Geometric Phase for Analytically Solvable Driven Time-Dependent Two-Level Quantum Systems
I. Mendaš, N. Burić, D.B. Popović, S. Prvanović and M. Radonjić
Institute of Physics, University of Belgrade, Pregrevica 118, 11080 Belgrade, Serbia
Received: May 11, 2013; Revised version: April 16, 2014; In final form: May 23, 2014
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Geometric phase for novel analytical solutions (Barnes and Das Sarma) of time-dependent two-level quantum systems is discussed, specifically for a general single-axis driving term, which is represented by a function J(t) in the Hamiltonian, and its corresponding evolution operator. It is demonstrated how general results for corresponding phases (total, dynamic and geometric) can be obtained. Using a specific case, it was found that over time in which the driving field is appreciably different from zero, the corresponding geometric phase changes (in the specific example by Δ β ≈ 0.8 radians) thus enabling detection. The results are relevant to qubit control and to quantum computing applications.

DOI: 10.12693/APhysPolA.126.670
PACS numbers: 03.65.Aa, 03.65.Vf, 07.05.Dz