Atomic coherence and interference

The atomic coherence and interference phenomenon in the simple three-level system sueh as EIT can be extended to more eomplicated multi-level atomic systems. A variety of other phenomena and applications involving three or four-level EIT systems have been studied in reeent years. In particular, phase-dependent atomic coherence and interference has been explored [52-66]. These studies show that in multi-level atomic systems coupled by multiple laser fields, there are often various types of nonlinear optical transitions involving multiple laser fields and the quantum interference among these transition paths may exhibit complicated spectral and dynamic features that can be manipulated with the system parameters such as the laser field amplitudes and phases. Here we present two examples of such coherently coupled multi-level atomic systems in which the quantum interference is induced between two nonlinear transition paths and can be eontrolled by the relative phase of the laser fields. 

Phase-dependent atomic coherence and interference in multi-level atomic systems... 

There have been several well-written review articles published in recent years to cover various aspects of atomic coherence and interference in multi-level systems. In this e-book, we put together reviews of several research topics related to laser-induced atomic coherence and interference, and its potential applications in atomic and solid media written by active researchers working in these fields. We hope that this e-book can serve as a good reference for graduate students and researchers interested in acquiring some general understanding and perspective of this active research field. 

Here we extend the simple three-level EIT system to mote complicated and versatile configurations in a multi-level atomic system coupled by multiple laser fields. We show that with multiple excitation paths provided by different laser fields, phase-dependent quantum interference is induced either constractive or destractive interfereiKe can be realized by varying the relative phases among the laser fields. Two specific examples are discussed. One is a three-level system coupled by bichromatic coupling and probe fields, in which the phase dependent interference between the resonant two-photon Raman transitions can be initiated and controlled. Another is a four-level system coupled by two coupling fields and two probe fields, in which a double-EIT confignration is created by the phase-dependent interference between three-photon and one-photon excitation processes. We analyze the coherently coupled multi-level atomic system and discuss the control parameters for the onset of constructive or destructive quantum interference. We describe two experiments performed with cold Rb atoms that can be approximately treated as the coherently coupled three-level and four-level atomic systems respectively. The experimental results show the phase-dependent quantum coherence and interference in the multi-level Rb atomic system, and agree with the theoretical calculations based on the coherently coupled three-level or four-level model system. 

Phase-dependent coherence and interference can be induced in a multi-level atomic system coupled by multiple laser fields. Two simple examples are presented here, a three-level A-type system coupled by four laser fields and a four-level double A-type system coupled also by four laser fields. The four laser fields induce the coherent nonlinear optical processes and open multiple transitions channels. The quantum interference among the multiple channels depends on the relative phase difference of the laser fields. Simple experiments show that constructive or destructive interference associated with multiple two-photon Raman channels in the two coherently coupled systems can be controlled by the relative phase of the laser fields. Rich spectral features exhibiting multiple transparency windows and absorption peaks are observed. The multicolor EIT-type system may be useful for a variety of application in coherent nonlinear optics and quantum optics such as manipulation of group velocities of multicolor, multiple light pulses, for optical switching at ultra-low light intensities, for precision spectroscopic measurements, and for phase control of the quantum state manipulation and quantum memory. 

Abstract In this chapter, we give a brief review of our recent research work related to atomic localization via the effects of atomic coherence and quantum interferences, as well as its application in atom nano-hthograph, which includes atomic localization based on double-daik resonance effects, sub-half-wavelength loealization via two standing-wave fields and an atom nano-lithograph scheme via two orthogonal standing-wave fields, ete.. 

At the same time, a diffraction grating with a period of about 1 A has the nature that the interatomic distances in crystals are about this size. As the interatomic distances are approximately 10 m and the size of even the smallest crystal is 10 m (repetition is 10 in the majority of cases), the crystal can be considered infinite. If a beam of X-rays falls on a crystal, under the action of an electromagnetic wave the atoms electrons begin to oscillate and scatter secondary radiation of the same wavelength in all directions (compare with Compton-effect, Section 6.6). As the atoms in a crystal are ordered, these secondary waves are coherent and interfere this defines the diffraction effect. 

