Behind the mass-media story: Bose-Einstein condensate slows light

From OE Reports Number 185 - May 1999
01 May 1999
Yvonne Carts-Powell

Lene Vestergaard Hau (Rowland Institute for Science and Harvard Univ.; Cambridge, MA) and coworkers used a macroscopic quantum effect, electromagnetically induced transparency to pass a laser pulse through a usually opaque medium. The medium -- a Bose-Einstein condensate of sodium atoms -- has optical properties that slow the group velocity of the pulses until they are 20 million times slower than the speed of light in vacuum.

Figure 1. Optical transmission in the Bose-Einstein condensate (top) is large at the resonance, but drops off sharply at higher or lower frequencies. The refractive index (bottom) shows a very steep slope, which also changes as the frequency tunes away from resonance conditions. An a. c. Stark shift between several hyperfine transitions causes the center of the transmission and refractive index profiles to shift by 0.6 MHz. Both transmission and refractive index are calculated properties, not experimental measurements.

If you tuned into the mass media at all in late February, you have probably already heard about how the researchers slowed the speed of light to 17 m/s. The story generated a great deal of excitement because the average newspaper reader assumes light travels at an unimaginably fast constant speed of 300,000 km/s. Although the mainstream news reports got the basic facts correct, they skimmed over the interesting details of how the group velocity of an optical pulse alters with refractive index and, in this case, with the differential of the refractive index to the frequency.

Hau, Steve Harris (Stanford Univ.; Stanford, CA), and Zachary Dutton and Cyrus H. Behroozi (Rowland Institute for Science; Cambridge, MA) cooled a dense, magnetically confined cloud of sodium atoms to a ground state. They trapped only those atoms with magnetic dipole moments directed opposite of a magnetic field. The researchers then cooled the cloud even further, to less than 435 nK. At these temperatures, the 1 to 2 million atoms condense into a state of matter predicted by Bose-Einstein statistics, in which the wave functions of the individual atoms merge -- in effect, creating coherent matter waves. (More recently, researchers at the National Institute of Standards and Technologies used this property of a Bose-Einstein condensate to create a well-collimated atom laser1.

Next, the researchers applied a coupling beam -- a linearly polarized laser beam tuned to the transition between two unpopulated hyperfine states (|2> and |3>) -- which couples the states. It creates a quantum-interference for a weaker circularly-polarized probe laser beam that is tuned to the |1> to |3> transition. The effect is to make the condensate transparent to the probe beam.

This is where the effects become very odd. At line center, all of the light is transmitted, but as the frequency changes slightly, the refractive index of the material changes very quickly, and thus the dispersion curve is much steeper than can be obtained by other methods.

Usually, the group velocity of a pulse is dominated by the inverse of the refractive index at the probe frequency. However, when the refractive index is equal to 1, a second term in the denominator dominates: the change in the refractive index with respect to the probe frequency.

Where vg = group velocity, c = speed of light, wp = frequency of the probe beam, and n = refractive index. Because vg is remarkably large, the value of the group velocity is unprecedentedly small. In other words, when the probe beam is slightly detuned from the resonance conditions, the speed of the light pulse passing through the Bose-Einstein condensate slows to 17 m/s. As a side effect, the length of the pulses is compressed as well -- in this case to only 43 microns.

The researchers see a relatively clear path to slower velocities, perhaps as low as centimeters per second, by avoiding laser heating of the condensate. A system with such unusual characteristics will enable researchers to test a variety of quantum optical properties, including optical squeezing, quantum nondemolition, and nonlocality, as well as potentially useful devices such as single-photon switching.


1. E.W. Hagley, et al., "A well-collimated quasi-continuous atom laser" Science 283, 1706 (1999).

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