Dressed states energies

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... 

Note that SPODS is nearly always operative in resonant strong-held excitation using modulated ultrashort laser pulses, the only exception being so-called real laser pulses [72, 77] (i.e., electric helds with only one quadrature in the complex plane) that are usually hard to achieve in ultrafast laser technology. This is why many different pulse shapes can lead to comparable dressed state energy shifts and... 

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...

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... 

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... 

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.

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. 

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... 

Figures 9A and 9B are photofragment images of D+ following irradiation of D2 with 532-nm light. All of the features can be assigned to dissociation of different vibrational levels of D2 by nominally either one-, two, or three-photon absorption. Because two-photon absorption to the 2p

Figure 11. Dressed state potential energy surfaces for D2 plus one, two, or three 532-nm photons. The avoided crossing gaps increase with increasing laser intensity.

Figure 11.13 Dressed state potentials for laser catalysis process at maximum pulse int Initial kinetic energy is 0.01 a.u. ...

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