Atoms in Strong Light Fields
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An atom initially prepared in a single site delta-like homogeneously fills the Brillouin zone. This explains the emergence of two ballistic peaks near the maximum range of the walk. Forces, for instance acceleration of the lattice or a field gradient, will lead to e.
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Bloch oscillations like free electrons in a crystal lattice. Interactions are characterized by a phase shift which occurs if and only if the walkers meet at the same site on-site collisions. The problem can be simulated on a computer but is also tractable in analytic terms. This situation resembles the textbook problem of molecular binding by a delta -like potential. Schawlow and C. Townes with a famous publication in 20 predicting the laser along with many of its properties in detail.
The race was won —mostly unexpected by the large mainstream technical laboratories— by T. For instance, James Bond was among its earliest clients. Obama to the congress and by numerous other activities In Europe, the anniversary of the laser seems to have attracted much less attention, in spite of the contribution by European scientists and in spite of the driving force that the laser keeps exerting on science and technology. Addressing the origin and future of the laser offers interesting insight into the interplay of basic and applied research and asks for the attention of society at an appropriate level.
Already in , one of the first laboratories began investigating the properties of black bodies. This work —in plain words— performed technology analyses for the rising industry producing electric lanterns for street lighting. It led directly into the discovery of quantum physics in by M. Planck, laying no less than the foundations of modern physics. At about the same time, the electron was discovered by J. Thomson, triggering the birth of the electronics industry. Moreover, in H. This hurdle provoked C. Townes 23 in parallel with N. Basov and N. Prokhorov in Russia to invent the maser micro wave amplification by stimulated emission of radiation based on the principle of stimulated emission: he left the machined electron tube type devices and resorted to oscillating molecules instead.
From there it was a small step only to extend the principles to laser radiation at visible wavelengths.
Atoms in Strong Light Fields (Springer Series in Chemical Physics)
However, the concept of achieving inversion, laid out by Einstein already but corresponding e. Perhaps the most relevant beacon was set in , when the operation of the first semiconductor laser —which had been predicted by J. Semiconductor lasers are a case in point where samples for room temperature laboratory use became available in the mid-to-late s only. Here, the final breakthrough was owed to the invention of heterostructures in GaAs, a material first used by H. Welker at Siemens laboratories. It is no surprise that the present world market of lasers is dominated by diode lasers.
The arrival of laser based technologies has been slower but they offer the potential for a similar impact —the 21 st century may indeed become a century of the photon. Meschede, A. Spethmann et al, Phys. Steffen et al.
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Science, , , Kimble in P. Berman, Cavity quantum electrodynamics , Academic Press, Boston, Reick et al. Brakhane et al, Phys. Lloyd, Science, , , Kempe, Cont.
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This rotation could be stopped or sped up by imparting an additional spin angular momentum of -1 or 1, by changing the beam polarization from left to right circular, so that the total angular momentum either vanishes or adds to 2. This experiment proved the mechanical equivalence of the rotational forces imparted by spin and orbital angular momenta. It may be worth noting that the tweezing force that leads to the trapping of particles has a different physical origin than the force that causes rotation.
The tweezing force results from the fact that light is refracted by the particles, thus transferring linear momentum from the light to the particle, and acts in the radial direction. The force causing rotation instead arises from a transfer of linear momentum in the azimuthal direction, the direction without an intensity gradient. In recent experiments twisted light carrying orbital angular momentum has been used to trap and manipulate atoms and even to transfer orbital angular momentum to cold atoms and BECs.
Initial atomic experiments with Laguerre-Gauss laser beams relied on the spatial intensity structure of twisted light rather than on its phase structure—the orbital angular momentum of the light played no role in these experiments. A single Laguerre-Gauss beam with its dark axis cylindrically surrounded by a bright tube of light can form an "optical pipe.
In Klaus Sengstock and colleagues at Hannover University in Germany guided Bose-Einstein condensates along such light tubes, and a few years earlier Takahiro Kuga and his group at Tokyo University "plugged" a light tube at both ends with additional blue-detuned light in order to trap cold atoms. If a red-detuned Laguerre-Gauss beam is used instead, atoms can be stored in the long, bright "optical cylinder.
