Effect of Berry's Phase in a Degenerte System II : Analysis of NQR Spectrum by Using a Hamiltonian in Rotating Frame

Pratul Bandyopadhyay

H. Asakura, Akio Sakurai

We examine the mixing effect induced by the non-Abelian Berry's phase appearing in a nuclear quadrupole system rotating about two axes by using the rotating frame formulation. A non-trivial mixing between spin states after one period of motion is found. The origin of the mixing is discussed.

Yuriy Mokrousov

Donald H. Kobe, Valdir C. Aguilera-Navarro, Samuel Maier Kurcbart +1 more

The probability amplitude for a spin-1/2 particle in a precessing magnetic field to be in an energy eigenstate is calculated exactly. The probability for the particle to be in a given energy eigenstate and the corresponding phase of the amplitude are obtained. In the adiabatic limit there are no transitions, and the phase is the sum of the dynamical phase and the Berry phase. When a unitary transformation is made, the Hamiltonian and the energy operator transform differently. The energy eigenvalues, Berry phases, and probability amplitudes calculated in a frame rotating with the magnetic field are the same as in the laboratory frame. If the energy operator is incorrectly taken to be the Hamiltonian in the rotating frame, incorrect energy eigenvalues, Berry phases, and probability amplitudes are obtained. Nevertheless, in the adiabatic limit the correct total phase results.

Dieter Suter, Gerard C. Chingas, Robert A. Harris +1 more

According to Berry, quantum states of a hamiltonian which varies adiabatically through a circuit C in parameter space may acquire geometrical phase factors exp (iγ(C)) in addition to the normal dynamical phase factors exp ((-i/ħ) ∝ E(t) dt). We present N.M.R. experiments in the rotating frame which bear out these predictions for simple conical circuits, and point out that they are related to familiar behaviour based on the classical Bloch equations and on Haeberlen-Waugh coherent averaging theory. Extensions to coupled spins and electric quadrupolar effects are discussed.

I. V. Bukanov, E. A. Tolkachev, A. Ya. Tregubovich