The generic Berry phase scenario in which a two-level system is coupled to a second system whose dynamical coordinate is slowly varying is generalized to allow for stochastic evolution of the slow system. The stochastic behavior is produced by coupling the slow system to a heat reservoir, which is modeled by a bath of harmonic oscillators initially in equilibrium at temperature $T$ , and whose spectral density has a bandwidth that is small compared to the energy-level spacing of the fast system. The well-known energy-level shifts produced by Berry's phase in the fast system, in conjunction with the stochastic motion of the slow system, leads to a broadening of the fast system energy levels. In the limit of strong damping and sufficiently low temperature, we determine the degree of level broadening analytically, and show that the slow system dynamics satisfies a Langevin equation in which Lorentz-like and electriclike forces appear as a consequence of geometrical effects. We also determine the average energy level shift produced in the fast system by this mechanism.The generic Berry phase scenario in which a two-level system is coupled to a second system whose dynamical coordinate is slowly varying is generalized to allow for stochastic evolution of the slow system. The stochastic behavior is produced by coupling the slow system to a heat reservoir, which is modeled by a bath of harmonic oscillators initially in equilibrium at temperature $T$, and whose spectral density has a bandwidth that is small compared to the energy-level spacing of the fast system. The well-known energy-level shifts produced by Berry's phase in the fast system, in conjunction with the stochastic motion of the slow system, leads to a broadening of the fast system energy levels. In the limit of strong damping and sufficiently low temperature, we determine the degree of level broadening analytically, and show that the slow system dynamics satisfies a Langevin equation in which Lorentz-like and electriclike forces appear as a consequence of geometrical effects. We also determine the average energy level shift produced in the fast system by this mechanism.

arXiv:quant-ph/9803026Physical Review ASep 1, 199822 citations

Dynamical manifestation of an evolving Berry phase as a frequency shift of the resonance transition between two eigenstates

Koichi Toriyama, Akihide Oguchi, Atsuo Morinaga

We investigate the phenomenon that a Berry phase evolving linearly in time induces a frequency shift of the resonance transition between two eigenstates, regardless of whether or not they are superposed. Using the magnetic-field-insensitive two-photon microwave---radio-frequency transition, which is free of any other dynamical frequency shift, we demonstrate that the frequency shift caused by a uniform rotation of the magnetic field corresponds to the derivative of the Berry phase with respect to time and depends on the direction of rotation of the magnetic field.We investigate the phenomenon that a Berry phase evolving linearly in time induces a frequency shift of the resonance transition between two eigenstates, regardless of whether or not they are superposed. Using the magnetic-field-insensitive two-photon microwave---radio-frequency transition, which is free of any other dynamical frequency shift, we demonstrate that the frequency shift caused by a uniform rotation of the magnetic field corresponds to the derivative of the Berry phase with respect to time and depends on the direction of rotation of the magnetic field.

Physical Review ADec 2, 20115 citations

T

, and whose spectral density has a bandwidth that is small compared to the energy-level spacing of the fast system. The well-known energy-level shifts produced by Berry's phase in the fast system, in conjunction with the stochastic motion of the slow system, leads to a broadening of the fast system energy levels. In the limit of strong damping and sufficiently low temperature, we determine the degree of level broadening analytically, and show that the slow system dynamics satisfies a Langevin equation in which Lorentz-like and electriclike forces appear as a consequence of geometrical effects. We also determine the average energy level shift produced in the fast system by this mechanism.