# Mesoscopic fluctuations in biharmonically driven flux qubits

**Authors:** Alejandro Ferrón, Daniel Domínguez, María José Sánchez  
**arXiv:** [1610.07502](https://arxiv.org/abs/1610.07502)  
**Date:** 2016-10-24  
**Summary page:** https://www.summarizepaper.com/en/paper/1610.07502v1/

## Key points

- Authors investigate flux qubits driven by a biharmonic magnetic signal with a phase lag
- Focus on driving-induced transition rate between ground and excited states of flux qubit
- Concept of effective transmitance based on analogy to interference effects in disordered electronic systems
- Experimentally accessed transition rate for time scales prior to full relaxation but larger than decoherence time
- Sensitivity of transition rate to phase lag and dc flux detuning explored
- Comparison of experimental results with phenomenological model considering only decoherence as classical noise
- Full dynamics of driven flux qubits solved using Floquet Markov Master equation in contact with quantum bath
- Relaxation and decoherence rates strongly depend on phase lag and dc flux detuning within this formalism
- Fluctuations in characteristic rates show significant differences compared to phenomenological model, including Weak Localization-like effect in average values of relaxation rate
- Predictions can be tested for longer time scales than currently accessible experimentally

## Summary

In this study, the authors investigate flux qubits driven by a biharmonic magnetic signal with a phase lag that acts as an effective time reversal broken parameter. They focus on the driving-induced transition rate between the ground and excited states of the flux qubit, which can be considered as an effective transmitance. This concept is based on the analogy between interference effects at avoided level crossings in flux qubits and scattering events in disordered electronic systems. The characteristic rate of this transition has been experimentally accessed for time scales prior to full relaxation but larger than the decoherence time. The authors explore its sensitivity to both the phase lag and the dc flux detuning. They compare these experimental results with a phenomenological model that only takes into account decoherence as classical noise. To provide a more comprehensive understanding of the dynamics of driven flux qubits, they solve the full dynamics of these systems in contact with a quantum bath using the Floquet Markov Master equation. Within this formalism, they find that relaxation and decoherence rates strongly depend on both the phase lag and dc flux detuning. By analyzing fluctuations in these characteristic rates, they observe significant differences compared to those obtained within the phenomenological model. Specifically, they demonstrate a Weak Localization-like effect in the average values of the relaxation rate. The predictions made in this study can be tested for longer time scales than those currently accessible experimentally. Overall, this research provides valuable insights into mesoscopic fluctuations in biharmonically driven flux qubits and highlights important factors influencing their dynamics.