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Chinese Physics Letters

Nonadiabatic Geometric Phase in Composite Systems and Its Subsystem

Xin Li

Published Oct 30, 2008• 0 citations
Publisher

Abstract

We point out that the time-dependent gauge transformation technique may be effective in investigating the nonadiabatic geometric phase of a subsystem in a composite system. As an example, we consider two uniaxially coupled spin —1/2 particles with one of particles driven by rotating magnetic Geld. The influences of coupling and precession frequency of the magnetic Geld on geometric phase are also discussed in detail.

DOI
10.1088/0256-307x/25/11/005

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We point out that the time-dependent gauge transformation technique may be effective in investigating the nonadiabatic geometric phase of a subsystem in a composite system. As an example, we consider two uniaxially coupled spin —1/2 particles with one of particles driven by rotating magnetic Geld. The influences of coupling and precession frequency of the magnetic Geld on geometric phase are also discussed in detail.
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The effect of intersubsystem coupling on the Berry phase of a composite system as well as that of its subsystem is investigated. We analyze two coupled spin-12\frac{1}{2}21​ systems with one driven by a quantized field as an example. The pure-state geometric phase of the composite system as well as the mixed-state geometric phase for the subsystem is calculated and discussed.
The influence of intersubsystem coupling on the cyclic adiabatic geometric phase in bipartite systems is investigated. We examine the geometric phase effects for two uniaxially coupled spin-12\frac{1}{2}21​ particles, both driven by a slowly rotating magnetic field. It is demonstrated that the relation between the geometric phase and the solid angle enclosed by the magnetic field is broken by the spin-spin coupling, in particular leading to a quenching effect on the geometric phase in the strong coupling limit.
The Berry phase in a composite system induced by the time-dependent interaction is discussed. We choose two coupled spin-1/2 systems as the composite system: one of the subsystems is subjected to a static magnetic field, and the coupling parameters between two spins are controllable in time. We show that the time-dependent interaction can induce the Berry phase in a similar way as that a spin-1/2 system (qubit) is driven by an effective time-dependent magnetic field.Furthermore, using two consecutive cycles with opposite directions of both the static magnetic field as well as opposite signs of the coupling parameters, a nontrivial two-qubit unitary transformation purely based on Berry phases can be constructed.