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Journal of Physics B Atomic Molecular and Optical Physics

The effect of intersubsystem coupling on the geometric phase in a composite system driven by decohering quantized fields

Jibing Liu, Jiahua Li, Wei Hua, Xiao-Tao Xie, Weibin Li

Published Feb 15, 2006• 5 citations
Publisher

Abstract

We investigate the behaviour of the geometric phase of a bipartite system with intersubsystem coupling via a quantum jump approach, where one of the subsystems is driven by a one- or two-mode quantized field which is also subjected to decoherence. The results show that the first correction due to the decohering field is only quadratic in decaying rate λ when the evolution of the system is adiabatic, and the lowest order correction is related to the first order in λ when the evolution of the system is non-adiabatic. Moreover, an interesting interpretation of this phenomenon is given.

DOI
10.1088/0953-4075/39/5/017

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We investigate the behaviour of the geometric phase of a bipartite system with intersubsystem coupling via a quantum jump approach, where one of the subsystems is driven by a one- or two-mode quantized field which is also subjected to decoherence. The results show that the first correction due to the decohering field is only quadratic in decaying rate λ when the evolution of the system is adiabatic, and the lowest order correction is related to the first order in λ when the evolution of the system is non-adiabatic. Moreover, an interesting interpretation of this phenomenon is given.
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.
Quantum computer takes advantages from properties of superposition and entanglement, which are also very fragile and easy to be error. But they may be destroyed easily by a process called decoherence. Therefore, how to overcome the effect of decoherence is key to implement quantum computer. Using the no-jump trajectory, Berry's and AA's formula for geometric phase, we calculate the geometric phase of a spin-1/2 system driven by one and two mode quantum fields subject to decoherence in the adiabatic and nonadiabatic case, respectively. By quantum jump method, we find that the corrections to its phase for the no-jump trajectory are different when considering adiabatic and nonadiabatic evolutions. Finally, we discuss the implications of our results from fundamental and quantum computational points.
We investigate the geometric phase for a quantum field driven by an external source and subjected to spontaneous decay from coupling to the reservoir. Starting from a coherent state, we analyze the effect of decoherence when the system undergoes a nonadiabatic cyclic evolution in phase space, and show that the lowest correction to the conventional geometric phase is quadratic in the decaying rate of the quantum field. This is in distinct contrast with the nonadiabatic geometric phase associated with the evolution of a spin system subjected to spontaneous decay, which contains the first-order correction term. We further show that the unconventional geometric phase is also robust to field decay.
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.