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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.

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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.

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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 electron.

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

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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 orientations. 

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.

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12d3/2 and 12d5/2 Spectral Lines

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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.

 

Table of Contents:

  • Title Page

  • Molecular Spectroscopy and the CO2Molecule

  • Molecular Vibration Theory
    Data and Analysis

  • Multi-Photon Absorption in Cesium

  • Ionization Spectra
    Quantum Defect
    Cesium Energy Levels

  • Raman Spectroscopy: Four-Wave mixing in Sodium Atoms

  • Theory: Raman Scattering and Four-Wave Mixing
    Four Wave Mixing Data

  • Spectroscopic Aparatus

  • Page the First


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