Description
A model of a two-level atom with quantized center of mass motion moving under two coupled linear potentials is established and an exactly solvable case is presented. If the atom is initially in one of its two internal states, for the exactly solvable case it is found that the coupling always sends half the population to the other level and that it leads to an exponential growth of the root- mean-square deviations of position and momentum. In the general case a criterion is deduced so one can determine when the coupling can be neglected. The model can describe an alkali-metal atom when the two levels are hyperfine ground states and it is moving under a constant gravitational acceleration and in the presence of a constant magnetic field gradient, since the use of the exact eigenvectors of an alkali-metal atom corresponding to the exact eigenvalues provided by the Breit- Rabi formula induce the aforementioned coupling. In this context it is used to determine the limits imposed to the total interferometer time in T3 atomic interferometry, since the coupling can lead to unwanted and uncontrollable transitions between the two internal levels of the atom.
