Rabi oscillations in gravitational fields: Exact solution

Mekki Aouachria, L. Chétouani

Jan Mostowski, Kazimierz Rza̧żewski

Bernard Deconinck, P. G. Kevrekidis, Hector E. Nistazakis +1 more

In this paper, an exact unitary transformation is examined that allows for the construction of solutions of coupled nonlinear Schr\"odinger equations with additional linear field coupling, from solutions of the problem where this linear coupling is absent. The most general case where the transformation is applicable is identified. We then focus on the most important special case, namely the well-known Manakov system, which is known to be relevant for applications in Bose-Einstein condensates consisting of different hyperfine states of $^{87}\mathrm{Rb}$. In essence, the transformation constitutes a distributed, nonlinear as well as multi-component generalization of the Rabi oscillations between two-level atomic systems. It is used here to derive a host of periodic and quasi-periodic solutions including temporally oscillating domain walls and spiral waves.

Mekki Aouachria

Yumei Gao

In this paper we obtained the exact solution of spin-1 particles under rotating magnetic field with the rotating frame method.The accurate analytic expressions of some important physical quantities,such as the polarization vector,three energies Rabi oscillation,non-adiabatic dynamic and geometric phases are obtained.The numerical results for above physical quantities are reasonable.The exact solution is useful for discussing some problems in quantum optics and quantum computation.

Elica S. Kyoseva, Nikolay V. Vitanov

An exact analytic solution is presented for coherent resonant excitation of a two-state quantum system driven by a time-dependent pulsed external field with a hyperbolic-secant shape in the presence of dephasing. Analytic results are derived for the amplitude and phase shift of the damped Rabi oscillations.