Interaction coherent

In certain situations involving coherently interacting pairs of transition dipoles, the initial fluorescence anisotropy value is expected to be larger tlian 0.4. As mdicated by the theory described by Wyime and Hochstrasser [, and by Knox and Gtilen [, ], the initial anisotropy expected for a pair of coupled dipoles oriented 90° apart, as an example. 

Figure 1. Diagram of the intensity / (W/cm2) vs. duration of laser pulse tp(s) with various regimes of interaction of the laser pulse with a condensed medium being indicated very qualitatively. At high-intensity and high-energy fluence 4> = rpI optical damage of the medium occurs. Coherent interaction takes place for subpicosecond pulses with tp < Ti, tivr. For low-eneigy fluence (4> < 0.001 J/cm2) the efficiency of laser excitation of molecules is very low (linear interaction range). As a result the experimental window for coherent control occupies the restricted area of this approximate diagram with flexible border lines.

Coherent interaction is called the dipoleJim e. The incoherent interaction that alters ihc momentum of an aiom is called the scntieruig /one. 

A number of interesting conclusions follow from Eq. (81). In the first place, we note that the superposition states decay at different rates, the symmetric state decays with an enhanced rate (F I T ), while the antisymmetric state decays at a reduced rate (r — 1)2). For F12 = T, the antisymmetric state does not decay at all. In this case the antisymmetric state can be regarded as a dark state in the sense that the state is decoupled from the environment. Second, we note from Eq. (81) that the state a) is coupled to the state j) through the splitting A, which plays a role here similar to the Rabi frequency of the coherent interaction between the symmetric and antisymmetric states. Consequently, an initial population in the state a) can be coherently transferred to the state j), which rapidly decays to the ground state. When A = 0, that is, the excited states are degenerate, the coherent interaction does not take place and then any initial population in a) will stay in this state for all times. In this case we can say that the population is trapped in the state u). 

The first terms on the right-hand side of Eq. (109) determine the spontaneous emission rates from the symmetric and antisymmetric states, while the second terms determine the coherent interaction between these two states. Note that the... 

According to Eq. (115), the CPT can also be destroyed by the presence of the coherent interaction Ac between the symmetric and antisymmetric states. This is shown in Fig. 9, where we plot the steady-state population p33 as a function of A for different values of lA/Ti. It is evident that the cancellation of the population p33 appears only at Ac = 0, that is, in the absence of the coherent interaction between the antisymmetric and symmetric states. For I i = T2 the cancellation appears at A = 0, while for I / r2 the effect shifts toward nonzero A given by... 

We have shown in Section V.A.2 that a laser field can drive the V-type system into the antisymmetric (trapping) state through the coherent interaction between the symmetric and antisymmetric states. Akram et al. [24] have shown that in the A system there are no trapping states to which the population can be transferred by the laser field. This can be illustrated by calculating the transition dipole moments between the dressed states of the driven A system. The procedure of calculating the dressed states of the A system is the same as for the V system. The only difference is that now the eigenstates of the unperturbed Hamiltonian Ho are 3, N - 1), 1,N), 2,N), and the dressed states are given by... 

The master equation (38) provides the simplest example of the effects introduced by the coherent interaction of atoms with the radiation field. These effects include the shifts of the energy levels of the system, produced by the dipole-dipole interaction, and the phenomena of enhanced (superradiant) and reduced (subradiant) spontaneous emission, which appear in the changed damping rates to (T + Ti2) and (T — Ti2), respectively. 

The decoupling of the antisymmetric state a ) from the coherent field prevents the state from the external coherent interactions. This is not, however, a useful property in terms of quantum computation, where it is required to... 

The second term in Eq. (57), proportional to the dipole-dipole interaction between the atoms, has two effects on the dynamics of the symmetric and antisymmetric superpositions. The first is a shift of the energies, and the second is the coherent interaction between the superpositions. It is seen from Eq. (57) that the contribution of Yin to the coherent interaction between the superpositions vanishes for Ti = T2, and then the effect of f > 12 is only the shift of the energies from their unperturbed values. Note that the dipole-dipole interaction Hi2 shifts the energies in the opposite directions. 

The parameters A and Ac allow us to gain physical insight into how the dipole-dipole interaction O12 and the frequency difference A can modify the dynamics of the two-atom system. The parameter A appears as a shift of the energies of the superposition systems, while Ac determines the magnitude of the coherent interaction between the superpositions. For Yl 2 / 0 and identical atoms the shift A / 0, but can vanish for nonidentical atoms. This occurs for... 

Thus, the condition V 2 = /1 1I2 for suppression of spontaneous emission from the antisymmetric state is valid for identical as well as nonidentical atoms, whereas the coherent interaction between the superpositions appears only for nonidentical atoms with different transition frequencies and/or spontaneous damping rates. 

This equation shows that the nondecaying antisymmetric state —) can be populated by spontaneous emission from the upper state e) and also by the coherent interaction with the state +). The first condition is satisfied only when Ti i=- T2, while the other condition is satisfied only when Ac / 0. Thus, the transfer of population to the state —) from the upper state e) and the symmetric state s) does not appear when the atoms are identical, but is possible for nonidentical atoms. 

King s analysis of this three-reactant case clearly shows that the symmetry properties of chemical reaction networks provide the basis for understanding what must be the case in order for such systems to generate a closed sequence of states, and thereby provide the basis of the coherent interaction necessary to qualify as a substance in Millikan s (and Husserl s) sense. 

To demonstrate the influence of longitudinal coherent interactions we have investigated the transmission and reflection spectra of ID photonic crystals based on close-packed silver nanosphere monolayers separated by thin solid dielectric films. The strongest spectral manifestation of longitudinal electrodynamic coupling was shown [2] to take place in the case of joint electron and photonic confinements. In order to achieve it we chose intermonolayer film thicknesses Im so that the photonic band gap and the metal nanoparticle surface plasmon band could be realized at close frequencies in the visible. 

O. Faucher, Y.L. Shao, D. Charalambidis, Modification of a structured continuum through coherent interactions observed in third harmonic generation, J. Phys. B 26 (1993) L309. 

So far, only coherent Interactions, which can be represented in the Hamiltonian, have been considered. There are, however, also incoherent pair interactions, in particular in the form of dipolar cross-relaxation and of chemical exchange processes. 

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