Nothing Travels Faster Than Light

Quantum Electronics Project December 14th 2000 Jonathan Stone AP4: 94538441 Rory Ryan AP4: 95307036

Introduction.

The speed of light is one of the fundamental constants of Physics. Measured at 300 million metres per second, it is the universal speed limit and the cornerstone on which most of Einstein’s theory of Relativity is based. By Einstein’s theory, no thing can travel faster than light, as this would breach the principle of causality, which states that cause must precede effect. If it were possible to send particles and objects faster than light we could expect strange things to happen For example, if we were to take a rifle a fire a bullet at 5 times the speed of light, by Einstein’s theory, the bullet would be out of the gun and flying towards it target before the trigger had even been pulled. And this is just the start. Scientists have dreamed up time machines and paradoxes to state why it should and how it could be possible, all based on the assumption that superluminal speeds are possible. With the motivation of becoming the man to break the light speed barrier (and the man who proved Einstein wrong!), many scientists have created experiments to try to propagate particles superluminally. And although they have all claimed to have broken the speed of light, most “Faster Than Light” experiments never seemed to rise above the clouds of doubt and uncertainty that descended upon them when they were investigated thoroughly. In 1974, a group of Australian scientists claimed that they had found cosmic ray particles that travelled faster than light, only to find out that they were incorrect. In 1982, Gustav Nimtz claimed to have transmitted Mozart’s 40th Symphony across his lab at many times the speed of light but senior physicists rejected his experiment also. And there have been many others. Needless to say, with this history, any new so-called superluminal experiments are met with a certain degree of scepticism. So, in July of this year, the world of science was gripped with the news that Dr Lijun Wang and his research group working at NEC labs in the USA, had in fact achieved this monumental feat, the grandmasters of physics wanted to take a closer look before committing themselves. Entitled “Gain-Assisted Superluminal Light Propagation”, details of the experiment were first sent to Nature in May 2000 and the article was published in the July 2000 issue. With such a sensational title, it is no wonder that the global physics community wanted to take a closer look at the Dr. Lijun Wang’s experiment. Wang and his team of scientists claimed to have propagated a light pulse through a chamber of specially prepared Caesium gas 310 times faster than the speed of light in a vacuum. But amidst the hype and headlines claiming Einstein’s theory of Relativity had been violated just five years before its 100th anniversary, Dr. Wang was quick to point out that the experiment was not at odds with Relativity at all, and could be explained using existing laws of wave propagation. In this project we will take a closer look at the “Gain Assisted SuperLuminality” experiment, describing the underlying principles on which it is based, and drawing some conclusions as to what possible uses it could have in the future.

(II) Fundamental Principles.

In this section we will describe some of the underlying concepts and principles that are needed to fully understand the “Gain Assisted Superluminality” experiment. Normal Dispersion and Anomalous Dispersion. White light is composed of many millions of light waves of different wavelength. In a vacuum all of these light waves travel at the same speed but in a dispersive medium, such as air or glass, this is no longer true. In a dispersive medium, different wavelengths of light will pass through with different velocities. This is demonstrated in Figure 1 (a) below. As the white light travels through the (dispersive) prism, each of the wavelengths passes through with it’s own wave velocity. This is because in a dispersive medium, refractive index is a function of wavelength [1]. Longer wavelengths of light such as red (700nm) will pass through more quickly, and will be deviated by a small amount. Shorter wavelengths, such as blue light (400nm) will be deviated more as it passes through more slowly. This effect is called “Normal” Dispersion.

Figure 1 [2]

(a)Normal Dispersion

(b)Anomalous Dispersion

In anomalous dispersion, however, there is an opposite effect. In a region of anomalous dispersion, long wavelengths of light will pass through more slowly than shorter wavelengths. This condition is demonstrated in Figure 1 (b) above. In this example, we show what would happen if a prism exhibited anomalous dispersion properties. The light is again dispersed (as in Normal dispersion), but this time the dispersion spectrum is reversed. Longer wavelengths are deviated more than shorter wavelengths so now the red appears at the bottom of the dispersion spectrum and the shorter wavelength blue appears at the top. Anomalous dispersion is not naturally occurring in transparent materials. It has only been found in (highly absorbing) opaque materials In mathematical terms, the group refractive index in a region of anomalous dispersion is:

n g = n + v.

dn dn where v. c [6] < 0 and the Group Velocity becomes V g = ng dv

So, by propagating a wave through such a region it is possible to achieve a group velocity that is greater than the speed of light. But in previous attempts to demonstrate this, which were usually carried out with opaque media, the pulse or wave-packet was severely absorbed and distorted as it passed through the region of anomalous dispersion. The results therefore, were inconclusive, and could not be taken as proof that the effect could work. Wang’s experiment demonstrates that this it is in fact possible to achieve superluminality with this anomalous dispersion effect and keep the pulse intact. He observed how the group velocity index was greatly enhanced using a lossless normal dispersion region between two closely spaced gain lines in an experiment entitled “Electromagnetically Induced Transparency”[4]. The effect of enhancing the group velocity index meant that a pulse passing through the medium would not experience any severe reshaping and the pulse should remain intact. It was also known that pulses could be propagated superluminally in regions of anomalous dispersion [3]. From this, Wang devised a means of creating a region of lossless anomalous dispersion using Caesium. Naturally occurring Caesium gas can exist in any one of 16 possible quantum mechanical states called “Hyperfine ground state magnetic sub-levels”. In the “Gain Assisted Superlumination” experiment, the Caesium atoms are pumped by two continuous wave lasers using a technique called optical pumping, to one of these hyperfine states [2]. In this hyperfine state, the Caesium gas has two absorption lines with a frequency separation of 1.9Mhz and a region of rapid decrease in refractive index with wavelength (or anomalous dispersion) between these lines (shown in Figure 3 below). A third probe laser was used to measure the refractive index and gain coefficients of the Caesium.

Figure 3 [2]

The green box in Figure 3 above indicates the region of frequencies Wang identified in the Caesium gas for which a light wave will experience anomalous and lossless dispersion. The pulse used for the experiment is a 3.7 microsecond, near-gaussian beam whose bandwidth lies between the two gain peaks of the atomic Caesium gas. This pulse is propagated into the caesium cell. As it passes through the Caesium cell, the pulse is anomalously dispersed.

Figure 4 To view what is happening in the region of anomalous dispersion on a wave level, look at Figure 4 above. The pulse is made up of many different wavelengths of light. In the anomalous dispersion region the shorter wavelengths of light travel faster than the long wavelengths. This changes the phase of the component waves in relation to each other and causes them to rephase further along the line of propagation. Normally, a pulse is not allowed to rephase further along its propagation but due to the properties of the medium it can be done. We can describe the passage of the pulse through the Caesium chamber in mathematical terms. For a normal dispersive medium (where v.dn/dv >1 and ng>1) of length L, the delay time experienced by light will be:

∆T =

(n g − 1) L c

However, in a region of anomalous dispersion, the value of ng is less than 1, the transit time for the light now becomes:

− ∆T =

(1 − n g ) L c

So when ng