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arXiv:quant-ph/0407231 · Physical Review A

Off-diagonal geometric phase in composite systems

X. X. Yi, Junli Chang

Published Jul 20, 2004• 8 citations
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Abstract

The effect of the intersubsystem coupling on the off-diagonal geometric phase in a composite system is investigated. We analyze the case where the system undergoes an adiabatic evolution. Two coupled qubits driven by time-dependent external magnetic fields are presented as an example; the off-diagonal geometric phase as well as the adiabatic condition are examined and discussed.

DOI
10.1103/physreva.70.012108

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The effect of the intersubsystem coupling on the off-diagonal geometric phase in a composite system is investigated. We analyze the case where the system undergoes an adiabatic evolution. Two coupled qubits driven by time-dependent external magnetic fields are presented as an example; the off-diagonal geometric phase as well as the adiabatic condition are examined and discussed.
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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.
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.
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