To study the coherence and the decoherence problem in a mesoscopic frozen Rydberg gas, a variant of the Ramsey interference method has been proposed. The experiment has been performed for the rubidium atom by considering the reaction studied in reference [Anderson 1998 (b)],... 

The quantum mechanical treatment of the electron distribution about an isolated atom nucleus gives an electron density, p(r), which is peaked at the nuclear position and falls off smoothly as a function of the distance from the nucleus. Each unit of volume, dv, around this center can scatter X-rays and those that are scattered coherently will interfere with those scattered from other unit volumes near this atom, depending on the scattering angle. From Chapter 1 we know that the interference occurs as a phase shift, 4>, between the scattered waves parallel to the vector, S, from two unit volumes separated by r by ... 

The concepts of coherence and incoherence are related to the way in which the neutron, both as a wave and as a particle, interacts with the scattering sample. Wave-like representations of the neutron view its interaction with solids as occurring simultaneously at several atomic centres these atoms become the sources of new wavefronts. Since the scattering occurs simultaneously from all of these atoms the new wavefronts will spread out spherically from each new source and remain in phase. Provided the lattice is ordered, the coherence of the incident wave has been conserved. Constmctive interference between the new wavefronts leads to the generation of distinctive diffraction patterns with well-defined beams, or reflections, appearing only in certain directions in space and no intensity in other directions. 

The possibility to use laser radiations to achieve the so-called "coherent control" of molecular dissociation or of atomic photoionization has been predicted since the advent of laser sources in the early sixties. It was expected that, thanks to the coherence and monochromaticity properties of the laser light, one could selectively choose a dissociation channel and the spatial orientation of ejection of the fragments (either ions or electrons or even neutrals) in an elementary chemical process. However, earlier attempts, based on simple photoabsorption processes, have been unsuccessful and it is only recentiy that experiments have been shown to enable one to achieve such a goal in some selected systems. Amongst the various scenarios which have been explored, one of the most promising is based on the realization of quantum interferences in so-called "two-colour" photodissociation or... 

It could be proved that the superposition of two coherent atom laser beams which were released from two separate atomic traps results in interference structures similar to the superposition of coherent light waves [1179]. In Eig. 9.38 the total intensity of the superimposed two beams from two different EEC traps is shown as a function of the delay time between the two beams. The active medium of the laser which acts as amplifier corresponds to the EEC of the EOSER which is the reservoir for the atom laser and acts as amplifier because nearly aU atoms in the EEC are in their ground state and feed the atom laser as long as the trapping potential is switched off. 

The solid states represent bounded atomic associations and the diffraction intensity is a result of coherently scattered wave interference. The neutron scattering can be coherent elastic or inelastic and incoherent. In coherent total scattering experiment both elastically and inelastically scattered neutrons are detected, thus performing energy integration over the whole range gives a value for The total differential cross-section is,... 

In all cases of anode selection one must ensure that the coherently and incoherently scattered characteristic lines from the x-ray tube do not interfere with characteristic lines to be analyzed from the specimen. On the other hand, the characteristic anode lines may also be chosen to enhance the sensitivities for elements of slightly longer wavelengths. This technique can be applied for high-atomic-number elements as well as low-atomic-number elements. 

In siammary, the preliminary results presented in this contribution already demonstrate that time resolving polarization spectroscopy offers a number of favourable and new features for direct observation of fast evolving events on a femtosecond time scale and detection of oscillations up to the THz-range. The described technique can be applied to free atoms, liquids and solids to measure coherent transients in groimd and excited states. Since the observed beats result from an atomic interference effect, narrow structures which may be hidden by inhomogeneous broadening mechanisms can still be resolved. 

The increasing research on laser cooling of atoms and molecules and many experiments with Bose-Einstein condensates have brought about some remarkable results and have considerably increased our knowledge about the interaction of light with matter on a microscopic scale and the interatomic interactions at very low temperatures. Also the realization of coherent matter waves (atom lasers) and investigations of interference effects between matter waves have proved fundamental aspects of quantum mechanics. 

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