Volume 3 No.4                                                                                                                     July 2000


Light Pulse Faster than Light

A recent experiment* at NEC Research Institute, Princeton, N.J., U.S.A., clearly demonstrated superluminal propagation of a light pulse through a specially engineered medium. Superluminal implies faster than the speed of light, and in this experiment the peak of the light pulse arrives at the output end of the medium even before it has entered the medium.

Confusing ? Yes. Sounds exotic ? Yes. Impossible? Not anymore.These first reactions, I hope, transform into Wow ! Incredible ! Neat ! ......

The experiment has created a great deal of excitement and rekindled discussions on a variety of fundamental issues like, the validity of Einstein's Special Theory of Relativity, the Principle of Causality, the possibility of a signal travelling faster than the speed of light in vacuum and so on. None of the principles or theories are violated, however, The question as to whether this light pulse can be considered a signal is much debated and complicated one. The smooth light pulse used in the experiment has a finite spectrum (limited number of colors or frequencies); however, traditionally a true signal is one with an infinite spectrum. We will not get into this discussion but focus mainly on the experiment itself and the basic physics involved.

In a nutshell, the observed superluminal velocity of a light pulse arises due to temporally advanced rephasing of different frequency components which have undergone anomalous dispersion inside an active medium.

Let us take this step by step: we will first discuss dispersion - compare normal versus anomalous dispersion, then look at what comprises a light pulse, its group velocity in contrast to the phase velocity, and lastly use these ideas to better appreciate the experiment.

Dispersion: Normal versus Anomalous Dispersion

Light travels in vacuum at a phenomenal speed of ~3 x 108 m/s and is denoted by the symbol c. This speed roughly corresponds to going around the earth in about one tenth of a second. Inside a medium light travels at a speed c/n(v), where n(v) is called the refractive index which characterizes the medium. The value of the refractive index n(v) not only depends on the specific medium, it also depends on the frequency v (or color) of the light that is travelling through it. Hence, different colors of light experience different refractive index in the same medium leading to dispersion.

In a normal dispersive medium the refractive index increases as the frequency of light increases. All of us are familiar with the rainbow like colors that appear from a glass prism when sunlight is incident on the prism. Each color travels differently through the prism due to normal dispersion; blue light bends more and travels slower than the red light. The emerging color sequence at the output end is important: red light is farthest from the base of the prism and blue light is the closest. Most naturally occurring transparent media exhibit normal dispersion in the visible range of the electromagnetic spectrum.

In an anomalous dispersive medium the refractive index decreases as the frequency of light increases, and the region of anomalous dispersion coexists with a strongly absorbing behavior making the medium opaque. There is no known naturally occurring anomalous dispersive medium which is transparent in the visible region of the spectrum. If a prism is made out of a transparent anomalous dispersive material, the sequence of the emerging colors would be reversed, with the blue light being farthest from the base of the prism and the red light closest to it, and of course, the blue light would travel faster than the red light inside such a medium.

Velocity of Light: Group versus Phase Velocity

Light, we all know is an electromagnetic wave; an ideal monochromatic (single frequency) wave is a disturbance that extends to infinity. A light pulse is a combination of waves of slightly different frequencies, which interfere constructively to form a pulse and cancel out each other completely everywhere else. There are two kinds of velocities associated with a light pulse: a group velocity and phase velocity. The pulse as a whole travels at a speed known as the group velocity, whereas, each component wave travels at its own speed known as the phase velocity. In general these need not be identical as seen in a dispersive medium.

In a normal dispersive medium the group velocity is always slower than the phase velocity. Locomotion of a caterpillar provides a good mental picture of group velocity in normal dispersive medium: a careful look at a caterpillar reveals a wave-like disturbance that travels on the caterpillar's body (phase velocity) which is much faster than the actual movement of the caterpillar as a whole (group velocity). Another group of researchers have recently produced a medium with such high normal dispersion that they managed to slow down a light pulse to a speed of just 8 m/s; on a pleasant day a cyclist could beat that speed.

In an anomalous medium, the group velocity is not only faster than the phase velocity it could also exceed the speed of light in vacuum as demonstrated in the experiment. One has to imagine an anomalous caterpillar that can perform this feat!

