Geometric phase with nonunitary evolution in presence of a quantum critical bath

TL;DR

This paper investigates how a quantum critical environment affects the geometric phase of a spin-1/2 system, using NMR simulations to reveal criticality information encoded in decoherence during nonunitary evolution.

Contribution

It introduces a method to measure geometric phase corrections in open quantum systems coupled to a tunable critical bath, with experimental validation using NMR.

Findings

Criticality influences the geometric phase via the decoherence factor.

The geometric phase encodes information about the quantum phase transition.

Experimental results confirm the theoretical predictions.

Abstract

Geometric phases, arising from cyclic evolutions in a curved parameter space, appear in a wealth of physical settings. Recently, and largely motivated by the need of an experimentally realistic definition for quantum computing applications, the quantum geometric phase was generalized to open systems. The definition takes a kinematical approach, with an initial state that is evolved cyclically but coupled to an environment --- leading to a correction of the geometric phase with respect to the uncoupled case. We obtain this correction by measuring the nonunitary evolution of the reduced density matrix of a spin one-half coupled to an environment. In particular, we consider a bath that can be tuned near a quantum phase transition, and demonstrate how the criticality information imprinted in the decoherence factor translates into the geometric phase. The experiments are done with a NMR quantum simulator, in which the critical environment is modeled using a one-qubit system.