Geometric phases in superconducting qubits beyond the two-level-approximation

TL;DR

This paper investigates the adiabatic geometric phase in a multi-level superconducting transmon circuit, highlighting the influence of higher energy levels and the limits of adiabaticity beyond the two-level approximation.

Contribution

It extends the study of geometric phases to multi-level superconducting qubits, experimentally measuring higher level effects and testing adiabaticity in a complex quantum system.

Findings

Higher energy levels contribute to the geometric phase as predicted by perturbation theory.

The geometric phase remains independent of evolution time within the adiabatic regime.

Transition to non-adiabatic regime affects the geometric phase validity.

Abstract

Geometric phases, which accompany the evolution of a quantum system and depend only on its trajectory in state space, are commonly studied in two-level systems. Here, however, we study the adiabatic geometric phase in a weakly anharmonic and strongly driven multi-level system, realised as a superconducting transmon-type circuit. We measure the contribution of the second excited state to the two-level geometric phase and find good agreement with theory treating higher energy levels perturbatively. By changing the evolution time, we confirm the independence of the geometric phase of time and explore the validity of the adiabatic approximation at the transition to the non-adiabatic regime.