Higher-order geometric phase for qubits in a bichromatic field

TL;DR

This paper investigates the higher-order geometric phase in a spin qubit driven by bichromatic fields, revealing that the phase manifests as a shift in Rabi frequency and is observable through frequency shifts in Rabi oscillations.

Contribution

The study demonstrates the existence of a higher-order geometric phase in qubits driven by bichromatic fields and experimentally detects it via frequency shifts in Rabi oscillations.

Findings

Higher-order geometric phase does not vanish at even orders of adiabaticity.

The phase manifests as a shift in Rabi frequency.

Experimental detection via electron paramagnetic resonance.

Abstract

The geometric phase in the dynamics of a spin qubit driven by transverse microwave (MW) and longitudinal radiofrequency (RF) fields is studied. The phase acquired by the qubit during the full period of the "slow" RF field manifests in the shift of Rabi frequency \omega_{1} of a spin qubit in the MW field. We find out that, for a linearly polarized RF field, this shift does not vanish at the second and higher even orders in the adiabaticity parameter \omega_{rf} / \omega_{1}, where \omega_{rf} is the RF frequency. As a result, the adiabatic (Berry) phases for the rotating and counter-rotating RF components compensate each other, and only the higher-order geometric phase is observed. We experimentally identify that phase in the frequency shift of the Rabi oscillations detected by a time-resolved electron paramagnetic resonance.