Geometric Phase and Non-Adiabatic Effects in an Electronic Harmonic Oscillator

TL;DR

This paper reports an experiment observing geometric phases in an electronic harmonic oscillator using a superconducting qubit, highlighting the effects of non-adiabatic dynamics and potential applications in quantum information processing.

Contribution

It demonstrates the measurement of geometric phases in an electronic oscillator with a superconducting qubit and explores non-adiabatic effects and phase corrections.

Findings

Geometric phase proportional to enclosed area in quadrature plane.

Non-adiabatic corrections and dephasing observed near transition regime.

System enables study of geometric phases and gates in open quantum systems.

Abstract

Steering a quantum harmonic oscillator state along cyclic trajectories leads to a path-dependent geometric phase. Here we describe an experiment observing this geometric phase in an electronic harmonic oscillator. We use a superconducting qubit as a non-linear probe of the phase, otherwise unobservable due to the linearity of the oscillator. Our results demonstrate that the geometric phase is, for a variety of cyclic trajectories, proportional to the area enclosed in the quadrature plane. At the transition to the non-adiabatic regime, we study corrections to the phase and dephasing of the qubit caused by qubit-resonator entanglement. The demonstrated controllability makes our system a versatile tool to study adiabatic and non-adiabatic geometric phases in open quantum systems and to investigate the potential of geometric gates for quantum information processing.