Theory

Two-Photon Absorption and Raman Scattering

Two-Photon Absorption and Ionization

The process of two-photon absorption is similar to ordinary single photon absorption. In this process an electron absorbs two photons at approximately the same time (or within less than a nanosecond) and achieves an excited state that corresponds to the sum of the energy of the incident photons. There need not be an intermediate state for the atom to reach before arriving at the final excited state (as if it were moving up two stair steps by stepping one at a time). Instead, the atom is excited to a "virtual state" which need not correspond to any electronic or vibrational energy eigenstate.

Selection rules for these transitions logically from selection rules for one photon transitions. With Cesium, the electron begins in the ground state s-orbit and has an angular momentum of zero. With one photon absorption, an electron may transition only if the change in angular momentum (change in L) is +1 or -1. Since photons have angular momentum of +1 or -1, an electronic state absorbing two photons simultaneously may change angular momentum by +2, 0. Two L =+1 photons cause a change of +2; a photon of L = +1 and L = -1 cause a change of 0. Thus the selection rules for two-photon absorption in Cesium allow the excited electron to either be in an s or d state. An electron cannot transition from an s-state to a p-state by two-photon absorption. The following diagram demonstrates these selection rules:

Through two-photon absorption we can populate high energy levels that are otherwise unreachable by single photon transitions from the ground state. Once electrons have absorbed two photons and are at a high energy level it takes no more than the absorption of another photon to release the electron and ionize the atom. If there is an intense, monochromatic photon source (such as a high energy laser) used to excite these atoms through two-photon absorption, it is assured that there are ample photons to continue the excitation process and ionize the electron before it radiates back to a lower energy level.

Rydberg Atoms

Rydberg Atoms are atoms that have a large atomic number, therefore having their outermost electrons already in a high energy level. Because they have so many inner core electrons, there behavior is analogous to the behavior of the Hydrogen atom. These atoms have relatively low ionization energies and are ideal to study in ionization experiments. Rydberg atoms are also convenient for the study of the process of two-photon absorption because the differences between the outer energy levels are not very large. For these reasons we chose to use Cesium (z number of 55) in our study of two-photon absorption and ionization.

Quantum Defect

In our experiment we are also concerned with the quantum defect, which is a correction variable involved in the expression for energy levels. The quantum defect essentially accounts for the variation in shielding that an outer electron of a Rydberg Atom will experience through the course of one of its orbits around the nucleus. A Rydberg Atom has a large nucleus filled with protons and thus produces a considerable eletric field. This electric field is mostly shielded by the electrons in the inner orbits. However, depending on the orbital of the outer electron (or the angular momentum quantum number L), the shielding experienced by the outer electron is not constant at all points in its orbit. The quantum defect then accounts for this variant shielding in our energy expression and depends on the orbit of the electron. The the quantum defect should be higher for states of lower angular momentum, since an electron in a state of low angular momentum undergoes considerable variant shielding. An s-state electron essentially passes through all the shielding since it has zero angular momentum. We later find the quantum defect of various energy levels for the s and d states of Cesium with the following expression (where R is the Rydberg constant).

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