Rabi oscillations excitation

Figure C 1.5.10. Nonnalized fluorescence intensity correlation function for a single terrylene molecule in p-terjDhenyl at 2 K. The solid line is tire tlieoretical curve. Regions of deviation from tire long-time value of unity due to photon antibunching (the finite lifetime of tire excited singlet state), Rabi oscillations (absorjDtion-stimulated emission cycles driven by tire laser field) and photon bunching (dark periods caused by intersystem crossing to tire triplet state) are indicated. Reproduced witli pennission from Plakhotnik et al [66], adapted from [118].

The discretized adiabatic procedure, and its analog with STIRAP, is but one possibility for achieving broadband response of an optical device. An alternative, which we discuss, relies on the analogy between the Jones vector description of an optical beam and the two-state time-dependent Schrodinger equation (TDSE). This equation has two commonly used solutions. One is rapid adiabatic passage (RAP), produced by swept detuning (a chirp), and the other is Rabi oscillations, specifically a pi pulse. The RAP has theoretical connection with STIRAP, but the pi pulses have no such connections. We describe application of a procedure that has been used to extend the traditional pi pulses to broadband excitation. This can accomplish the present goal of PAP, under complementary conditions. 

The process of the excitation transition opens up new opportunities for controlling the dynamics of Rabi oscillations. For identification of control factors we need to know general solution of the system (2)-(3). It can be found by using the Fourier transform with respect to x and has the form... 

From the two previous sections, it is clear that the dynamics of exciting an autoionising resonance, which has a mixture of bound state and continuum character, will be rather complex, involving both reversible and irreversible contributions, i.e. a combination of Rabi oscillations and damping. 

Use of a surfactant allows solubilization of the polyoxometalate cluster K6[Vi5As6042(H20)] 8H20 (V15) in the organic solvent chloroform. Spin echo measurements revealed a phase memory time of Tm = 340 ns, which was attributed to resonances in the 5 = 3/2 excited state of the cluster [166]. No quantum coherence was detected in the pair of 5 = 1/2 ground states [151]. By measurement of the z-magnetization after a nutation pulse, and a delay to ensure decay of all coherences, Rabi oscillations were observed. From the analysis of the different possible decoherence mechanisms, it was concluded that decoherence is almost entirely caused by hyperfine coupling to the nuclear spins. 

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.

Fig. 7.24 (a) Optical nutation in CH3p observed with CO2 laser excitation at A = 9.7 pm. The Rabi oscillations appear because the Stark pulse lower trace) is longer than in Fig. 7.23. (b) Optical free-induction decay in I2 vapor following resonant excitation with a cw dye laser at = 589.6 nm. At the time = 0 the laser is frequency-shifted with the arrangement depicted in Fig. 7.22 by Au = 54 MHz out of resonance with the I2 transition. The slowly varying envelope is caused by a superposition with the optical nutation of molecules in the velocity group Vz = o) — (oo)/k, which are now in resonance with the laser frequency oj. Note the difference in time scales of (a) and (b) [705]... 

Different from these normal dark states are the coherent dark states. Here two lasers are used (Fig. 7.27c). If laser 1 excites the atoms from 11) into 3) they can be transferred by laser 2 into level 2). From here they can be pumped again by laser 2 into level 3) and further by laser 1 into 11). For sufficiently large laser intensities the stimulated processes are fast compared with the spontaneous emission and the Raby oscillations dominate which periodically alter the populations of 1) and 2). 

In Figure 7.4a, we have displayed the probability of population transfer to vibrational levels in the Cs2 0 (65 + 6P3/2) excited state. During the pulse, many levels are populated, including highly nonresonant levels, due to time-energy uncertainty at short times. Rabi oscillations are visible diuing the pulse. Pulse transients are also observed, due to interferences between amplitudes of population coherently transferred to one level at different times they are discussed in Section 7.3.6. 

