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Chinese Journal of Quantum Electronics

Geometric phase of a spin-1/2 particle driven by decohering quantum in adiabatic and nonadiatic evolution

Feng Fu

Published Jan 1, 2006• 0 citations
OpenAlex

Abstract

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.

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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.