System Rydberg atomic

The problem of the interaction between the electromagnetic field created due to the NSCE and various detectors (harmonic oscillators, two-level systems, Rydberg atoms, etc.) placed inside the cavity with moving walls was studied by different methods [188,189,234-238]. It is also discussed in this chapter. 

The interaction of very excited atomic systems (Rydberg atoms) with electromagnetic fields has been the object of a large number of theoretical... 

A term that is nearly synonymous with complex numbers or functions is their phase. The rising preoccupation with the wave function phase in the last few decades is beyond doubt, to the extent that the importance of phases has of late become comparable to that of the moduli. (We use Dirac s terminology [7], which writes a wave function by a set of coefficients, the amplitudes, each expressible in terms of its absolute value, its modulus, and its phase. ) There is a related growth of literatm e on interference effects, associated with Aharonov-Bohm and Berry phases [8-14], In parallel, one has witnessed in recent years a trend to construct selectively and to manipulate wave functions. The necessary techifiques to achieve these are also anchored in the phases of the wave function components. This bend is manifest in such diverse areas as coherent or squeezed states [15,16], elecbon bansport in mesoscopic systems [17], sculpting of Rydberg-atom wavepackets [18,19], repeated and nondemolition quantum measurements [20], wavepacket collapse [21], and quantum computations [22,23], Experimentally, the determination of phases frequently utilizes measurement of Ramsey fringes [24] or similar" methods [25]. 

In this context, it should be pointed out that an algebraic decay has also been numerically observed in classical Coulomb-type models of atomic autoionization processes by Blumel [141]. This might turn out to be relevant for Rydberg molecules, which also represent Coulomb-type systems. For the recent observation of algebraic decays in Rydberg atoms, see Ref. 142. 

Using a simple, three level model we can develop a feeling for the microwave powers required to observe radiatively assisted collisional energy transfer between Rydberg atoms.3 Consider the dipole-dipole atomic system shown in Fig. 15.1(a). In the Na ns + ns— np + (n - l)p resonant collisions described in the previous chapter the ns state corresponds to both s and s of Fig. 15.1(a) and the n — 1 and np states correspond to p and p of Fig. 15.1(a), respectively. The collisions occurs via the interaction... 

Chaos does not only wreak havoc in otherwise orderly atomic spectra, it also provides a natural framework, indeed a common language, in which one can discuss such seemingly unrelated systems as, e.g., ballistic electrons in mesoscopic semiconductor structures, the hehum atom, and Rydberg atoms in strong external fields. All these systems have one feature in common their classical counterparts are chaotic. Chaos imprints its presence on their spectra and manifests itself in spectral features which are very similar for all these systems (universahty). 

There are three main reasons for presenting the SSE system in this book, (i) Due to its low dimensionality it is a fundamental system. It is described with the help of analytical tools that are widely used in the analysis of Rydberg atoms in strong radiation fields, (ii) The classical version of the SSE system is chaotic, (iii) Surface state electrons possess an ionization continuum, an important feature in all of atomic physics. Since the SSE system is both simple and physical, it is a natmral candidate for research in classically chaotic driven systems that allow ionization to take place. 

Bayfield and Koch (1974) provided the first experimental results on a manifestly quantum, but classically chaotic, system hydrogen Rydberg atoms in a strong microwave field. Both pioneers, Bayfield at Pittsburgh and Koch at Stony Brook, continue to contribute actively to the investigation of time dependent chaos in Rydberg atoms. 

Main, J. and Wunner, G. (1994). Rydberg atoms in external fields as an example of open quantum systems with classical chaos, J. Phys. B27, 2835-2848. 

Shepelyansky, D.L. (1985). Quantum diffusion limitation at excitation of Rydberg atom in variable field, in Chaotic Behaviour in Quantum Systems, ed. G. Casati (Plenum, New York). 

Rydberg atoms and microwave fields constitute an ideal system for the study of atom-strong field effects, and they have been used to explore the entire range of one electron phenomena [5]. Here we focus on an illustrative example, which has a clear parallel in laser experiments, a series of experiments which show that apparently non-resonant microwave ionization of nonhydronic atoms proceeds via a sequence of resonant microwave multiphoton transitions and that this process can be understood quantitatively using a Floquet, or dressed state approach. 

The interpretation of the evolution of the total system has been proposed in several references [Mourachko 1998 Akulin 1999 Frasier 1999]. We do not develop in this article the details of the different theoretical approaches. It is clear that the pairs of closest neighboring Rydberg atoms play a particular role in the reaction. They can be considered as two-level systems coupled with a... 

If we turn this requirement around, it is clear that high Rydberg states themselves may be used as excellent probes to reveal the influence of external fields on quantum systems. In fact, Rydberg atoms are widely used to probe the influence of either static electric and magnetic or AC fields, or combinations of fields. Examples of how the influence of external fields can be studied will be presented in chapters 9 and 10. 

On the other hand, the rapid advancement of laser spectroscopy has made it possible to produce atoms in highly exited states. It has been realized, that these Rydberg atoms in uniform external fields are gateway systems for studying various aspects of chaos in... 

Thus the spontaneous emission rate for a two-level system is increased if the atom is surrounded by a cavity tuned to the transition frequency. This was already noted years ago by Purcell [9]. Conversely, the decay rate decreases when the cavity is mistuned [10]. In the case of an ideal cavity far off the atomic resoncance, no mode is available for the photon, and spontaneous emission cannot occur. In order to eliminate spontaneous emission completely, every propagating mode must be suppressed. The advent of Rydberg atoms has rendered the realisation of such experiments possible. 

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