Controlling the Frequency of Light
with Moving Mirrors

The current work has been motivated by an interest in Bose-Einstein condensates (BECs). To create a BEC atoms are cooled in part by lasers to temperatures of just billionths of a degree above absolute zero (typically 100 nK). Two essential aspects of laser cooling are the Doppler frequency shifts experienced by the moving atoms and the need for very precise control of the laser frequencies. In our project we have demonstrated methods for precisely controlling the frequency of a laser beam by amounts as small as one Hz and as great as several 100 MHz (10⁸ Hz) by taking advantage of the Doppler shift that occurs when light is reflected from two very different types of moving mirrors. Even the larger of these frequency shifts is still a minute fraction of the enormous frequency of visible light, which is about 400 THz (4 x 10¹⁴ Hz). Because these optical frequencies are so high they can never be measured directly. But even very tiny differences between two stable optical frequencies can be measured by the method of ``beats,'' similar to the way the frequency difference of two tuning forks can be precisely determined by sounding them together. Doppler shifts are most commonly associated with sound waves, as when the pitch of a car's horn changes dramatically as it drives by. But Doppler shifts also occur with light, and we often speak of the "red shifts" of distant galaxies moving away from us at speeds comparable to the speed of light. In laser cooling, and our experiments, the relative velocities β = v/c and corresponding frequency shifts Δ f / f are are much smaller, and the Doppler shift simplifies to Δ f = β f.

In our first experiments red light from a HeNe laser was reflected from a conventional mirror placed in one arm of an optical interferometer. The mirror was moved at about 1 μm per second by gently pulling on a rubber band attached to the mirror mount. (At this tiny velocity it would take several months for the mirror to cross an average room.) The resulting frequency shift was also tiny, but was readily detectable by the movement of interference fringes as the original and frequency-shifted light waves recombined in the interferometer. In a later version of this experiment, still underway, the mirror is moved at a somewhat larger (16.67 μm/s) and more carefully controlled velocity for a longer time, and the frequency shift measured more precisely.

In our second series of experiments the `moving mirror' is a periodic sequence of virtual mirrors created by a sound wave that travels across a crystal at about 4000 m/s. The sound wave is produced by a piezoelectric transducer attached to one end of the crystal in response to an applied radio-frequency (rf) voltage. As with sound waves in air, the sound waves in the crystal are periodic regions of alternating compression and expansion. If the angle of incidence is correct, a beam of light sent across the crystal is reflected from the moving planes in a process known as Bragg diffraction. Because of the way it brings together sound and light this device is called an acousto-optic modulator or AOM. AOM's produce frequency shifts of the order of 10⁸ Hz, an ideal range for laser cooling of atoms.

We verified that the frequency of our laser beam had been shifted in the AOM by the expected amount (80.000 MHz) exactly as before, by comparing frequency shifted and unshifted beams in an interferometer. The initial laser beam was divided into two beams by a beam splitter. One of these beams was sent through the AOM while the other, called the reference beam, was directed on to a fast photodetector. Finally the frequency-shifted beam was also sent to the same photodetector. The result was the formation of a beat signal that could be observed and precisely compared with the applied rf voltage in an oscilloscope. In a extension of this phase of the project now underway, the shifted light is made to pass through the AOM twice before being compared with the reference. The result should be a frequency shift twice as large as before, 160 MHz.