Transition dipole matrix elements states

The other comment I would like to make is that the positive value of the 0 parameter you observe is due to a quantum interference effect. A simple mixing of the ground state with the excited state in the final continuum state hardly affects the directional properties of the dipole matrix elements per se because the transition dipole matrix elements between different states within the ground state are very small. Namely, if... 

Continuum-continuum transitions involving excited electronic states [368 be thought useful insofar as they ought to require less power than those occ1 the ground state because in this case the laser can couple to strong elec transition dipoles. However, in this case the continuum-continuum nuclear lead to smaller transition dipole matrix elements, and moreover, once the i deposited on an unbounded excited electronic surface, it is impossible to reaction on that surface and the resultant retention of the absorbed photon] chain of events resembles that of conventional (weak-field) photochemistry the laser is used to impart energy to the reaction, rather than to catalyze it ./... 

Ordinary STIRAP is only sensitive to the energy levels and the magnitudes of transition-dipole coupling matrix elements between them. These quantities are identical for enantiomers. Its insensitivity to the phase of the transition-dipole matrix elements renders STIRAP incapable of selecting between enantiomers. Recently we have demonstrated [11] that precisely the lack of inversion center, which characterizes chiral molecules, allows us to combine the weak-field one-and two-photon interference control method [29,54,95,96] with, the strong-field STIRAP to render a phase-sensitive AP method. In this method, which we termed cyclic population transfer (CPT), one forms a STIRAP loop by supplementing the usual STIRAP 1) o 2) <=> 3) two-photon process by a one-photon process 1) <=> 3). The lack of inversion center is essentrat, because one-photon and two-photon processes cannot connect the same states in the presence of an inversion center, where all states have a well defined parity, because a one-photon absorption (or emission) between states 1) and 3) requires that these states have opposite parities, whereas a two-photon process requires that these states have the same parity. 

For many molecules of interest there exist radiationless transitions that couple the levels of an electronically excited surface to a dense manifold of quasidegenerate levels on one or more other electronic surfaces, and these latter levels have vanishingly small transition dipole matrix elements with the initial level on the ground state surface. As shown in the preceding section, exponential decay of the amplitude of a wavepacket on an excited state surface via, say, a radiationless process, reduces the amplitude of a coherent emission signal but does not destroy the coherence. 

In the above expression u)M(0) = E (0)/h, where E (0) is the energy of a mechanical exciton p for k = 0, P0.0 (0) is the transition dipole matrix element of a unit cell, which is obtained by using the crystal ground state wavefunctions and the wavefunctions of a crystal with the mechanical exciton of type p for k = 0 A is the unit cell volume. 

The residue at the pole = ( — q) contains the transition dipole matrix element between the states 0) and m),... 

Thus, if state IE2) is unstable, giving rise to the /T2 term, there is no real E for which the transition dipole matrix element vanishes. In case of 2 = 0 detuning and cos 16 = 0, we have... 

There are a number of interesting cases in which full control is still attainable. For example, when only one n state at energy E for a given q exists. In particular when the number of product channels is only two, (as in diatomic molecules), the Schwarz equality (Eq. 13a) holds and full control can be attained. In the polyatomic case, the Schwarz equality holds whenever the bound-free transition-dipole matrix elements, are facorizeable. 

The term for magnetic interactions in Eq. (9.1) gives rise to a magnetic transition dipole matrix element (wi/,a) for a transition of a system between different states. A magnetic transition dipole is a vector analogous to an electric transition dipole but with the magnetic-dipole operator in replacing p ... 

H) = component of with Cartesian index fia y, Rab component along fi of the transition dipole matrix element for transitions from a to b Tj = population relaxation characteristic time T2 = phase relaxation characteristic time V t) = interaction operator (a,((o))g= Raman scattering tensor for transitions from state g to state / ... 

For a fundamental transition from ground to one of the first excited vibrational states associated with a normal vibration described by the coordinate Q] the transition dipole matrix element is reduced simply to... 

