Population control in nearly degenerate N-state atoms

Kh. Yu. Rakhimov

Thomas J. Carroll, Donald P. Fahey, Michael W. Noel +2 more

Wolff, J., C. Newell, A. Martin +1 more

We consider the time evolution of nearly degenerate two-state systems with an external interaction. Conditions in which full population transfer is possible when the two-states become degenerate are considered. A new variation of the coupled differential equations for the probability amplitudes suggests a possible singularity in the time evolution of the system. The singularity occurs at the point in time where full control in the degenerate limit is achieved. We solve this new variation to derive more information about non-degenerate population control. The new results of numerical calculations for occupational probabilities of non-degenerate systems are presented and interpreted. These results are used to understand how population control breaks down as the photon energy and the energy of the system are changed. Applications are discussed, with an emphasis on interactions of twisted-vortex and plane-wave photons with a variety of targets, including macroscopic gas cells of atoms, of large single crystals, and of molecules.

Nirit Dudovich, Dan Oron, Yaron R. Silberberg

The newly developed technique of polarization pulse shaping is applied to the control of two-photon absorption in atomic rubidium. This technique enables the manipulation of the transient vector properties of a light matter interaction. We establish that control can be exerted on the angular distribution of the final state, and demonstrate the ability to control the final state population of a nearly degenerate system, as well as to perform M-state resolved spectroscopy.

Moorad Alexanian, Subir K. Bose

Ioannis Thanopulos, Petr Král, Moshe Shapiro

We present an analytic solution to the "degenerate quantum control problem," which enables the transfer of any desired fraction of population between arbitrary initial and final pure wave packets, made up of nearly degenerate energy eigenstates. It consists of two two-photon adiabatic passage steps, in which the population of the initial wave packet is first transferred, via a number of nondegenerate intermediate states, to a single eigenstate and then returned to a different target superposition state. We demonstrate the approach by executing a stepwise isomerization of three Jahn-Teller states of the Al3O molecule, where a proper optical coupling can easily be established.