Geometric Phase with Nonunitary Evolution in the Presence of a Quantum Critical Bath

F.M. CUCCHIETTI, J.-F. ZHANG, F.C. LOMBARDO, P.I. VILLAR, AND R. LAFLAMME

PHYSICAL REVIEW LETTERS

AMER PHYSICAL SOC

Lugar: New York; Año: 2010 vol. 105 p. 2404061 - 2404064

0031-9007

Geometric phases, arising from cyclic evolutions in a curved parameter space, appear in a wealth ofphysical settings. Recently, and largely motivated by the need of an experimentally realistic definition forquantum computing applications, the quantum geometric phase was generalized to open systems. Thedefinition takes a kinematical approach, with an initial state that is evolved cyclically but coupled to anenvironment—leading to a correction of the geometric phase with respect to the uncoupled case. We obtainthis correction by measuring the nonunitary evolution of the reduced density matrix of a spin one-halfcoupled to an environment. In particular we are interested in baths near a quantum phase transition, which areknown to induce strong decoherence. The experiments are done with a NMR quantum simulator, where weemulate qualitatively the influence of a critical environment using a simple one-qubit model.