2 00 6 Full and partial reversed transitions in a vertical optical lattice

Physical explanation of the origin of quantum resonances in a periodically kicked Bose-Einstein condensate is proposed. It is based on the assumption of inequality of the differential cross-sections of forward and partially reversed optical transitions. For quantitative determination of such differences, we propose to study the Bloch oscillations in a vertical optical lattice with short pulses of laser radiation. Rather usual situation in nonlinear optics is a case, when a physical phenomenon has good mathematical description, but without clear physical explanation. The most demonstrative example here is the Bloch equations, which give excellent description of the dynamics of optical transitions, but which do not have clear physical sense. Other example is the description of a cold atoms motion in an optical lattice with mathematical model based on the Gross-Pitaevskii equation [1]. It is supposed here, that the polarization interaction of atoms with a periodic standing wave is the physical base of the phenomenon. However, there is a fact, that the amplitude of the Bloch oscillations greatly exceeds the lattice period. It makes physically meaningless the polarization explanation. In this note we shall discuss the origin of the so-called quantum resonances in a periodically kicked Bose-Einstein condensate (BEC) [2, 3]. The essence of the phenomenon is that the most efficient increasing of the momentum spread of the atoms under action of pulses of laser radiation occurs at some " resonance " time delay between the laser pulses. The value of " resonance " delay corresponds to the time at which the atoms pass in space the distance multiple of the optical lattice period. As usually, the phenomenon has good mathematical description, but does not have physical explanation. It was proposed early, that the inequality of forward and reversed processes is a physical base of the majority of phenomena in nonlinear optics [4]. This concept has several direct and enormous numbers of indirect experimental proofs. The essence of the concept is that in spite of the equality of integral cross-sections of forward and reversed transitions, its differential cross-sections can differ in many orders of magnitude. The cross-section of the reversed transition has very sharp dependence from the orientation of molecule in space, from