Rabi frequency intensity

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-...

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.

In the upper parts of Figs. 6a-c the time-dependent Rabi frequencies of both laser pulses are shown for different delays. In all cases the dump laser pulse has a higher Rabi frequency than the pump laser pulse and twice its duration. Note that the Rabi frequency is proportional to the laser held strength and therefore to the square root of the pulse intensity. In the lower part the population dynamics for the three different pulse sequences is shown. The part of population transferred to the ionization continuum is indicated by a strong line. 

Iplgure 11.8 Rates of association (Prec), back-dissociatioin (Pdiss), and total molecule Bti tion (P) vs. t in the counterintuitive scheme. Dashed lines are pulse intensity profile, spitted lines denote effective Rabi frequency d2(t)/% where is peak pulse intensity and (a) Initial wave packet width of SE = 10 3 cm-1 and other pulse parameters as fi Fig. 11.7. (b) Dynamics scaled by s— 10 [Eq. (19.81)] Initial wave packet width of 10 4 cm-1 both pulses lasting 85 ns pump pulse peaking at / =200 ns and dump... 

The RWA is appropriate when the Rabi frequency is much smaller than the other frequencies in the problem, viz. the transition frequency and the detuning. The first of these conditions limits the intensity, and so ultimately RWA breaks down it then becomes necessary to include the effects of the counterrotating terms, and one returns to solving the time-dependent Schrodinger equation, with a Hamiltonian which is periodic in time this is done in a more general way by applying Floquet s theorem for differential equations with periodically varying coefficients. 

Now, we consider the important limit of weak laser intensity. In this limit, the Wiener-Khintchine theorem relating the line shape to the one-time correlation function holds. As we shall show now, a three-time correlation function is the central ingredient of the theory of fluctuations of SMS in this limit. In Appendix B, we perform a straightforward perturbation expansion with respect to the Rabi frequency Q in the Bloch equation, Eq. (4.6), to find... 

This demonstrates that the saturation parameter can also be expressed as the square of the ratio f2i2/VPi P2 of the Rabi frequency f2i2 at resonance (geometric mean of the relaxation rates of 1) and 2). In other words, when the atoms are exposed to light with intensity I = h, their Rabi frequency is f2i2 = VPi P2-... 

The Stokes laser generates a coherent superposition of the wavefunctions of levels 2) and 3). The states 2) and 3) are, however, not occupied before the pump pulse arrives. The wavefunction oscillates between levels 2) and 3) with the Rabi frequency which depends on the intensity of the Stokes pulse and its detuning from resonance. Now the pump pulse comes with a time delay At with respect to the Stokes pulse, where At is smaller than the width of the Stokes pulse, which means that the two pulses still overlap (Fig. 7.15b). This places the molecule at a coherent superposition of levels 1) and 2) and 2) and 3). If the delay At, the detuning A v and the intensities of the two lasers are correctly chosen, the population in level 11) can be completely transferred into level 13) without creating a population in level 2) (Fig. 7.15c). The coherently excited levels 1) and 2) are described by the wavefunction... 

Figure 14. Simulation of the fluorescence intensity autocorrelation function (t) for a single pentacene molecule for different values of the Rabi-frequency 2 ...

This demonstrates that the saturation parameter can also be expressed as the square of the ratio y yi of the Rabi frequency Q 2 at resonance (co = cji>]2) and the geometric mean of the relaxation rates of 1) and 2). In other words, when the atoms are exposed to light with intensity I = 7s, their Rabi frequency is 2 2 = y K2- The saturation parameter defined by (7.6) for the open two-level system is more general than that defined in (3.69) for a closed two-level system. The difference lies in the definition of the mean relaxation probability, which is / = (7 i-h 7 2)/2 in the closed system but 7 = R R2j R +R2) in the open system. We can close our open system defined by the rate equations (7.3) by setting C = R2N2, C2 = R Ni, and N + N2 = N = const, (see Fig. 7.1b). The rate equations then become identical to (3.66) and 7 converts to R,... 

