale devices.

Two-dimensional surrogate Hamiltonian calculations determine the physical quantities of the system, and a low-energy effective model provides deeper physical insight. The research demonstrates that when only one quantum dot exhibits Coulomb interaction, the system undergoes a phase transition between singlet and doublet states. Magnetic flux has a minor influence on the singlet state, but significantly affects the doublet state. When both quantum dots have interactions, the system undergoes two phase transitions as the superconducting phase difference increases.

Josephson Current Modulation Via Quantum Dots

This research area explores the fundamental behaviour of Josephson junctions incorporating quantum dots. Scientists investigate how the Josephson current, or supercurrent, is affected by the presence of these quantum dots. Studies focus on the coupling between two quantum dots and how this interaction influences current flow. Different configurations, such as parallel and series coupling, alongside various geometries like T-shaped and side-coupled quantum dots, are examined to understand their impact on transport properties. Researchers also manipulate the phase of the supercurrent through the quantum dots and investigate effects like the Aharonov-Bohm and Casher phenomena, which demonstrate how magnetic and electric fields influence the current.

A crucial aspect of this research involves Andreev bound states and Yu-Shiba-Rusinov states, localized states forming at the interface between a superconductor and a quantum dot. Scientists focus on controlling these states to manipulate the Josephson current and characterize their properties through spectroscopy. Investigations extend to systems with multiple quantum dots, exploring their combined effect on these bound states, and examining non-local effects and the splitting of Cooper pairs, the fundamental charge carriers in superconductors. Beyond basic configurations, researchers explore more complex arrangements of quantum dots, including double quantum dot arrays and networks.

They investigate side-coupled and T-shaped quantum dots to tune electronic properties and treat coupled quantum dots as quantum dot molecules with unique characteristics. These studies build upon the core physics to create more sophisticated systems. Theoretical advancements are also central to this field. Scientists employ exact diagonalization, a powerful but computationally intensive method, to solve the many-body Schrödinger equation. Improved versions, such as distributional and infinite-dimensional exact diagonalization, are developed to handle larger systems.

Surrogate model solvers and self-consistent calculations are used to speed up calculations, and spectral function calculations determine the energy spectrum of the system. These computational techniques are essential for understanding the complex behaviour of these nanoscale devices. Specific phenomena, such as the Kondo effect and Mott transition, are also investigated. The Kondo effect arises from the interaction between electrons and localized magnetic moments, while the Mott transition involves a shift from a metallic to an insulating state. Researchers also study superconductivity and supercurrent control, as well as spin-dependent transport and thermal effects, to gain a comprehensive understanding of the system’s behaviour.

A key trend in this research is the focus on control and tuning of the Josephson junctions and quantum dots to achieve desired functionalities. This involves manipulating the geometry, applying external fields, and tuning the electronic properties. Understanding the complex many-body effects arising from the interactions between electrons is also crucial. The field is driven by the potential to create nanoscale devices with novel functionalities based on Josephson junctions and quantum dots, requiring continuous development of new theoretical methods and computational techniques to overcome the inherent challenges.

Flux and Interactions Control Junction Transitions

This research investigates the behaviour of Josephson junctions incorporating quantum dots, exploring how magnetic flux and interactions between the dots influence the system’s quantum state and critical current. By employing both direct Hamiltonian diagonalisation and a low-energy effective model, scientists have demonstrated a complex interplay between these factors, revealing transitions between doublet, singlet, and triplet states as the strength of interactions and magnetic flux are varied. Notably, the system exhibits a unique phase transition, shifting from a conventional 0-π transition to a 0-0 transition between different singlet states, influenced by the magnetic flux and interaction strength. The findings reveal that at specific interaction strengths, the critical current reaches a maximum, coinciding with a point where energy levels of different quantum states align, facilitating enhanced tunnelling and current flow.

Furthermore, the study demonstrates that increasing the tunnelling rate between the quantum dots and the superconducting electrodes can lead to a triple point in the system’s phase diagram, where singlet, doublet, and triplet states converge. The authors acknowledge that their low-energy effective model has limitations when the tunnelling rate becomes very high, and the quasi-particle excitation becomes significant. Future work could focus on refining these models to accurately capture the system’s behaviour across a wider range of parameters, and potentially exploring the implications of these findings for the development of novel quantum electronic devices.