Cavity fields interaction

More specifically, the unique modal field profile and characteristics of the CBNL structure are advantageous for biochemical sensing applications, but also for surface emitting lasers and for studies involving strong atom-field interactions such as nonlinear optics and cavity QED. 

In the absence of noise, the system [179] describes the generation of a singlemode laser field interacting with a homogeneously broadened two-level medium [180]. The variables and parameters of the Lorenz system can be interpreted in terms of a laser system as q is the normalized electric field amplitude, the normalized polarization, q3 the normalized inversion, a = fe/y1 r = A+l, b = 72/71, with k the decay rate of the field in the cavity, yj and y2 the relaxation constants of the inversion and polarization, and A the pump parameter. Far-infrared lasers have been proposed as an example of a realization of the Lorenz system [162]. A detailed comparison of the dynamics of the system (42) and a far-infrared laser, plus a discussing the validity of the Lorenz system as laser model, can be found in Ref. 163. 

The key differences between the PCM and the Onsager s model are that the PCM makes use of molecular-shaped cavities (instead of spherical cavities) and that in the PCM the solvent-solute interaction is not simply reduced to the dipole term. In addition, the PCM is a quantum mechanical approach, i.e. the solute is described by means of its electronic wavefunction. Similarly to classical approaches, the basis of the PCM approach to the local field relies on the assumption that the effective field experienced by the molecule in the cavity can be seen as the sum of a reaction field term and a cavity field term. The reaction field is connected to the response (polarization) of the dielectric to the solute charge distribution, whereas the cavity field depends on the polarization of the dielectric induced by the applied field once the cavity has been created. In the PCM, cavity field effects are accounted for by introducing the concept of effective molecular response properties, which directly describe the response of the molecular solutes to the Maxwell field in the liquid, both static E and dynamic E, [8,47,48] (see also the contribution by Cammi and Mennucci). 

The usefulness or the IEF approach relies on the possibility of expressing physical properties, which depend on the interaction between the molecular charges and the reaction/cavity field, as surface integrals of the general form [8,9,18] ... 

This model may describe, for example, a spin -particle confined to move in a one-dimensional harmonic potential whose spin is subject to a harmonic magnetic field or a two-level atomic system interacting with a single mode of a cavity field. It is of interest here as example of an interaction between a discrete- and a continuous-variable system. 

In addition, the molecules properties are changed due to the interaction with the surrounding medium. Several computational schemes have been proposed to address these effects. Tliey are essentially based on the extension of the Onsager reaction field cavity model and give effective hyperpolarizabilities, i.e. molecular hyperpolarizabilities induced by the external fields that include the modifications due to the surrounding molecules as well as local (cavity) field effects [40 2]. These condensed-phase effects have, however, not yet been included in the SFG hyperpolarizability calculations, which are therefore strictly gas-phase calculations. 

There have been several proposals to generate the antisymmetric state a) in a system of two identical atoms interacting with a single-mode cavity field. For... 

Our consideration so far have applied to photons in an ideal spherical cavity. Consider now the very important case of interaction between a single atom with electric dipole transition and cavity field in the case of Fabry-Perot resonator formed by two parallel ideal reflecting mirrors. In this case, the cavity field can consist only of the photons propagating along the axis of resonator (z axis) because all other photons should leave the space limited by the mirrors. This means that the cavity photons have well-defined direction and therefore are in a state with given linear momentum (21)-(22). Hence, the radiation emitted by the electric dipole transition consists of the two modes with m = 1, while the radiation of the third mode m 0 is forbidden. In this case, the photons with given helicity can be represented in terms of linearly polarized photons as follows [27] ... 

Figure 8.2 Time dependence of the probability Pe(t) of observing the spontaneously decaying two-level system in its excited state at the center of a closed spherical cavity The number of resonantly interacting field modes is of the order of rR/ 7rc and depends on the size of the cavity R. For FR/c = 10 (upper figure) a spatially localized photon wave packet is generated by spontaneous emission and can be reabsorbed again by the two-level system at the center of the cavity at later times. For FR/c = 1 (lower figure) only a small number of cavity modes interact resonantly and the two-level system performs approximate Rabi oscillations governed by the vacuum Rabi frequency.

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