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Exercises




D

History teaches us that new phenomena and structures are discovered as a result of improved precision in measuring. A splendid example is atomic spectroscopy, which studies the structure of energy levels in atoms. Improved resolution has given us a deeper understanding of both the fine structure of atoms and the properties of the atomic nucleus. The other half of this year’s Nobel Prize in Physics, awarded to John L. Hall and Theodor W. Hä nsch, is for research and development within the field of laser-based precision spectroscopy, where the optical frequency comb technique is of special interest. The progress that has been made in this field of science can give us previously unthought of possibilities to investigate constants of nature, find out the difference between matter and antimatter and measure time with unsurpassed precision. Precision spectroscopy was developed when trying to solve some quite clear and straightforward problems as follows below.

E

The problem of determining the exact length of a metre illustrates one of the challenges offered by laser spectroscopy. The General Conference of Weights and Measures, which has had the right to decide on the exact definitions since 1889, abandoned the purely material measuring rod in 1960. This was kept under lock and key in Paris and its length could only with difficulty be distributed throughout the world.

By use of measurements of spectra, an atom-based definition was introduced: a metre was defined as a certain number of wavelengths of a certain spectral line in the inert gas krypton.

Some years later also an atom-based definition of a second was introduced: the time for a certain number of oscillations of the resonance frequency of a particular transition in cesium, which could be read off the cesium-based atomic clocks. These definitions made it possible to determine the speed of light as the product of wavelength and frequency.

John Hall was a leading figure in the efforts to measure the speed of light, using lasers with extremely high frequency stability. However, its accuracy was limited by the definition of the metre that was chosen. In 1983, therefore, the speed of light was defined as exactly 299, 792, 458 m/s, in agreement with the best measurements, but now with zero error! In consequence, a metre was the distance travelled by light in 1/299, 792, 458 s.

However, measuring optical frequencies in the range round 1015 Hz still proved to be extremely difficult due to the fact that the cesium clock had approximately 105 times slower oscillations. A long chain of highly-stabilised lasers and microwave sources had to be used to overcome this problem. The practical utilisation of the new definition of a metre in the form of precise wavelengths remained problematic; there was an evident need for a simplified method for measuring frequency.

Parallel with these events came the rapid development of the laser as a general spectroscopic instrument. Also, methods for eliminating the Doppler effect were developed, which if not dealt with leads to broader and badly identifiable peaks in a spectrum. In 1981 N. Bloembergen and A. L. Schawlow were awarded the Nobel Prize in Physics for their contribution to the development of laser spectroscopy. This becomes especially interesting when an extreme level of precision can be attained, allowing fundamental questions concerning the nature of reality to be tackled. Hall and Hä nsch have been instrumental in this process, through the development of extremely frequency-stable laser systems and advanced measurement techniques that can deepen our knowledge of the properties of matter, space and time.

F

Measuring frequencies with extremely high precision requires a laser which emits a large number of coherent frequency oscillations. If such oscillations of somewhat different frequency are connected together, the result will be extremely short pulses caused by interference. However, this only takes place if the different oscillations (modes) are locked to each other in what is called mode-locking. The more different oscillations that can be locked, the shorter the pulses. A 5 fs long pulse (a femtosecond, fs [10-15 s], is a millionth billionth of a second) locks about one million different frequencies, which need to cover a large part of the visible frequency range. Nowadays this can be attained in laser media such as dyes or titanium-doped sapphire crystals. A tiny “ball of light” bouncing between the mirrors in the laser arises because a large number of sharp and evenly distributed frequency modes are shining all the time! A little of the light is released as a train of laser pulses through the partially transparent mirror at one end. Since pulsed lasers also transmit sharp frequencies, they can be used for high-resolution laser spectroscopy. This was realised by Hä nsch as early as in the late 1970s and he also succeeded in demonstrating it experimentally. V. P. Chebotayev, Novosibirsk, (d. 1992) also came to a similar conclusion.

However, a real breakthrough did not occur until around 1999, when Hä nsch realised that the lasers with extremely short pulses that were available at that time could be used to measure optical frequencies directly with respect to the cesium clock. That is so because such lasers have a frequency comb embracing the whole of the visible range. Thus the optical frequency comb technique, as it came to be called, is based on a range of evenly distributed frequencies, more or less like the teeth of a comb or the marks on a ruler. An unknown frequency that is to be determined, can be related to one of the frequencies along the “measuring stick”.

Hä nsch and his colleagues convincingly demonstrated that the frequency marks really were evenly distributed with extreme precision. One problem, however, was how to determine the absolute value of the frequency; even if the separation is very well-defined between the teeth of the comb, an unknown common frequency displacement occurs. This deviation must be determined exactly if an unknown frequency is to be measured. Hä nsch developed a technique for this purpose in which the frequency also could be stabilised, but the problem was not solved practically and simply until Hall and his collaborators demonstrated a solution around the year 2000. If the frequency comb can be made so broad that the highest frequencies are more than twice as high as the lowest ones (an octave of oscillations), the frequency displacement can be calculated by simple subtraction involving the frequencies at the ends of the octave. It is possible to create pulses of this kind with a sufficiently broad frequency range in so-called photonic crystal fibres, in which the material is partially replaced by air filled channels. In these fibres a broad spectrum of frequencies can be generated by the light itself. Hä nsch and Hall and their colleagues have subsequently, partly in collaborative work, refined these techniques into a simple instrument that has already gained wide use and is commercially available. An unknown sharp laser frequency can now be measured by observing the beat between this frequency and the nearest tooth in the frequency comb; this beat will be in an easily-managed radio frequency range. This is analogous to the fact that the beat between two tuning forks can be heard at a much lower frequency than the individual tones.

Quite recently frequency comb techniques have been extended to the extreme ultraviolet range, which can be attained by generating overtones from short pulses. This may mean that extreme precision can be achieved at very high frequencies, thereby leading to the possibility of creating even more accurate clocks at X-ray frequencies.

Another aspect of the frequency comb technique is that the control of the optical phase, that it permits, is also of the greatest importance in experiments with ultra short femtosecond pulses and in ultra-intense laser-matter interaction. The high overtones, evenly distributed infrequency, can be phase-locked to each other, whereby individual attosecond pulses approximately100 as long (1 as = 10-18 s) can be generated by interference in the same way as in the mode-locking described above. Thus the technique is of the greatest relevance for precision measurements in both frequency and time.

G

It now seems possible, with the frequency comb technique, to make frequency measurements in the future with a precision approaching one part in 1018. This will soon lead to actualize the introduction of a new, optical standard clock. What phenomena and measuring problems can take advantage of this extreme precision?

The precision will make satellite-based navigation systems (GPS) more exact. Precision will be needed in, for example, navigation on long space journeys and for space-based telescope arrays that are looking for gravitational waves or making precision tests of the theory of relativity. Applications in telecommunication may also emerge.

This improved measurement precision can also be used in the study of the relation of antimatter to ordinary matter. Hydrogen is of special interest. When anti-hydrogen can be experimentally studied like ordinary hydrogen, it will become possible to compare their fundamental spectroscopic properties.

Finally, greater precision in fundamental measurements can be used to test possible changes in the constants of nature over time. Such measurements have already begun to be made, but so far no deviations have been registered. However, improved precision will make it possible to draw increasingly definite conclusions concerning this fundamental issue.

 

(http: //www. nobelprize. org/nobel_prizes/physics/laureates/2005/public. html)

 

 

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