Geometric phases in open tripod systems

TL;DR

This paper investigates geometric phases in a four-level tripod quantum system during STIRAP, analyzing how decoherence affects phase acquisition and gate fidelity, with implications for quantum information processing.

Contribution

It introduces a method to calculate complex geometric phases in open quantum systems and links these phases to the fidelity of quantum gates.

Findings

Open systems acquire complex geometric phases due to decoherence.

Fidelity of the implemented gate decreases with increasing decoherence.

The deviation from ideal gate operation correlates with the complex phases acquired.

Abstract

We first consider stimulated Raman adibatic passages (STIRAP) in a closed four-level tripod system. In this case, the adiabatic eigenstates of the system acquire real geometric phases. When the system is open and subject to decoherence they acquire complex geometric phases that we determine by a Monte Carlo wave function approach. We calculate the geometric phases and the state evolution in the closed as well as in the open system cases and describe the deviation between these in terms of the phases acquired. When the system is closed, the adiabatic evolution implements a Hadamard gate. The open system implements an imperfect gate and hence has a fidelity below unity. We express this fidelity in terms of the acquired geometric phases.