Molecular point-group symmetry can often be used to determine whether a particular transition s dipole matrix element will vanish and, as a result, the electronic transition will be "forbidden" and thus predicted to have zero intensity. If the direct product of the symmetries of the initial and final electronic states /ei and /ef do not match the symmetry of the electric dipole operator (which has the symmetry of its x, y, and z components these symmetries can be read off the right most column of the character tables given in Appendix E), the matrix element will vanish. 

In the lowest optieally excited state of the molecule, we have one eleetron (ti ) and one hole (/i ), each with spin 1/2 which couple through the Coulomb interaetion and can either form a singlet 5 state (5 = 0), or a triplet T state (S = 1). Since the electric dipole matrix element for optical transitions — ep A)/(me) does not depend on spin, there is a strong spin seleetion rule (AS = 0) for optical electric dipole transitions. This strong spin seleetion rule arises from the very weak spin-orbit interaction for carbon. Thus, to turn on electric dipole transitions, appropriate odd-parity vibrational modes must be admixed with the initial and (or) final electronic states, so that the w eak absorption below 2.5 eV involves optical transitions between appropriate vibronic levels. These vibronic levels are energetically favored by virtue... 

FRET is a nonradiative process that is, the transfer takes place without the emission or absorption of a photon. And yet, the transition dipoles, which are central to the mechanism by which the ground and excited states are coupled, are conspicuously present in the expression for the rate of transfer. For instance, the fluorescence quantum yield and fluorescence spectrum of the donor and the absorption spectrum of the acceptor are part of the overlap integral in the Forster rate expression, Eq. (1.2). These spectroscopic transitions are usually associated with the emission and absorption of a photon. These dipole matrix elements in the quantum mechanical expression for the rate of FRET are the same matrix elements as found for the interaction of a propagating EM field with the chromophores. However, the origin of the EM perturbation driving the energy transfer and the spectroscopic transitions are quite different. The source of this interaction term... 

Figure 6.6 Two-state quantum system driven on resonance by an intense ultrashort (broadband) laser pulse. The power spectral density (PSD) is plotted on the left-hand side. The ground state 11) is assumed to have s-symmetry as indicated by the spherically symmetric spatial electron distribution on the right-hand side. The excited state 12) is ap-state allowing for electric dipole transitions. Both states are coupled by the dipole matrix element. The dipole coupling between the shaped laser field and the system is described by the Rabi frequency Qji (6 = f 2i mod(6Iti-...

We now suppose that the molecular ground state is accurately described as a BO state, and that the ground state and the BO state dipole-transition matrix element, but that dipole transitions between the ground state and the BO states > or are forbidden (see Fig. 26). Thus the dipole matrix element < o e-p., F(0)> is proportional to the coefficient, a(E), of the BO state in the state [Pg.261]

The central problem is to calculate the field required to drive the n — n + 1 transition via an electric dipole transition. In the presence of an electric field, static or microwave, the natural states to use are the parabolic Stark states. While there is no selection rule as strict as the M = 1 selection rule for angular momentum eigenstates, it is in general true that each n Stark state has strong dipole matrix elements to only the one or two n + 1 Stark states which have approximately the same first order Stark shifts. Red states are coupled to red states, and blue to blue. Explicit expressions for these matrix elements between parabolic states have been worked out,25 and, as pointed out by Bardsley et al.26, the largest matrix elements are those between the extreme red or blue Stark states. These matrix elements are given by (n z n + 1) = n2/3.26... 

Using this approach the +) and —) states are not coupled by the field of the ion, but are only split in energy. At high collision velocities the initial state 0) is simply projected onto the 0 + 1) state, a coherent superposition of +) and -) states, by the dipole matrix element. However, at lower velocities the change in energy of the +) and -) states during the collision allows the +) and -) states themselves to be populated rather than only a coherent superposition. The latter feature allows nondipole transitions at lower collision velocities, as observed experimentally. 

While the fine structure transitions are inherently magnetic dipole transitions, it is in fact easier to take advantage of the large A = 1 electric dipole matrix elements and drive the transitions by the electric resonance technique, commonly used to study transitions in polar molecules.37 In the presence of a small static field of 1 V/cm in the z direction the Na ndy fine structure states acquire a small amount of nf character, and it is possible to drive electric dipole transitions between them at a Rabi frequency of 1 MHz with an additional rf field of 1 V/cm. 

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