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Transcript
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. <0 dv dv Using this we find that the group velocity now becomes greater than the speed of light. This is one of the most important fundamentals for understanding the Gain Assisted Superluminality experiment. Group Velocity. A light pulse is composed of many constituent waves of varying wavelength (or frequency). Consider, as an example, figure 2 (a). Wave 1, Wave 2 and Wave 3 are harmonic waves of different wavelength. If we get a superposition of the three waves and all of the other component waves of the light, we get a beat pattern similar to Figure 2 (b). The rate at which the modulation envelope of this beat pattern advances is called the Group Velocity. Wave Group In a non-dispersive medium, the group velocity of the wave group (or beat) is equal to the wave velocity of each of the component waves (i.e. light waves of all wavelengths travel the same speed in a non-dispersive medium). This is not the same for a dispersive medium. In a dispersive medium, such as glass, light waves of different wavelength travel at different velocities. This means that the group velocity is also dependent on the refractive index of the dispersing medium. We will see in the next section how this is important for superlumination. (III) Experimental Description. Wang’s experiment was carried out at NEC Labs in the USA. It is based on the wave propagation nature of light and anomalous dispersion. Wang combines the results of previous experiments based on anomalous dispersion and absorption gain lines, to successfully propagate a 3.7 microsecond light pulse superluminally through a 6cm chamber of Caesium gas. Here’s how he did it: The fact that the group velocity could exceed c in a region of anomalous dispersion is nothing new to physics. It is consistent with theory in modern optics textbooks. In a region of anomalous dispersion, the rate of change of refractive index with increasing frequency is negative. In mathematical terms, v. c dn > 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 <1, the delay time across the medium is negative. In other words the pulse appears to leave the cell even before it has entered. Wang measured that the propagation time for the pulse to pass through the cell was 62 nanoseconds quicker than it would have taken if the chamber were a vacuum. A demonstration of this effect can be seen below in Figure 5[2]: T1 - Pulse before entering chamber T2 – Pulse passing through chamber T3 – Pulse on the far side of chamber Figure 5 (the full animation can be downloaded from Wang’s web site [2]) At time T1 the pulse travels toward the chamber. At time T2 the pulse is just entering the chamber, yet it has already exited the far side due to the nature of the Caesium. The leading edge of the pulse has been rephased further along the propagation line due to the anomalous dispersion in the gas. At time T3 the pulse has exited the chamber superluminally. In distance terms the advanced pulse would have travelled 19 metres past the chamber before the original pulse would have exited the chamber. NB The diagrams in Figure 5 are greatly exaggerated for the purpose of demonstration. We do not presently know whether this effect can be used to speed up optical signalling. Wang has applied for a patent, but there is an issue that still has not been resolved as to whether the signal velocity (the speed at which a signal is transmitted using a light pulse) can be faster than light. Most textbooks suggest that the signal velocity must always remain below c even when travelling through a region of anomalous dispersion [6]. In this case it is assumed that the signal velocity must stay at c. Wang published a document on the issue, in which he ruled out superluminal signalling [7] but the discussion as to whether it will be possible to send information faster than light is still ongoing. (IV) Conclusion. When Dr. Lijun Wang’s experiment was first released to the media, it was sensationalised with headlines such as “Eureka! Scientists break the speed of light” [5]. The papers spoke of how Wang and his team had broken the speed of light, proved Einstein “wrong” and showed that there were inconsistencies in his theory of Relativity. This created a wrong impression of what Wang was actually doing. All aspects of the “Gain Assisted Superluminality” experiment can be explained by existing laws of physics. No laws of physics were broken and no new laws were created. Even Wang himself says that the experiment is not “at odds” with Relativity [2]. The prospect of projecting light superluminally using anomalous dispersion had been with us well before Wang embarked on this project. Steven Chu and Stephen Wong, who were researching at Bells Labs at the time, had previously carried out similar experiments with anomalous dispersion and group velocities in 1982 [3], which showed that light could be propagated superluminally. Wang just took his work one step further. Historically, these anomalous effects had only been seen in opaque materials, but Wang showed that by manipulating Caesium gas with lasers and pumping it to a certain state, it was possible to demonstrate these conditions in a transparent medium also. So, what are the practical uses of this experiment, if we can’t build time machines or send information into the past? When the experiment was originally unveiled in July 2000, it was initially suggested that the superluminality effect could be used to speed up electronic circuitry. Seeing as how that article was released nearly six months ago, I thought I’d mail Dr. Wang for an update. Dr Wang said, “it has not been used in any electronic equipment as yet”. So, at the present moment, no real uses have come from the Gain assisted Superluminality experiment. References: 1. “Gain Assisted Superluminal Light Propagation” – L.J.Wang, A Kuzmich and A.Dogariu. 2. Dr Lijun Wang’s web site - http://www.neci.nj.nec.com/homepages/lwan/gas.htm 3. “Linear Pulse Propagation in an absorbing medium” – S. Chu and S. Wong (1982) 4. “Electromagnetically Induced Transparency” S.E. Harris – Physics Today issue 50. 5. “Eureka! Scientists Break The Speed Of Light” – Sunday Times June 4 2000 6. “Optics” – Hecht. 7. “Signal velocity, Causality and quantum noise in Superluminal Light Pulse Propagation”L.J. Wang, A. Doragiu and A. Kuzmich.