From the conclusion of Section 7.5, a pulse has been designed to optimize the compression effect in the ground-state wavepacket. The new pulse, described as in Table 7.2, is obtained from by increasing the chirp rate x and therefore the duration. For this pulse, the duration xc = 376.13 psec is comparable to half the vibration period TVib in the excited state. The intensity was increased to obtain 24 Rabi oscillations, close to a (2n)n-pulse. The probability of excitation is markedly decreased (3 x 10 " instead of 2 x 10 ). As displayed in Figure 7.14, a spectacular compression effect, maximum at f p, = fp -F 350 psec, is observed. The compressed wavepacket is associated with large values for the time-dependent Franck-Condon factor with low-lying levels in the external well of the excited state, suited for PA with a second pulse red-detuned from and delayed by 350 psec. 

The dynamics of the PA reaction corresponding to the narrowband pulse and broadband pulse are compared in Figure 7.16. Whereas for adiabatic transfer occurs within the PA window, for the time evolution of the population in the excited state presents Rabi oscillations, which are the signature of sig-... 

The pump pulse leaves about half the population still in the ground electronic state. This population mostly remains in the initial ground vibrational state, but some low vibrational states (up to 2 quanta for bending, 3 for symmetric stretch) are excited due to the Rabi oscillation. These low energy (< 0.7 eV) components were projected out of the wavefunction when plotting for clarity of presentation. 

The pump pulse causes 74% excitation into the A state (between t = —8 and 4 fs). Afterwards the probe pulse train causes transfer of population between the A and B states, and between B and C (and X) states. Transfer of population occurs synchronous with the pulses in the pulse train, causing the step-like appearance seen in Fig. 5.35(a). The pulse train causes ionization simultaneously with population transfer among the neutral states. Time evolution of the ionized population is also seen to be step-like, with change synchronous with the pulses. Thus the electronic excitation and deexcitation seems to be a Rabi oscillation whose timing of transition is well controlled. On the other hand, the relevant nuclear vibrational motion is autonomously evolved in time during the refractory period. 

B state, and 1.8-2.5 A for the C state. In these ranges, electronic transition takes place as though it makes a copy of vibrational wavefunction in the common regions between the relevant electronic states. This is a reflection of the Condon principle. We note that there is counter-intuitive decrease of population in the potential well of the X state when omitting ionization, especially in the panels for Pulse 2 and Pulse 6, indicating there is some deexcitation from the excited electronic states via Rabi-oscillation like coupling with the ion continuum. Thus, complicated transfer, overlapping, and dispersion of the vibrational wavepackets proceed in each electronic state in a stepwise manner. Very fine information in the attosecond time scale is thus folded in the complicated structures and phases of the set of vibrational wavepackets [305]. 

Our goal is to induce a full population inversion between the two localized states by a single laser pulse in a time much smaller than the field-free tunneling time defined above. In a previous work, it was shown that this can be achieved by a 27r-pulse that selectively couples one of the two delocalized states to an intermediate excited state, noted xe)- The 27r-pulse induces a full Rabi oscillation between the two coupled states and the required tt phase to the delocalized state that has been addressed by the... 

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. 

Actually two hyperfine ground state Zeeman sublevels have been used which are separated by 1.250 GHz (microwave transition). However, Rabi oscillations between these two levels can be induced with optical lasers by using a Raman transition involving a common excited state. 

The proposed solution to this problem is based on dark states , an effect which can only be understood quantum mechanically. A detailed explanation of dark states and their use in quantum computing would exceed the scope of this chapter. Instead, a short outline of the basic idea may suffice. Let us consider an atom with three levels, two energetically lower-lying stable states pi) and p2) 2is well as a (decaying) excited state e). If a laser is coupled to one of the transitions pi) k) or p2) — je) Rabi oscillations as discussed in Sect. 6.2.2 will take place. Every time the atom is in the excited state it can decay by spontaneous emission of a photon. However, if both transitions are driven by lasers a very interesting effect can take place the Rabi oscillations will cease and the atom remains in the stable ground states. No excitation will take place even though two lasers... 

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]. 

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