Dressed state

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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. 

The process starts in the ground state, where the electron is described by an Y-wave. For this highly symmetric charge distribution, the dipole moment, and hence the interaction energy, vanishes exactly indicating equal population of the dressed states. The weak pre-pulse serves to launch the coherent charge oscillation. Designed with a pulse area [92] of... 

State. The latter is verified by the population dynamics in frame (ii) around t = 0. Subsequently, the pulse continues to invert the bare state system, which is typical for RAP. Just like the ground state the excited p-state exhibits no permanent dipole moment. Therefore, both (/ )(t) and V) t) converge back to zero as the system is steered adiabatically toward state 2). This indicates the successive loss of selectivity among the dressed states, which is in fact observed in frame (ii) for f > 0. By the end of the pulse, both dressed states are again fully equalized. 

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.

Section 6.5.1), two avoided crossings arise in Figure 6.10c at t = +10 fs between states /) and 1 3), the first of which is marked by a gray circle. Due to the highly nonadiabatic time evolution, diabatic transitions between these dressed states are likely to occur. The Landau-Zener model [48, 104, 105] estimates the probability for a diabatic transition at the avoided crossings as... 

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... 

In order to switch the system into the upper target state 5) merely the sine-phase 0 has to be varied by half an optical cycle, that is, by A(p = n. In this case, the main pulse is phase-shifted by Af = -l- r/2 with respect to the pre-pulse and couples in antiphase to the induced charge oscillation. Hence, the interaction energy is maximized and the upper dressed state u) is populated selectively. Due to the energy increase, the system rapidly approaches the upper target state 5). The ensuing nonadiabatic transitions between the dressed states u) and 1 5) result in a complete population transfer from the resonant subsystem to the upper target state, which is selectively excited by the end of the pulse. 

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