Section 5: Slowing Light: Lasers Interacting with Cooled Atoms
So far, we have focused on the motion of atoms—how we damp their thermal motion by atom cooling, how this leads to phase locking of millions of atoms and to the formation of Bose-Einstein condensates.
For a moment, however, we will shift our attention to what happens internally within individual atoms. Sodium belongs to the family of alkali atoms, which have a single outermost, or valence, electron that orbits around both the nucleus and other more tightly bound electrons. The valence electron can have only discrete energies, which correspond to the atom's internal energy levels. Excited states of the atom correspond to the electron being promoted to larger orbits around the nucleus as compared to the lowest energy state, the (internal) ground state. These states determine how the atom interacts with light—and which frequencies it will absorb strongly. Under resonant conditions, when light has a frequency that matches the energy difference between two energy levels, very strong interactions between light and atoms can take place.
Figure 11: Internal, quantized energy levels of the atom.
Source: © Lene V. Hau. More info
When we are done with the cooling process, all the cooled atoms are found in the internal ground state, which we call 1 in Figure 11. An atom has other energy levels—for example state 2 corresponds to a slightly higher energy. With all the atoms in state 1, we illuminate the atom cloud with a yellow laser beam. We call this the "coupling" laser; and it has a frequency corresponding to the energy difference between states 2 and 3 (the latter is much higher in energy than either 1 or 2). If the atoms were actually in state 2, they would absorb coupling laser light, but since they are not, no absorption takes place. Rather, with the coupling laser, we manipulate the optical properties of the cloud—its refractive index and opacity. We now send a laser pulse—the "probe" pulse into the system. The probe laser beam has a frequency corresponding roughly to the energy difference between states 1 and 3. It is this probe laser pulse that we slow down.
The presence of the coupling laser, and its interaction with the cooled atoms, generates a very strange refractive index for the probe laser pulse. Remember the notion of refractive index: Glass has a refractive index that is a little larger than that of free space (a vacuum). Therefore, light slows down a bit when it passes a window: by roughly 30%. Now we want light to slow down by factors of 10 to 100 million. You might think that we do this by creating a very large refractive index, but this is not at all the case. If it were, we would just create, with our atom cloud, the world's best mirror. The light pulse would reflect and no light would actually enter the cloud.
To slow the probe pulse dramatically, we manipulate the refractive index very differently. We make sure its average is very close to its value in free space—so no reflection takes place—and at the same time, we create a rapid variation of the index so it varies very rapidly with the probe laser frequency. A short pulse of light "sniffs out" this variation in the index because a pulse actually contains a small range of frequencies. Each of these frequency components sees a different refractive index and therefore travels at a different velocity. This velocity, that of a continuous beam of one pure frequency, is the phase velocity. The pulse of light is located where all the frequency components are precisely in sync (or, more technically, in phase). In an ordinary medium such as glass, all the components move at practically the same velocity, and the place where they are in sync—the location of the pulse—also travels at that speed. In the strange medium we are dealing with, the place where the components are in sync moves much slower than the phase velocity; and the light pulse slows dramatically. The velocity of the pulse is called the "group velocity," because the pulse consists of a group of beams of different frequencies.
Figure 12: Refractive index variation with the frequency of a probe laser pulse.
Source: © Reprinted by permission from Macmillan Publishers Ltd: Nature 397, 594-598 (18 February 1999). More info
Another interesting thing happens. In the absence of the coupling laser beam, the "probe" laser pulse would be completely absorbed because the probe laser is tuned to the energy difference between states 1 and 3, and the atoms start out in state 1 as we discussed above. When the atoms absorb probe photons, they jump from state 1 to state 3; after a brief time, the excited atoms relax by reemitting light, but at random and in all directions. The cloud would glow bright yellow, but all information about the original light pulse would be obliterated. Since we instead first turn the coupling laser on and then send the probe laser pulse in, this absorption is prevented. The two laser beams shift the atoms into a quantum superposition of states 1 and 2, meaning that each atom is in both states at once. State 1 alone would absorb the probe light, and state 2 would absorb the coupling beam, each by moving atoms to state 3, which would then emit light at random. Together, however, the two processes cancel out, like evenly matched competitors in a tug of war—an effect called quantum interference.
The superposition state is called a dark state because the atoms in essence cannot see the laser beams (they remain "in the dark"). The atoms appear transparent to the probe beam because they cannot absorb it in the dark state, an effect called "electromagnetically induced transparency." Which superposition is dark—what ratio of states 1 and 2 is needed—varies according to the ratio of light in the coupling and probe beams at each location—more precisely, to the ratio of the electric fields of the probe pulse and coupling laser beam. Once the system starts in a dark state (as it does in this case: 100 percent coupling beam and 100 percent state 1), it adjusts to remain dark even when the probe beam lights up. The quantum interference effect is also responsible for the rapid variation of the refractive index that leads to slow light. The light speed can be controlled by simply controlling the coupling laser intensity: the lower the intensity, the steeper the slope, and the lower the light speed. In short, the light speed scales directly with the coupling intensity.