For the precise observation of dark resonances in cesium vapor we need an 852 nm wavelength light field containing two frequency components with a separation of 9.2 GHz. The light field can optionally be spatially filtered and then traverses a cesium vapor cell at room temperature. The total transmitted intensity is detected on a photo diode. In order to increase the signal-to-noise ratio the difference frequency is usually modulated at a few kHz, and the resulting intensity variation on the photo diode demodulated with a lock-in amplifier.

Since the observed width of the resonance depends on how well one can control the frequency difference of the two components in the light field it is best to use two phase-coupled light fields. We have developed two methods to provide this special light field.

1) Laser phase-locked loop

Until fairly recently we have stabilized the phases of the optical light waves provided by two extended-cavity diode lasers to each other with an electronic servo loop which means that also the difference frequency is kept exactly fixed. In this way we obtain resonance linewidths of less than 50 Hz which is very narrow in comparison to the linewidth of the ordinary bright resonance of 5.3 MHz. Details can be found in one of our publications. While the servo loop works well, the setup is rather sensitive to external perturbations like acoustic noise. One also has to couple both laser beams into the same stretch of single-mode fiber in order to make the beams exactly parallel (10 µrad of angle between the beams already broadens the dark resonance to about 10 kHz because of the residual Doppler effect!).

2) Current-modulated VCSEL

Now we have a much easier way to provide two phase-stable light fields. When the injection current of a special prototype of a vertical-cavity surface-emitting laser (VCSEL) is modulated at 9.2 GHz, sidebands at that frequency offset from the carrier frequency are generated with an efficiency of a few percent. This is enough to observe the dark resonance using the carrier and either one of the two first-order modulation sidebands, while the other sideband is far off-resonant and does not have an influence. At the same time, both frequency components are already perfectly overlapping. This setup is very compact and mechanically robust, and no fancy high-speed servo loop is required. See here for details.

The VCSEL setup has a number of advantages. The laser itself does not need external optics, and no optical fiber is needed. Since there are no critically aligned parts (like extended laser cavities or fiber couplers) the setup is completely insensitive to mechanical vibrations and acoustic noise. The overall size of the system is greatly reduced:

In the meantime we have managed to squeeze a complete dark-resonance spectrometer into only a few cubic centimeters of volume!

The coherent dark resonance can be extremely narrow and therefore is very interesting for precision applications like the measurement of magnetic fields or the construction of highly stable clocks, and the more so the narrower the resonance linewidth is. Because the coherent dark state is composed basically of ground states it has a very long lifetime: the lifetime of the excited state of the Lambda system is irrelevant, and only the relaxation between the ground states is important. The natural lifetime of the ground state coherence is several thousand years because it is a magnetic dipole transition, so that "technical" aspects determine the observable dark resonance width.

The stability of the laser difference frequency is of particular importance for the width of the resonance line. We have developed two ways of reducing the jitter of the laser difference frequency virtually to zero (see above) so that other processes determine the dark resonance linewidth.

Another limit to the linewidth stems from the fact that the cesium atoms (having a mean velocity of 230 m/s) fly through the laser beams so quickly that they interact with them for a few microseconds only. Due to the quantum mechanical uncertainty relation the position of the resonance can only be determined to within about 10 kHz under these conditions, i.e., the resonance line appears 10 kHz wide. This so-called time-of-flight broadening can drastically be reduced through the introduction of several 10 mbar of a noble gas, e.g., neon, into the cesium cell. The cesium atoms collide with the gas atoms so frequently that it takes them many milliseconds to cross the laser beams. With the help of such "buffer gases" we can now obtain resonance linewidths of less than 50 Hz for the coherent dark state.

A measure for the steepness of the dispersion is the group velocity which under certain conditions is the propagation velocity of a light pulse inside the medium. From our measured dispersion profiles for cesium cells without additional buffer gas group velocities of less than one fifty-thousandth of the vacuum speed of light can be calculated (in this figure the group velocity at the steepest slope is about one three-thousandth of the vacuum speed of light). Other groups have recently performed very similar experiments in high-density vapors and found even lower group velocities.