Rabi oscillations interaction

Figures 6a-c show the population dynamics encountered in a three-level system (see Fig. 4) interacting resonantly with two Fourier-transform-limited laser pulses with three different delay times between the two pulses. The calculation was done assuming that the chosen Rabi frequencies fulfill the relation > 1/pulse duration) in all three cases. This relation ensures that the typical time for a Rabi oscillation of the population in an isolated two-level system is shorter than the pulse duration. Ionization from level 2 was introduced as a fast laser intensity-dependent decay of level 2 [6, 60], and resonant laser frequencies were assumed.

To summarize this section, we have presented a new technique for studying radiation absorption in the molecular system Vi5 constituting a first step towards the observation of Rabi oscillations in molecular nanomagnets. The main results are the observation of relatively narrow resonant absorption lines that are dominated by hyperfine interaction. In order to observe Rabi oscillations in a magnetic system, an important requirement is a large AC field amplitude. 

If we now send the second atom, which is in its ground state, with the selected velocity such that during the interaction with the cavity mode the atom undergoes half of the vacuum Rabi oscillation, the final state of the system becomes... 

Figure 8.2 Time dependence of the probability Pe(t) of observing the spontaneously decaying two-level system in its excited state at the center of a closed spherical cavity The number of resonantly interacting field modes is of the order of rR/ 7rc and depends on the size of the cavity R. For FR/c = 10 (upper figure) a spatially localized photon wave packet is generated by spontaneous emission and can be reabsorbed again by the two-level system at the center of the cavity at later times. For FR/c = 1 (lower figure) only a small number of cavity modes interact resonantly and the two-level system performs approximate Rabi oscillations governed by the vacuum Rabi frequency.

The physics of the multistep excitation of atoms is, of course, much more profound than may be inferred from the simplest qualitative considerations given above. The whole picture can be found in the two-volume comprehensive monograph by Shore (1990). The approximation of incoherent interaction between a laser field and a real multilevel atom, described by rate equations, is quite acceptable (Ackerhalt and Eberly 1976), especially if account is taken of the degeneracy in the magnetic sublevels mp. Resonance transitions to various mp values differ in the projection of the dipole moment d 2, and hence in the Rabi oscillation frequency (eqn 2.44). This generally smooths out oscillations and makes the interaction incoherent. It is only in the ideal case of a two-level system free from level degeneracy that one can observe Rabi oscillations, as illustrated in Fig. 9.3. 

The modification of the electronic potentials due to the interaction with the electric field of the laser pulse has another important aspect pertaining to molecules as the nuclear motion can be significantly altered in light-induced potentials. Experimental examples for modifying the course of reactions of neutral molecules after an initial excitation via altering the potential surfaces can be found in Refs 56, 57, where the amount of initial excitation on the molecular potential can be set via Rabi-type oscillations [58]. Nonresonant interaction with an excited vibrational wavepacket can in addition change the population of the vibrational states [59]. Note that this nonresonant Stark control acts on the timescale of the intensity envelope of an ultrashort laser pulse [60]. 

In this case, the populations of states 1 and 2 oscillate at the Rabi frequency, as shown in Fig. 2.6. The only difference is that the oscillations decay exponentially during the phase relaxation time T2- If condition (2.62) is satisfied, the interaction of the two-level system with the laser-light field is said to be coherent. 

The quantum levels of a real atom or molecule are usually degenerate. In that case, the description of the interaction between a field and degenerate two-level system becomes more complicated. In particular, there is no longer any simple, graphic picture of the particle s Rabi-frequency oscillations between the two levels. There are, instead, the particle s oscillations between individual sublevels with frequencies of their own, which combine to smooth out the oscillations of the net level populations. 

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