Strong-coupling BCS models of Josephson qubits.

Area of Science:

• Condensed Matter Physics
• Quantum Computing

Background:

• Superconducting qubits are crucial for quantum computing, but their theoretical descriptions often rely on simplified models.
• Existing phenomenological models for Josephson junctions may not fully capture their complex quantum behavior.

Purpose of the Study:

• To derive microscopic models for small Josephson junctions (charge, flux, and phase qubits) using the strong-coupling BCS theory.
• To present alternative formulae for superconducting qubit spectra incorporating microscopic parameters.
• To investigate the emergence of degenerate energy levels and their implications for qubit behavior.

Main Methods:

• Application of the strong-coupling version of the Bardeen-Cooper-Schrieffer (BCS) theory.
• Derivation of microscopic models for various Josephson qubit types.
• Comparison of derived formulae with experimental data.

Main Results:

• Microscopic models reveal more complex energy level structures than phenomenological models.
• Highly degenerate energy levels identified, acting as probability sinks for qubits.
• Novel formulae for superconducting qubit spectra incorporating microscopic parameters are presented.
• First-time estimation of Cooper pair density at zero temperature for an Al-based flux qubit.

Conclusions:

• The strong-coupling BCS theory provides a more detailed description of Josephson qubits.
• The identified degenerate levels highlight potential challenges and features in qubit design.
• The developed formulae offer a more accurate and physically grounded approach to analyzing superconducting qubit spectra.
• The study contributes to understanding small Josephson junctions as macroscopic quantum systems.