Berry phase in entangled systems: A proposed experiment with single neutrons

Abstract

The influence of the geometric phase, in particular the Berry phase, on an entangled spin-1 2 system is studied. We discuss in detail the case, where the geometric phase is generated only by one part of the Hilbert space. We are able to cancel the effects of the dynamical phase by using the "spin-echo" method. We analyze how the Berry phase affects the Bell angles and the maximal violation of a Bell inequality. Furthermore we suggest an experimental realization of our setup within neutron interferometry.

Entanglement, Bell Inequalities and Decoherence in Particle Physics

“…In this case it is physically rather contextuality than nonlocality which is tested experimentally [118,112,119,120].…”

“…However, above Theorems (117), (118) are necessary and sufficient separability conditions -and so surprisingly simple-only for dimensions 2 ⊗ 2 and 2 ⊗ 3 [97]. A more general separability-entanglement criterion, valid in any dimensions, does exist; it is formulated by a so-called generalized Bell inequality, see Ref.…”

“…Geometric phases such as the Berry phase [113] play a considerable role in physics and arise in a quantum system when its time evolution is cyclic and adiabatic. There is increasing interest in combining both the geometric phase and the entanglement of a system [114,115,116,117,118].…”

“…[118] we have studied the influence of the Berry phase on the entanglement of a spin-1 2 system by generating the Berry phase with an adiabatically rotating magnetic field in one of the paths of the particles, and we have eliminated the dynamical phase -being sensitive just to the geometric phase-by a "spin-echo" method. We have considered a pure entangled system where a phase -like our geometrical one-does not change the amount of entanglement and therefore not the extent of nonlocality of the system, which is determined by the maximal violation of a BI.…”

“…ii) Entanglement or lack of separability is determined by Theorems (117) and (118). The Peres-Horodecki partial transposition criterion (117) (…”