Rabi field

On one visit to Stern s molecular beam laboratory Rabi made a casual suggestion to Stern for an experiment, which brought the immediate response Why don t you do it Rabi was told it was an honor to receive such an invitation from Stern. I was in no position to refuse an honor, said Rabi. Rabi s experiment introduced a novel configuration of the magnetic field for deflecting particles in a molecular beam—a configuration now called the Rabi field. 

In equations (Cl. 4.4) and (Cl. 4.5) Acoj = cu - coj is the detuning of the optical field from the atomic transition frequency Q is the natural width of the atomic transition and m is tenned the Rabi frequency and reflects the... 

In equation (Cl.4.14) the saturation parameter essentially defines a criterion to compare the time required for stimulated and spontaneous processes. If I then spontaneous coupling of the atom to the vacuum modes of the field is fast compared to the stimulated Rabi coupling and the field is considered weak. If s" 1 then the Rabi oscillation is fast compared to spontaneous emission and the field is said to be strong. Setting s equal to unity defines the saturation condition... 

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].

Brunei C, Lounis B, Tamarat P and Orrit M 1998 Rabi resonances of a single molecule driven by rf and laser fields Phys. Rev. Lett. 81 2679-82... 

Figure 7.7 (a) Rabi oscillations of the mag netic moments of Er(lll) ions diluted in a single crystal of CaW04, measured under a magnetic field fiQH = 0.522T applied along the c crystallographic axis and at T = 3.5 K. 

Because the Stokes pulse precedes but overlaps the pump pulse, initially Up and all population initially in field-free state 11) coincides with flo(0)- At the final time, ilp Q5 so all of the population in flo(0) projects onto the target state 6). Note that flo(0) has no projeetion on the intermediate field-free state 5 ). The Rabi frequencies of the Stokes and pump pulses that are required for efficient STIRAP-generated population transfer satisfy the condition [66]... 

The hopping rate is a function of R and site numbers as noted above, it will play the role of the half Rabi frequency of the Stokes and pump fields in a STIRAP process with Vq = 0. Assuming T pp(m, t) 0 (0 (m, R(t)) 0) we divide Eq. (3.120)... 

The Rabi frequencies Qp and appearing here parameterize the pulsed pump and Stokes field strengths, controlled by the experimenter. To write this as a torque equation... 

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]. 

Figure 6.6 Two-state quantum system driven on resonance by an intense ultrashort (broadband) laser pulse. The power spectral density (PSD) is plotted on the left-hand side. The ground state 11) is assumed to have s-symmetry as indicated by the spherically symmetric spatial electron distribution on the right-hand side. The excited state 12) is ap-state allowing for electric dipole transitions. Both states are coupled by the dipole matrix element. The dipole coupling between the shaped laser field and the system is described by the Rabi frequency Qji (6 = f 2i mod(6Iti-...

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). 

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... 

Crowell discovered a variety of effects numerically, including modified Rabi flopping, which has an inverse frequency dependence similar to that observed in the solid state in reciprocal noise [73]. The latter is also explained by Crowell [17] using a non-Abelian model. A variety of other effects of RFR on the quantum electrodynamical level was also reported numerically [17]. The overall result is that the occurrence, classically, of the B V> field means that there is a quantum electrodynamical Hamiltonian generated by the classical term proportional to 3 2. This induces transitional behavior because it contributes to the dynamics of probability amplitudes [17]. The Hamiltonian is a quartic potential where the value of determines the value of the potential. The latter has two minima one where B = 0 and the other for a finite value of the B i) field, corresponding to states that are invariants of the Lagrangian but not of the vacuum. 

The use of strong fields to drive the dynamics leads to somehow similar effects than those of ultrafast pulses. If the Rabi frequency or energy of the interaction is much larger than the energy spacing between adjacent vibrational states, a wave packet is formed during the laser action. The same laser can prepare and control the dynamics of the wave packet [2]. Both short time widths and large amplitudes can concur in the experiment. However, the precise manipulation of dynamic observables usually becomes more difficult as the duration of the pulses decreases. 

Similar transient signals were obtained from time-dependent quantum mechanical calculations performed by Meier and Engel, which well reproduce the observed behavior [49]. They show that for different laser field strengths the electronic states involved in the multiphoton ionization (MPI) are differently populated in Rabi-type processes. In Fig. 13 the population in the neutral electronic states is calculated during interaction of the molecule with 60-fs pulses at 618 nm. For lower intensities the A state is preferentially populated by the pump pulse, and the A state wavepacket dominates the transient Na2+ signal. However, for the higher intensities used in the... 

V. S. Letokhov In the case of very intense IR fields we should take into consideration the effects of both (1) rearrangement of quantum vibrational levels (e.g., Rabi splittings) and (2) distortion of potential molecular curves. But with such strong IR femtosecond pulses we perhaps cannot ignore the excited electronic states. I believe that a simple molecule can be excited to some higher vibrational levels and subse-quently can be involved in a multiphoton jump to excited electronic states. As a result, it will be difficult to observe the effect of distortion of molecular potential curves. 

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