A study published in Phys. Rev. B discusses two methods to calculate Andreev bound state (ABS) energies of a single-level quantum dot connected to superconducting leads, forming a functionalized Josephson junction.
Extraction from quantum Monte Carlo (QMC) Data: The first method allows for extracting ABS energies from finite-temperature, imaginary-time (QMC) data without needing analytic continuation techniques. The analytic continuation of stochastic data produced by the Monte Carlo method is a notorious ill-conditioned problem which can be circumvented by the method presented in this work.
Generalized Atomic Limit (GAL): The second method maps the full model onto an exactly solvable superconducting atomic limit with renormalized parameters. This provides a fast and reliable way to scan the parameter space of the model for interesting regimes. The GAL method, with a simple additional band correction, can provide solid quantitative agreement with computationally intensive techniques as numerical renormalization group (NRG) and quantum Monte Carlo (QMC) for measurable quantities like the ABS energies and Josephson current while being orders of magnitude less expensive.
ABSs play a crucial role in the transport properties of Josephson junctions. By making it easier to understand and control their behavior, researchers can explore new possibilities in quantum computing, sensing, and other advanced technologies and accelerate the development of quantum devices.
Contact person: Vladislav Pokorný