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Geometric nature of the environment-induced Berry phase and geometric dephasing

Robert S. Whitney·Yuriy Makhlin·Alexander Shnirman·Yuval Gefen
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Abstract

We investigate the geometric phase or Berry phase (BP) acquired by a spin-half which is both subject to a slowly varying magnetic field and weakly-coupled to a dissipative environment (either quantum or classical). We study how this phase is modified by the environment and find that the modification is of a geometric nature. While the original BP (for an isolated system) is the flux of a monopole-field through the loop traversed by the magnetic field, the environment-induced modification of the BP is the flux of a quadrupole-like field. We find that the environment-induced phase is complex, and its imaginary part is a geometric contribution to dephasing. Its sign depends on the direction of the loop. Unlike the BP, this geometric dephasing is gauge invariant for open paths of the magnetic field.

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Robert S. Whitney, Yuriy Makhlin, Alexander Shnirman, Yuval Gefen. 2005-01-26. Geometric nature of the environment-induced Berry phase and geometric dephasing. https://doi.org/10.1103/physrevlett.94.070407

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