Laser fields moments

The simplified theory is adequate to obtain qualitative agreement with experiment [1,16]. Comparisons between the simplified and more advanced versions of the theory show excellent agreement for the dominant (electronic) contribution to the time-dependent dipole moment, except during the initial excitation, where the k states are coupled by the laser field [17]. The contributions to the dipole from the heavy holes and light holes are not included in the simplified approach. This causes no difficulty in the ADQW because the holes are trapped and do not make a major contribution to the dynamics [1]. This assumption may not be valid in the more general case of superlattices, as discussed below. 

Considering that J 2 I 2 and that the ionization rates at R = Rq have little 9 dependence [35], the dominant difference should be due to the electron and nuclear dynamics in the steps 2 and 3. The observed single molecule responses are obtained by superposing the radiation from all the molecules with random orientation coherently. For linearly polarized laser field, whose direction is defined as x axis, the observed dipole moment is given by... 

Figure 6.19 Quantum dynamics simulations for the two distinct situations of selective population of the (a) upper and (b) the lower target state. The frame (iv) shows the population dynamics induced by the shaped laser field pictured in (iii). The remaining panels depict (ii) the oscillations of the laser field together with the induced dipole moment and (1) the induced energetic splitting in the X-A-subsystem along with the accessibility of the target states. Gray backgrounds highlight the relevant time windows that are discussed in the text.

The last term in Eq. (1) describes the coupling to the laser field which has the form (t) = 00(t)0(r — t) sin2(7rt/r) cos(flt), where 0 is the amplitude, r the duration, and the center frequency of the pulse. The dipole moment vector is oriented in the plane of the molecule da0 are the respective matrix elements. Here, we will focus on the excitation of the stretching vibration which in our coordinate system is mostly polarized along the x axis. Thus, we will take into account only the x component of the dipole moment, assuming that the laser field is polarized accordingly [10],... 

Here Hq is the molecular Hamiltonian, and fi e(t) is the interaction between the molecule and the laser field in the dipole approximation, where (i is the transition dipole moment of the molecule. Time evolution of the system is determined by the time-dependent Schrodinger equation,... 

In order to evaluate the matrix elements of the dipole moment operator in Eq. (24), it is convenient to separate out the geometrical aspects of the problem from the dynamical parameters. To that end, it is convenient to decompose the LF scalar product of the transition dipole moment d with the polarization vector of the probe laser field e in terms of the spherical tensor components as [40]... 

In the following calculations, the laser field is assumed to be linearly polarized parallel to the transition dipole moment /x, which is almost perpendicular to the molecular plane. The initial wavepacket is a two-dimensional symmetrical Gaussian wavepacket of form... 

Figure 3. Scheme of the LIDDI interaction a traveling laser field induces dipole moments in the atoms, thereby causing the interatomic interaction. The laser field is propagating in the direction x along which the atoms are weakly confined. The electric field vector is in the xy plane. 

Our review of the phase control of spontaneous emission will concentrate on the example of a V-type atom with nondegenerate transitions and nonorthogonal dipole moments driven by two laser fields. The lasers can have equal or different frequencies and each laser can couple to only one or both atomic transitions. 

Thus, in the case of parallel dipole moments the spectrum is composed of two lines of equal band widths ( F) located at frequencies %/ A2 + 21 i2 and there is no the central component in the fluorescence spectrum at the laser frequency a>i. The eigenvalue X = 0 contributes to the coherent scattering of the laser field. When Ti2 = 0, the spectrum is composed of three lines the central line of the bandwidth i T located at the laser frequency and two sidebands of band widths [ ... 

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. 

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... 

Consider the Menon-Agarwal approach to the Autler-Townes spectrum of a V-type three-level atom. The atom is composed of two excited states, 1) and 3), and the ground state 2) coupled by transition dipole moments with matrix elements p12 and p32, but with no dipole coupling between the excited states. The excited states are separated in frequency by A. The spontaneous emission rates from 1) and 3) to the ground state 2) are Tj and T2, respectively. The atom is driven by a strong laser field of the Rabi frequency il, coupled solely to the 1) —> 2) transition. This is a crucial assumption, which would be difficult to realize in practice since quantum interference requires almost parallel dipole moments. However, the difficulty can be overcome in atomic systems with specific selection rules for the transition dipole moments, or by applying fields with specific polarization properties [26]. 

An alternative method in which one could create a V-type system with parallel or antiparallel dipole moments is to apply a strong laser field to one of the two transitions in a A-type atom. The scheme is shown in Fig. 18. When the dipole moments of the 11) —> 3) and 2) —> 3) transitions are perpendicular, the laser exclusively couples to the 2) —> 3) transition and produces dressed states... 

Figure 18. Laser induced V-type system with nondegenerate transitions. A laser field applied to the 12) —> 3) transition of a A system creates nondegenerate dressed states separated by fl = a+ A[. The subsystem with the upper dressed atates a), b) and the ground state 1) behaviors as a V-type system with parallel dipole moments.

Transitions with parallel or antiparallel dipole moments can be created not only in multilevel systems but also in a two-level system driven by a polychromatic field [63]. In order to show this, we consider a two-level atom driven by a bichromatic field composed of a strong resonant laser field and a weaker laser field detuned from the atomic resonance by the Rabi frequency of the strong field. The effect of the strong field alone is to produce dressed states [35]... 

In order to correlate them, we can introduce a second (weaker) laser field of frequency coo — and the Rabi frequency IT < if which couples the degenerate transitions with dipole moments pn 7 and p22 v i as indicated in Fig. 19b. Treating the second field perturbatively, at zeroth order the coupling results in new doubly dressed states [63]... 

Figure C3.2.14. Electron population difference x t) = Pj(t) - PJt) for three electron transfer reactions in the presence of a pulsed laser field. Frequency of the field is tuned to solvent reorganization energy A, = 1 eV and the field strength is such that coupling potential (charge transfer dipole moment times the field strength) is twice the...

V and Af are the classical velocity and the difference of slopes of the diabatic potentials at the diabatic crossing point Rq. /r(Ro) is the electronic transition moment at the diabatic crossing point and q the electric field amplitude of the laser field. 

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