Field-dressed states

Consider a molecule prepared in the absolute ground state in the absence of the field and subjected to microwave field of frequency . If collided with a structureless atom in the absence of the field and at collision energies below the first excitation threshold, the molecule can undergo only elastic scattering. In the presence of the field, the ground state of the molecule becomes a field-dressed state X). And for every field-dressed state X), there is an infinite number of replica states 2 - A ), lower in energy. The states 2 - A ) and X) are coupled by the anisotropy of the atom-molecule interaction potential, so collisions can induce... 

In Figure 9.7 we illustrate the formation of the analogous EIT dark state, as described by Eq. (9.59), as a function of time. We see that when the pulse is weak (t = 1.7) the (Autler-Townes) splitting between the two field-dressed states is small and the EIT dark state resembles a very narrow hole. As the pulse gets... 

Figure 22 The populations, given as St (t) s ( . (t) 0(O) 2, of the field dressed states, given that iff (t = 0)) = 1) and

Figure 22 displays the evolution of the populations Si it) = Eiit) ili(0) P of the field dressed states, having started with i/f it = 0)) = 1). The parameters are as in Fig. 21, with

avoided crossing region, where... 

Figure 33. Same as Fig. 32 but for an excitation from an initial field dressed state being displaced in comparison to the field free state. An effective selective counterclockwise rotation is induced. 

The differential cross-section for the transition between the field-dressed states a and a can be written as [13,44]... 

T, it may undergo rapid time evolution over many adiabatic states due to the interaction with the external field. Such behavior of the Floquet state is sometimes described as a field-dressed state. Its importance in analysis in the field-induced dynamics is analogous to that of the energy eigenstate under a time-independent Hamiltonian. We will further show that even a small non-periodic term can be incorporated in this framework in an analogous manner as the nonadiabatic transitions in the field-free dynamics. 

Once the mechanisms of dynamic processes are understood, it becomes possible to think about controlling them so that we can make desirable processes to occur more efficiently. Especially when we use a laser field, nonadiabatic transitions are induced among the so-called dressed states and we can control the transitions among them by appropriately designing the laser parameters [33 1]. The dressed states mean molecular potential energy curves shifted up or down by the amount of photon energy. Even the ordinary type of photoexcitation can be... 

Fig. 1.2. Potential energy curves of H2 and Hj showing ionization and dressed states in a laser field. The dressed curves lead to bond softening and a distortion of the potential curve of the ground state of the ion, as will be discussed in Sect. 1.2.3...

The new diagonal elements are the eigenenergies e (t) and e (t) of the lower and upper dressed state /) and u), respectively. In intense laser fields, the dressed states split up according to... 

For resonant excitation, 5 = 0, the splitting is determined only by the amplitude of the Rabi frequency, which is conveniently adjusted via the laser field amplitude. Finally, we obtain the population dynamics d t) = dJ(t)Y in the dressed state picture from the bare state amplitudes by the transformation d t) = V t)c t). 

In order to relate the dressed state population dynamics to the more intuitive semiclassical picture of a laser-driven charge oscillation, we analyze the induced dipole moment n) t) and the interaction energy V)(0 of the dipole in the external field. To this end, we insert the solution of the TDSE (6.27) into the expansion of the wavefunction Eq. (6.24) and determine the time evolution of the charge density distribution p r, t) = -e r, f)P in space. Erom the density we calculate the expectation value of the dipole operator... 

In the following, we will discuss two basic - and in a sense complementary [44] - physical mechanisms to exert efficient control on the strong-field-induced coherent electron dynamics. In the first scenario, SPODS is implemented by a sequence of ultrashort laser pulses (discrete temporal phase jumps), whereas the second scenario utilizes a single chirped pulse (continuous phase variations) to exert control on the dressed state populations. Both mechanisms have distinct properties with respect to multistate excitations such as those discussed in Section 6.3.3. 

Figure 6.10 Ultrafast efficient switching in the five-state system via SPODS based on multipulse sequences from sinusoidal phase modulation (PL). The shaped laser pulse shown in (a) results from complete forward design of the control field. Frame (b) shows die induced bare state population dynamics. After preparation of the resonant subsystem in a state of maximum electronic coherence by the pre-pulse, the optical phase jump of = —7r/2 shifts die main pulse in-phase with the induced charge oscillation. Therefore, the interaction energy is minimized, resulting in the selective population of the lower dressed state /), as seen in the dressed state population dynamics in (d) around t = —50 fs. Due to the efficient energy splitting of the dressed states, induced in the resonant subsystem by the main pulse, the lower dressed state is shifted into resonance widi die lower target state 3) (see frame (c) around t = 0). As a result, 100% of the population is transferred nonadiabatically to this particular target state, which is selectively populated by the end of the pulse.

Herein a is the rate of change of the lower dressed state energy i(t) (black dashed line in Figure 6.10c) evaluated at the inflection points at t = +15 fs, and the Rabi frequency H22 is evaluated at the crossing times. For symmetry reasons, the Landau-Zener probability is the same for both avoided crossings. Now the second requirement concerning the field amplitude is to tailor the Rabi frequency of the main pulse such that = 0.5. Then 50% of the population is transferred... 

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