Coherent states atomic transitions

We consider the NMOR in coherent atomic media, where the basic mechanism of NMOR is the laser-induced coherence between the Zeeman sublevels of atomic ground state and, hence, the detected NFS is sensitive to the damping rate of atomic coherence. An atomic transition is chosen such that both A- and M-systems are created. Under usual conditions, the contributions of these systems to the Faraday signal cannot be separated, because their manifestations are similar. On the other hand, it is well known that for a given state the highest order atomic coherence is uniquely associated with the atomic polarization moment (PM) of the same order. This means that if we are able to detect the NMOR signal separately from different PM, the corresponding atomic coher-... 

Two-dimensional constant matrix, transition state trajectory, white noise, 203-207 Two-pathway excitation, coherence spectroscopy atomic systems, 170-171 channel phases, 148-149 energy domain, 178-182 extended systems and dissipative environments, 177-185 future research issues, 185-186 isolated resonance, coupled continuum, 168-169... 

UPS from Adsorbate Core Levels.—As outlined above, an out-going photoelectron in its final state is a super-position of two coherent contributions a direct wave whose amplitude and symmetry are determined by the intra-atomic transition at the emitting site and an indirect wave generated by repeated scattering of the direct wave by the local atomic environment. It was suggested by Liebsch that this final-state scattering should lead to angular variations in the photoemission spectrum and would be examined best in core-level emission, which involves the simplest possible initial... 

Another area of interest in quantum interference effects, which has been studied extensively, is the response of a V-type three-level atom to a coherent laser field directly coupled to the decaying transitions. This was studied by Cardimona et al. [36], who found that the system can be driven into a trapping state in which quantum interference prevents any fluorescence from the excited levels, regardless of the intensity of the driving laser. Similar predictions have been reported by Zhou and Swain [5], who have shown that ultrasharp spectral lines can be predicted in the fluorescence spectrum when the dipole moments of the atomic transitions are nearly parallel and the fluorescence can be completely quenched when the dipole moments are exactly parallel. 

In order to calculate the stationary state of the two-atom system, we have to know the steady-state populations pu of the collective atomic states and the coherencies Py(i 7 j)- First, we consider a system of two identical atoms (A = 0, Tj = r2) separated by an arbitrary distance rn and interacting with a squeezed vacuum field. Moreover, we assume that the carrier frequency (as of the squeezed vacuum field is resonant to the atomic transition frequencies (0)s = Mo). 

To illustrate the exchange of the phase information between the atomic transition and the multipole field, consider the electric dipole Jaynes-Cummings model (34). Assume that the field consists of two circularly polarized components in a coherent state each. The atom is supposed to be initially in the ground state. Then, the time-dependent wave function of the system has the form [53]... 

When a coherent laser field with average incident energy density W and frequency co interacts with a collection of N two-level atoms in ordinary vacuum, the steady state behavior of the system is governed by the well-known Einstein rate equations. These equations implicitly make use of the smooth nature of the vacuum density of states = o l 7t c ) in the vicinity of the atomic transition frequency co coq. In steady state equilibrium, the ratio of the number of excited atoms N2 to the total number of atoms is given by (Laudon, 1983)... 

For amide enolates (X = NR2), with Z geometry, model transition state D is intrinsically favored, but, again, large X substituents favor the formation of nt/-adducts via C. Factors that influence the diastereoselectivity include the solvent, the enolate counterion and the substituent pattern of enolate and enonc. In some cases either syn- or unh-products are obtained preferentially by varying the nature of the solvent, donor atom (enolate versus thioeno-late), or counterion. Most Michael additions listed in this section have not been examined systematically in terms of diastereoselectivity and coherent transition stale models are currently not available. Similar models to those shown in A-D can be used, however all the previously mentioned factors (among others) may be critical to the stereochemical outcome of the reaction. 

We use a7r/2 — vr — vr/2 pulse sequence to coherently divide, deflect and finally recombine an atomic wavepacket. The first vr/2 pulse excites an atom initially in the l,p) state into a coherent superposition of states l,p) and 2,p + hkeff). If state 2) is stable against spontaneous decay, the two parts of the wavepacket will drift apart by a distance hkT/m in time T. Each partial wavepacket is redirected by a vr pulse which induces the transitions... 

Single atomic ions confined in radio frequency traps and cooled by laser beams (Figure 7.4a) formed the basis for the first proposal of a CNOT quantum gate with an explicit physical system [14]. The first experimental realization of a CNOT quantum gate was in fact demonstrated on a system inspired by this scheme [37]. In this proposal, two internal electronic states of alkaline-earth or transition metal ions (e.g. Ba2+ or Yb3+) define the qubit basis. These states have excellent coherence properties, with T2 and T2 in the range of seconds [15]. Each qubit can be... 

In studying this system, the first femtosecond pulse takes the ion pair M+X to the covalent branch of the MX potential at a separation of 2.7 A. The activated complexes [MX], following their coherent preparation, increase their intemuclear separation and ultimately transform into the ionic [M+ X ] form. With a series of pulses delayed in time from the first one the nuclear motion through the transition state and all the way to the final M + X products can be followed. The probe pulse examines the system at an absorption frequency corresponding to either the complex [M X] or the free atom M. 

Figure 14. (a) Potential-energy surfaces, with a trajectory showing the coherent vibrational motion as the diatom separates from the I atom. Two snapshots of the wavepacket motion (quantum molecular dynamics calculations) are shown for the same reaction at / = 0 and t = 600 fs. (b) Femtosecond dynamics of barrier reactions, IHgl system. Experimental observations of the vibrational (femtosecond) and rotational (picosecond) motions for the barrier (saddle-point transition state) descent, [IHgl] - Hgl(vib, rot) + I, are shown. The vibrational coherence in the reaction trajectories (oscillations) is observed in both polarizations of FTS. The rotational orientation can be seen in the decay of FTS spectra (parallel) and buildup of FTS (perpendicular) as the Hgl rotates during bond breakage (bottom). 

R. A. Marcus In the case of the reaction Klippenstein and I studied, which showed two transition states [1], the motion was that largely of heavy atoms rather than hydrogen atoms. We assumed incoherent motion between the two, though in some systems, such as the one you treated, coherence can certainly be important. In your ketene system was tunneling involved in passage through the two barriers ... 

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