Arrival Times: Pulse Delay versus Pulse Advancement

A few simple equations neatly summarize the above discussion, the group velocity Vg= c/ng where the group-velocity index n = n(v) + v dn(v) / dv, v being the frequency of light. The phase velocity of each constituent wave is Vp = c/n(v) with n(v) > 1. In a normal dispersive medium the factor dn(v)/dv is positive and hence ng> n(v) resulting in the group velocity which is always slower than the phase velocity. Whereas, in an anomalous dispersive medium the factor dn(v)/dv is negative, which results not only in the fact that ng < n(v), but ng could also be negative. If one looks at the corresponding time of traversal through a medium and compares it with the travelling time for the same length in vacuum, one can understand the negative group velocity. The time of traversal through a medium of length L is given as Tm = L/Vg , and through vacuum the time is Tv = L/c, thus the pulse delay is Tm - Tv = L/Vg - L/c = (ng - 1)L/c, which is negative when ng < 1. A negative pulse delay implies pulse advancement. In contrast to the conventional view that negative group velocity has no physical meaning, it implies that the pulse arrives earlier than if it had travelled the same distance in vacuum.

The Experiment

Coming to the experiment, the NEC Research Institute group created a lossless anomalous dispersive medium and achieved propagation of a pulse at superluminal speed. The experiment was performed, with brilliant engineering of the active medium which resulted in a large time difference of 310 times the vacuum transit time, without leaving room for any doubt on the experimental outcome. Atomic caesium gas confined in a pyrex glass cell under a uniform magnetic field as the active medium was used. The magnetic field separates (lifts the degeneracy of) the hyperfine magnetic sub-levels of the ground state. The relevant energy levels are shown in Fig. A. Using polarized light the electron in the outermost shell, which could exist in 16 possible quantum mechanical states, is put into the state |1ñ. Such preparation of the atom does not occur in nature,

Fig. A

the temperature corresponds to nearly zero degree Kelvin (-273oC). This technique of putting the electron in a specific atomic sub-level using a combination of polarized light and natural decays is known as optical pumping. The 1966 Nobel prize was awarded to Alfred Kastler for its development. Two intense lasers (El and E2 in Fig.A) which have slightly different frequencies are applied, their frequencies are such that they are close to the frequency associated with the difference in energy of the levels |1ñ and |0ñ. The laser pulse (Ep in figure A) which travels at superluminal velocity, has a frequency close to the 2ñ « |0) transition energy and is less intense than the other two lasers.

For a careful choice of frequencies of these three lasers, the weak laser pulse (Ep or probe field in figure A) travels at superluminal velocity inside the active medium. The two intense lasers El and E2, and the electron in state |1ñ, create two gain peaks that sandwich between them a region of anomalous dispersion, as seen in Fig. B. The central region of the refractive index curve (lower curve in Fig. B) has a negative slope as the pulse frequency is increased from left to right. The pulse experiences a little gain as it traverses the medium and the electron initially in level |1ñ makes a transition to

Probe Detuning
Fig. B

level |2ñ. This gain compensates for any losses that the pulse experiences along the way. If the pulse frequency is varied out of this anomalous region, it travels through the medium slower or comparable to the speed of light. The superluminal speed is realizable only for a narrow frequency region.

Fig. C

In Fig.C, the solid line depicts the pulse A, that travelled through the medium at the speed c, and the dashed line represents the superluminal pulse B that arrived 62 ns (nanoseconds) (1 ns=10-9 sec) earlier. The length of the medium is 6 cm and light takes mere 0.2 ns to travel that length in vacuum at the speed c. This pulse advancement corresponds to a group index ng = -310.

Rephasing not Reshaping

One way to understand this dramatic pulse advancement is to look at the different wave components that make up the pulse. Just before the pulse enters the medium the various wave components are in phase and interfere constructively to produce the pulse. As the pulse enters the medium, the wavelength which was shortest outside becomes the longest wavelength inside the active medium, and vice-versa. This complete reversal of roles inside the anamolous medium is undone as the pulse exits the medium and the original relationship between different wavelengths is re-established. This leads to the possibility of rephasing of the wave components which occurs at a time earlier than the vacuum propagation time. Even though all the constituent waves travel at a maximum speed of c, rephasing of the wave components causes the pulse to travel at superluminal speed. Under normal circumstances, any pulse that is propagating through space can never rephase itself at a later time along its propagation path. Here, the anomalous dispersive medium creates the reversal of relationship between the constituent waves thus making rephasing possible along the propagation direction.

The highlights of the experiment are as follows: the superluminal velocity results only from the anomalous dispersion region created with the assistance of two nearby gain lines. It is not an effect that arises due to reshaping of the pulse, like amplification of pulse front edge and absorption of the tail end. It is to be re-emphasized that the superluminal light propagation is a result of the wave nature of light. There are potential applications in communications, although the present day signal transmission speed is a measly fraction of the speed of light, hopefully the signal transmission speed can be taken to its maximum theoretical limit of c in the near future.

* Gain-assisted superluminal light propagation, L.J. Wang, A. Kuzmich and A. Dogariu, Nature Vol. 406, Page 277-279 (2000).

Harshwardhan Wanare

Department of Physics

Indian Institute of Technology, Kanpur

Kanpur -208016