Circuit QED theory of direct and dual Shapiro steps with finite-size transmission line resonators
arXiv:2405.12935 · doi:10.1103/PhysRevApplied.22.054061
Abstract
We investigate the occurrence of direct and dual Shapiro steps for a Josephson junction coupled to a finite-size transmission line resonator. We treat both problems through a circuit QED approach with a large, but finite number of photon modes. For the dual case, we do not assume the (approximate) charge-phase duality, but include the full multi-band dynamics for the Josephson junction. Mean-field equations within such Hamiltonian approach reproduce the result obtained through a dissipative classical equation when the number of transmission line modes is large enough. To account for quantum and thermal fluctuations, we go beyond the mean-field treatment within a truncated Wigner approach. The fluctuations are shown to modify both the direct and the dual steps. We show how the dual steps are very sensitive to these fluctuations and identify the key physical parameters for the junction and the transmission line controlling their robustness, which is essential for applications to close the quantum metrological triangle.
15 pages, 9 captioned figures. Version accepted for publication in Physical Review Applied. Minor additions to figures 5, 7, and 9
References in corpus (16)
- Charge insensitive qubit design derived from the Cooper pair box
- Quantum fluids of light
- Circuit Quantum Electrodynamics
- Dynamics and statistical mechanics of ultra-cold Bose gases using c-field techniques
- Quantized current steps due to the a.c. coherent quantum phase-slip effect
- Observation of quantum many-body effects due to zero point fluctuations in superconducting circuits
- Inelastic scattering of a photon by a quantum phase-slip
- Down-conversion of a single photon as a probe of many-body localization
- Superconductivity from a melted insulator
- On chip synchronization of Bloch oscillations in a strongly coupled pair of small Josephson junctions
- Demonstration of dual Shapiro steps in small Josephson junctions
- Emergent quantum phase transition of a Josephson junction coupled to a high-impedance multimode resonator
- Tuning the inductance of Josephson junction arrays without SQUIDs
- Heat bath in a quantum circuit
- Bloch oscillations in a transmon embedded in a resonant electromagnetic environment
- High-frequency suppression of inductive coupling between flux qubit and transmission line resonator