Multi-Photon Absorption and Ionization
In his famous discovery of the photoelectric effect, Albert Einstein reasoned that
photons might ionize an atom only if they had an energy greater than a particular
threshold energy corresponding to the ionization energy of the atom. In 1929, Maria
Göppert-Mayer predicted theoretically that an atom might absorb two or more photons
simultaneously, thus allowing an electron to transition to states unreachable by single
photon absorption (Andrews 319). An atom absorbing multiple photons simultaneously might
be ionized by photons with energies less than the threshold energy of which
Einstein spoke. Because any observable effect of this phenomenon could not be possible
without a very intense beam of radiation, her prediction could not be investigated in
detail until the construction of the first laser in 1960. We examined the phenomenon of
two-photon absorption or three-photon ionization using a Nd-YAG laser and DCM dye laser.
When a single photon collides with a ground state Cesium atom, the atom can absorb the
photon via electronic transitions to energy levels higher than the ground state by d E=hb w
. Flowing out of the mathematics of quantum mechanical wave functions, selection rules
govern these transitions such that the change in angular momentum in single photon
transitions is d l = +1, -1. Thus, an electron in a ground
state s-state may transition by one photon only to a higher p-state. When an atom absorbs two
photons simultaneously, the electron will change angular momentum by d
l = +2, 0, or -2, since each photon has angular momentum of +1 or 1. This allows an
s-state electron to transition to another s-state or to a d-state: states out-of-reach by
single photon absorption. If a third photon interacts with the atom soon after the
two-photon process, the third photon may ionize the atom. An s-state electron may
not transition to a p-state by two photon absorption.
When absorbing multiple photons simultaneously, an atom will
proceed to an intermediate state corresponding to a characteristic eigenstate or to a
"virtual state." These virtual states are not eigenstates; they correspond
to no specific n or l state. Instead, they are merely superpositions of waves.
No population of electrons transitions to the virtual state. The lifetime of
a virtual state is short, relative to eigenstates. Actually, the closer the virtual
state is to an actual eigenstate, the longer the lifetime of the virtual state. Think of
this as a result of the Werner Heisenburg's Uncertainty Principle: dE dt > h. These virtual states are discussed
further with the topic of Raman Scattering. If the photons
corresponding eigenstate energies are incident on the Cesium, the effect of two-photon
absorption will be enhanced.
We used the DCM dye laser to scan through a range of wavelengths and probe the Cesium
atoms for S and D lines reached by two-photon absorption. When the incident wavelength
corresponded to half the energy needed for two-photon absorption, a large population of
atoms absorbed two photons and quickly ionized. The anode in the heat pipe collects the
electrons which generate a sharp peak in the current signal. So, if we look at the current
between the cathode and anode over a range of wavelengths, we should see spike
corresponding to ionization by three photons at that wavelength. Because S and D states
alternate as electronic energy increases in the atom, the peaks on the ionization spectrum
should correspond alternately to S and D transitions.
Using this ionization spectrum, were able to identify energy levels up to the 48d
state and the 41s state. Click here to view a table
of the levels we found.
You will now see how spectroscopy can reveal information about the dynamics of the
Each s-state transition shows up as one peak on the
spectrum. With the d-state transitions, there are technically two peaks, though
this is observable in our data only at lower energy states. If you look closely at
the 11d, 12d, and 13d lines, you will observe that they have two smaller peaks within the
larger peaks. These hyperfine levels result from spin-orbit interaction in states
with angular momentum>0.
11d3/2 and 11d5/2 Spectral Lines
Each electron can be either spin up or spin down. Because of the spin, the
electrons have spin angular momentum and a spin magnetic moment caused by the spin.
Electron spin, however, can have only two orientations with respect to the z-axis.
Because of this restriction, the spin magnetic moment can have only two
When an external magnetic field is applied to the atom, the
interaction between the spin magnetic moment and the electric field causes an addition or
subtraction of potential energy from the electron's energy level. As a result,
electrons with spin up will have slightly different energy that electrons in the same
state with spin down. When an electron is in a state with angular momentum greater
than zero (p, d, f, . . .) the angular magnetic moment will be greater than zero.
Thus, for p, d and higher L-states, there will be an intrinsic magnetic field in the atom
caused by the angular momentum. This magnetic field causes the spliting of spectral
lines when it interacts with the spin magnetic moment of electrons in these higher
states. In our experiement we see this splitting only in d-states; s-states have
angular momentum zero and, therefore, have no angular magnetic moment to interact with the
spin magnetic moment.
12d3/2 and 12d5/2 Spectral Lines
One major goal of our spectroscopy experiment was to understand Rydberg
atoms and to calculate the quantum defect for Cesium. Click
here to proceed to the discussion of Rydberg Atoms and the Quantum Defect.
Otherwise, continue on to a discussion of Raman Spectroscopy.
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