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38 Fig. 7 One-dimensional cut through the potential in Fig 6. In this simpler picture I include the electron wave function. It has two parts, the part trapped by the ion and the part that is pulled free of the ion – called a wave packet. The likelihood of re-collision Max Born • Paul Corkum is driven so strongly by the light field and returns to the atoms so quickly after its birth that it can hardly miss! Still, in science, it is important to measure to make sure. In quantum mechanics, the way measurements are made determines what we can learn about the object that we measure. We start with a hydrogen molecule. Although we do not know if the electron makes it through the beam-splitter (ie, ionizes), the molecule itself can tell us – if we measure a hydrogen molecular ion, then we know that the molecule ionized. The molecule can tell us even more. Whenever the electron is removed from the hydrogen molecule, one of the two electrons binding hydrogen is removed. With that one electron gone, the bond weakens. The molecular ion stretches. That is, it starts to vibrate much like a vibrating quartz crystal in a watch, or the oscillation of a pendulum in a grandfather clock. In other words, removing the electron starts a clock ticking – starts a stopwatch [10]. If the removed electron re-collides with the ion, it can dislodge the one remaining electron. Should this occur, the vibration ceases – the watch stops ticking – and the molecule is transformed into two hydrogen ions in close proximity. We are interested in the delay between ionization and re-collision and the likelihood that re-collision will occur. We determine the probability of re-collision by comparing the number of atomic hydrogen ions that are produced to the total number of ionization events. Since we know that like charges repel and that the kinetic energy they gain depends on how close they were to each other when the second electron was dislodged, measuring the ion’s kinetic energy reveals how far they were separated when the re-collision occurred (in other words, measuring the delay between ionization and re-collision). Figure 9 shows a light wave on which we have superimposed the time and probability of the re-collision. For illustration purposes, the figure assumes that ionization occurred near the field maximum represented by the arrow. In the language of “collision physics,” we use the term “current density,” by which we mean the electrical current per unit area of an electron beam that would be needed to simulate the re-collision. The current density is closely related to the time dependent probability of an electron ion re-collision. The solid curve is from a simulation. The data points (not shown here, but available in [10]) are obtained by reading the molecular clock. The electron is most likely to return about 1.7 femtoseconds after it has left, and most of the probability of the electron re-colliding is confined to about 1 femtosecond (1000 attoseconds).
Not shown in Fig. 9 is that those electrons that re-collide early in the pulse (for example about 1 femtosecond after ionization) have low velocity (long wavelength). Those that re-collide near the peak of the pulse (about 1.7 femtoseconds) have high velocity (shorter wavelengths). Those that re-collide after the pulse peak (for example about 2.5 femtoseconds) have longer wavelengths again. It is this well-confined re-collision, combined with the energy sweep that accompanies it, that ultimately allows us to produce attosecond pulses. We have already shown that when intense laser pulses ionize atoms or molecules, an electron interferometer is naturally formed. To use the interferometer to characterize the waves, we must find a way to “see” the interference. Figure 10 (which is a three-dimensional version of Fig. 7) concentrates on the region where the re-collision electron and the initial wavefunction overlap. This is where the interference actually occurs. The wave in blue on the top left and right images represents the re-collision electron. It looks like a uniform wave passing over the initial wave function. The left and right images represent the wave at two closely spaced instants. In Fig. 10, the re-collision wave has advanced by 1/2 wavelength between the two images. When waves interfere, we add the overlapping components of the wave – in this case, the recollision wave packet and the bound-state wave function. (The same things happen in a swimming pool when the wave packets created by two divers meet.) The upper images contain this addition. The biggest peak on the sum wave moves from one side of the atom to the other between the two images. We highlight this in the colour coding. Max Born taught us that the square of the image represents the probability of finding the electron in any region of space. The square of the wave function is shown on the middle image. The bottom images are two-dimensional projections of the 3-D images in the middle frames. They are included as an alternative (and perhaps easier) way to visualize the process. The middle images or their 2-D projections show that interference between the bound and the re-collision electron transfers the charge from left to right. This rapid oscillating motion continues as long as the re-collision lasts. The faster the re-collision electron moves, the faster the oscillation. An oscillating charge produces radiation at the frequency of the oscillation. Observing this light solves our third challenge – “how to read the interference pattern.” Scientists have known for some time that gases of ionizing atoms produce extreme ultraviolet light. Since 1993, it has been known that re-collision explained the physics that underlies this light source [9]. Thus, Fig. 8 An optical interferometer is compared with the laser induced electron re-collision. Recording the electron interference Measuring the interference – High harmonics and attosecond optical pulses Max Born • Paul Corkum 39
Page 1: Max Born A Celebration Max Born A C
Page 4 and 5: Wolfgang Sandner, Managing Director
Page 6 and 7: Fig. 3 Max Born with the King and Q
Page 8 and 9: 6 Max Born • Gustav Born
Page 10 and 11: Fig .8 The Borns’ house in Bad Py
Page 12 and 13: Fig. 14 Max Born with his grandsons
Page 14 and 15: Fig. 21 A view of Cambridge College
Page 16 and 17: Fig. 23 Max Born with Gustav Born i
Page 18 and 19: Fig. 27 Albert Einstein: photograph
Page 20 and 21: 18 Fig. 34 Erwin Schrödinger, Max
Page 22 and 23: Fig. 37 The original paper by Doll
Page 24 and 25: Fig. 41 Analysis of end-plate poten
Page 26 and 27: Fig 46. Effect of mean blood flow v
Page 28 and 29: Fig. 49 The same quotation in Germa
Page 30 and 31: 28 Max Born • Gustav Born Fig. 52
Page 32 and 33: 30 Max Born • Gustav Born Fig. 54
Page 34 and 35: 32 Max Born • Paul Corkum
Page 36 and 37: 34 Fig. 1 A group of portraits from
Page 38 and 39: 36 Fig. 5 A sketch of a 5 femtoseco
Page 42 and 43: 40 Fig. 9 The probability of re-col
Page 44 and 45: Fig. 11 A sketch of the idea behind
Page 46 and 47: 44 Fig. 14 A reconstructed image of
Page 48 and 49: 46 Max Born • Paul Corkum
Page 50 and 51: i(pq - qp) = (h/2π), statistical o
Page 52 and 53: always remained 50 Max Born • Pau
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Page 56 and 57: 54 Address by the Rector of the Uni
Page 58 and 59: 56 Gustav Born, The William Harvey

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