Figure 5. The best way to create a steady interference pattern between two lasers is to start out with one laser beam and split it in two, creating a pair of identical beams. The beams are then focused onto a spatial light modulator top right. This liquid crystal display is programmed with a pair of different holographic patterns, one for each beam, that diffract the beams by different amounts and give them different amounts of orbital angular momentum here, an l of 3 on the left and 11 on the right.
This optical Ferris wheel can then trap and rotate atoms. What happens when we add another twisted laser beam to the mix?
We are surrounded by innumerable waves of many different kinds: water waves, sound waves and the huge range of electromagnetic waves, which span the spectrum from radio waves through visible light, right out to gamma- and x-ray radiation. One thing all waves have in common is that when two waves overlap they interfere: Two wave crests at the same place and time are in phase and add constructively to form a larger wave crest.
If, however, one wave's crest and another equal-sized wave's trough coincide, the waves cancel. When the light from two horizontally separated coherent light sources is combined on a distant screen, we observe a pattern of bright and dark vertical interference fringes where the light waves from the two sources combine with equal and opposite phases, respectively. Now consider two Laguerre-Gauss beams traveling in the same direction. Unlike interfering water waves or plane light waves, the phase of each wave is not uniform over the beam profile but changes with azimuth angle.
Interaction of super-intense light fields with atoms and surfaces
The two Laguerre-Gauss beams will thus be in phase at some angles and not at others. To some extent we can illustrate this effect with an analog clock. The minute hand rotates around the clock face 12 times faster than the hour hand. The minute and hour hands are aligned at 11 distinct times during a day, such as at , and The clock hands are also furthest apart at 11 different times such as and , corresponding to the angles at which the Laguerre-Gauss beams are exactly out of phase, so that the combined beam is darkest. To continue the analogy for more general Laguerre-Gauss beams, one would require a funky clock where one hand rotates l 1 times for every l 2 rotations of the other hand negative l values imply counter-clockwise rotation.
The limitation of the analogy is that for the combined Laguerre-Gauss laser beams, all bright and dark regions can be seen simultaneously. We use such interference to generate optical ring lattices suitable for confining atoms at either the bright or the dark region within the interference pattern. Optical lattices are ironically a very hot, dynamic topic in cold atoms.
An optical lattice confines atoms at regularly spaced positions, similar to the lattice of atoms that exist in a pure crystal of, say, diamond. Superimposing different light beams generates an interference pattern with alternating bright and dark regions—an optical crystal. Optical lattices could provide a physical realization of a quantum register, where atoms in each light cell correspond to one quantum bit of information.
Optical lattices also allow the investigation of problems commonly associated with solid-state physics but enable the experimenters to change certain parameters of their artificial crystal at will. Very recently we have investigated an optical setup that will be used to trap cold atoms in a ring lattice. A standard optical lattice is a "cube" with sides of about sites, but pure crystals in the solid state can be much more extensive. Because a ring has no end or beginning point, a ring lattice is a good approximation of an infinite one-dimensional lattice, which is particularly interesting as quantum effects are strongest at low dimensions.
We have realized our optical ring lattice experimentally by superimposing two light beams that carry orbital angular momentum.
Overlapping two co-propagating Laguerre-Gauss beams with opposite values of l, the beams interfere constructively at angles where their phases match and destructively in between, where they are exactly out of phase. The resulting interference pattern is a ring of 2 l bright regions. Using red-detuned light, atoms can be trapped at these lattice sites by the optical dipole force. Alternatively, lattices with dark intensity regions surrounded by bright light can be generated by choosing appropriate pairs of Laguerre-Gauss beams with different orbital angular momenta.
The radius of the bright intensity rings of Laguerre-Gauss beams increases with the square root of the absolute value of l , so the intensity ring of the beam with the larger orbital angular momentum has a larger radius. At the same time, the peak intensity of a beam decreases again by the same value, the square root of the absolute value of l , and for equal power, the outer intensity ring is dimmer than the other.
Complete constructive or destructive interference, however, requires equal light intensities and therefore occurs at a radius where the light intensities of the two beams balance.