Slow Light

On the photo: our slow light experiment.

Abstract: Electromagnetically induced transparency (EIT) in atomic vapors induces extremely steep dispersion which gives rise to the phenomenon known as the slow light. Group velocity of slow light can be many orders of magnitude less than the speed of light in vacuum. Our research is carried out in the context of the slow light applications for communications and data processing. It includes the study of slow light Doppler dragging, the effects of the drive standing wave, nonlinearity with respect to the probe light, and others.

Electromagnetically induced transparency (EIT) occurs due to coherent population trapping (CPT) in quantum systems that can be generally described as L-systems: they have a short-lived excited state |a> and two long-lived ground states |b> and |c>. A diagram of such a system is shown in Fig. 1.

Figure 1. An energy diagram of a three-level “L-system”.

Coupling the ground states to the excited state by two optical fields, it is possible to drive the system into a superposition “dark” state that has a long-lived coherence between the ground states. Making one field (the probe) much weaker than the other (the pump), one can see that the systems with EIT have extremely steep frequency dispersion with respect to the former. This dispersion can be controlled by detuning the drive field from optical resonance as well as by changing its power.

Recalling the definition of group velocity, we see that the probe light propagates in the EIT media very slowly. The ultimate limit for how slow the light signal can propagate is given by the ground state coherence decay rate gcb. As a “rule of thumb” one can estimate the signal delay in the EIT media as the inverse width of the EIT two-photon resonance (that is, the EIT resonance width with respect to detuning of the pump and probe fields frequency difference w1-w2 from the ground state splitting w). This maximum delay varies from a fraction of millisecond in hot vapor cells to a fraction of a second in cold atomic clouds and in solids, or seconds in BECs. The delay can be rapidly controlled by the pump field.

It is not surprising that EIT and associated with it slow light phenomenon attracted great interest as a foundation for new optical information technology. However before becoming a technology, the slow light phenomena should be studied in its full complexity. Much of this complexity comes from the fact that realistic atomic systems cannot be considered as closed L-systems. For example, one of the most often used transitions in 87Rb, the D1 F=2 -> F=1, consists of eight Zeeman levels that couple to each other. The population dynamics in such a system is different from that in a L-system, one of the difference being that it exhibits strong nonlinearity with respect to the probe field. As a result, one has to be careful consider even a weak probe as a “perturbation” on top of a strong pump field. We carry out experimental and theoretical study of such a nonlinearity.

Another layer of interesting phenomena inherent to the realistic atomic systems with EIT is related to inhomogeneous broadening. For example, atomic motion in a hot vapor cell results in different frequency tuning of the light with respect to different velocity groups of atoms, via Doppler effect. For those groups of atoms, the light signal delay takes on different values. This effect can be explained as light dragging in the media moving along with the light signal (when it is blue-detuned), or opposite to it (when it is red-detuned ). In a hot gas cell, the net effect is the increase of the maximum optical group delay and its displacement of the red from the center of the Doppler profile. This effect has been recently observed by our group (see physics/0312138 article in the LANL archive).

More complexity comes from the fact that in most of EIT experiments there is some amount of reflected light that is present in the system. We show that even weak reflection leads to the effects that can considerably modify the spectral properties of the system. The essence of these effects is the partial standing wave formed by the direct and reflected light beams. This can be an actual standing wave of amplitude, when both direct and reflected waves have the same polarization, a standing wave of polarization, if the traveling waves’ polarizations are orthogonal, or any case in between. The resulting population and coherence “grating” imprinted on the media is resonant with the incoming light, and therefore even with a very small contrast (very weak reflection) it can produce a sizable effect. Remarkably, these effects are different for the amplitude and polarization standing waves. Moreover, we show that with a suitable choice of the reflected light polarization these effects can be made to compensate each other. This approach may lead to a practical alternative to anti reflective coating of the cell window and other anti-reflection precautions.