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Precision Dark Resonance Spectroscopy
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Why is it called a "dark" resonance?

We are performing the experiment using a thermal vapor of cesium, the heaviest of the stable alkali metals. Cesium has only one outer electron, and its optical excitation spectrum can relatively easily be described theoretically. We concentrate on one of the main excitation lines, the so-called D2 line. It lies at 852 nm wavelength where compact and inexpensive semiconductor lasers are available as light sources. With some simplification the cesium atom can be described as a system of two ground states, separated by 9,192,631,770 Hz, and an energetically excited state (fig. 1). Because of its similarity to the capital Greek letter Lambda this arrangement of levels and light fields is called a Lambda system.

Figure 1: Simplified energy level scheme for cesium atoms cesium level scheme: Lambda configuration

When cesium vapor in a glass cell is illuminated by resonant laser light the atoms can absorb the light and in this way be transferred to the excited state. This state decays through the emission of light which can then be detected outside the cell with a video camera (fig. 2), the cell appears "bright" (fig. 3). Near the end of the cell the intensity of the fluorescence light is lower than at the beginning because absorption makes the laser beam weaker and weaker as it traverses the vapor cell.

Figure 2: Experimental setup for fluorescence light measurements with a video camera setup for fluorescence imaging
Figure 3: Fluorescence of a cesium vapor cell in the vicinity of a bright resonance. This picture shows a 7 cm stretch of the cesium cell. In this false-color image red means high, blue means low fluorescence light intensity. bright resonance fluorescence

When the light field contains another frequency component with an optical frequency which differs by 9,192,631,770 Hz from the first, quantum mechanical effects can lead to vanishing absorption, an effect sometimes called "electromagnetically induced transparency". This is because the atoms make a transition to a quantum mechanical superposition state of the two ground states which does not interact with the light beam any more (find more details here (simple theoretical model) or here (simple intuitive model)). Since there are less excited atoms now the cell does not emit as much light as before, the cell becomes "dark" (fig. 4). This type of resonance is therefore called a "dark resonance". The superposition state that the atoms are in is called a "coherent dark state" because the mutual coherence of the two light fields and the atomic states is essential. Because the atoms cannot be excited anymore once they are in this coherent trapping state the process is called "coherent population trapping".

Figure 4: Fluorescence of a cesium vapor cell in the vicinity of a coherent dark resonance. This picture shows a 7 cm stretch of the cesium cell. In this false-color image the color scale is the same as in fig. 3. dark resonance fluorescence

This effect was first observed in 1976 (G. Alzetta et al., Il Nuovo Cimento 36B, 5-20 (1976)). You can find a mathematical description and an intuitive model on this web site.

Transmission spectrum of the dark resonance

In our experiment we usually look at the total transmitted intensity behind the sample cell (see experimental setup) as a function of the difference frequency between the two light fields. In a typical experiment we keep one optical frequency fixed and scan the other through the resonance. The deviation of the difference frequency of the light fields from the ground state splitting of the undisturbed cesium atom is the quantity plotted on the horizontal axis in the experimental spectra. An example for an experimental curve is shown in figure 5.

dark resonance absorption profile dark resonance dispersion profile
Figure 5: An example for the reduction of absorption in the vicinity of the dark resonance Figure 6: Change of refractive index corresponding to the absorption spectrum of figure 5

The dispersion has the opposite sign as in a conventional absorption resonance, i.e., it is "normal" in the center of the resonance and "anomalous" near its flanks. This is because it is a dark resonance. After all, also the absorption signal has the other sign!

For fundamental reasons the index of refraction of any substance must change in the vicinity of an absorption resonance, an effect called "dispersion". Since the dark resonance is rather strong but extremely narrow the refractive index changes substantially in a narrow frequency interval. This is called "steep" dispersion (see width of the resonance). For figure 6 the change in refractive index was measured by placing the cesium cell inside an optical interferometer (we now routinely use an easier way). In that setup dispersion and absorption in the vicinity of the dark resonance could be measured simultaneously. Figure 6 shows the dispersion spectrum corresponding to the absorption spectrum of figure 5. Of particular importance for possible applications is the fact that the absorption vanishes in the region of steepest dispersion.

The steep dispersion also means that the group velocity of the light is strongly reduced there, the light becomes "slow". Already in 1995 we observed a reduction by a factor of 10000 and in 1999 we reported a reduction by a factor of 55000. Since then other groups have continued this work and have achieved further thousand-fold slowing-down, down to complete stand-still.