Figure 14 The zero-frequency output spectram F(0) versus the cooperativity parameter Cq for 0=1.00 (solid), 1.25 (dotted), and 1.50 (dashed) and Yi=4.0, A=0.5. Shown in the inset are the steady state intensities I f) in units of y Rabi frequency and all rates are in imits of Y2-...

In our numerical calculation, we scale the Rabi frequency Q and various rates in units of yi. The intensities (/g) = B B ) is in units of yf. Plotted in Fig. 16 is the zero-frequency output... 

If the laser pulse applied to the sample molecules is sufficiently long and intense, a molecule (represented by a two-level system) will be driven back and forth between the two levels at the Rabi flopping frequency (2.134). The time-dependent probability amplitudes a (t) and a (t) are now periodic functions of time and we have the situation depicted in Fig.2.30. Since the laser beam is alternatively absorbed (induced absorption E ) and amplified (induced emission E2-> E ), the intensity of the transmitted beam will display an oscillation. Because of relaxation effects this oscillation is damped and the transmitted intensity reaches a steady state determined by the ratio of induced to relaxation transitions. According to (2.133) the Rabi frequency depends on the laser intensity and on the detuning molecular eigenfrequency o) 2 laser frequency co. This detuning can... 

The difference between optical nutation and free induction decay should be clear. While the optical nutation occurs at the Rabi frequency which depends on the product of laser field intensity and transition moment, the free induction decay is monitored as a heterodyne signal at the beat frequency 0) 2 which depends on the Stark shift. The importance of these coherent transient phenomena for time-resolved sub-Doppler spectroscopy is discussed in the next section. Its application to the study of collision processes is treated in Chap.12. For more detailed information the excellent reviews of BREWER [11.43,48] are recommended. 

Rabi is the Rabi frequency which is determined by intrinsic atomic properties and by the intensity of the laser. By proper timing of the laser pulse any rotation between the two states ) and e) can be performed. For example, by choosing Rabi = 7t/2 transformation (6.8) is realized. As a sideremark we note that for microwave transitions Rabi oscillations can be induced by exposing the atom to a microwave field. 

The first optical laser, the ruby laser, was built in 1960 by Theodore Maiman. Since that time lasers have had a profound impact on many areas of science and indeed on our everyday lives. The monochromaticity, coherence, high-intensity, and widely variable pulse-duration properties of lasers have led to dramatic improvements in optical measurements of all kinds and have proven especially valuable in spectroscopic studies in chemistry and physics. Because of their robustness and high power outputs, solid-state lasers are the workhorse devices in most of these applications, either as primary sources or, via nonlinear crystals or dye media, as frequency-shifted sources. In this experiment the 1064-mn near-infrared output from a solid-state Nd YAG laser will be frequency doubled to 532 nm to serve as a fast optical pump of a raby crystal. Ruby consists of a dilute solution of chromium 3 ions in a sapphire (AI2O3) lattice and is representative of many metal ion-doped solids that are useful as solid-state lasers, phosphors, and other luminescing materials. The radiative and nonradiative relaxation processes in such systems are important in determining their emission efficiencies, and these decay paths for the electronically excited Cr ion will be examined in this experiment. 

With increasing RF intensity, however, saturation broadening is observed (Vol. 1, Sect. 3.6) and the double-resonance signal may even exhibit a minimum at the center frequency 0)23 (Fig. 5.9). This can readily be understood from the semiclassical model of Vol. 1, Sect. 2.7 for large RF field amplitudes Erf the Rabi flopping frequency Vol. 1, (2.90)... 

The time window, resonance window, and PA window have been indicated in Figure 7.1. The sensitivity of the results to the choice of the pulse parameters (detuning, intensity, spectral width, linear chirp rate) is discussed in detail in Refs. [18] and [19], where many different pulses have been considered. In the present work, we concentrate on two typical pulses, hereafter referred to as and with a central frequency chosen to be resonant with the vibrational levels v = 98 and 122, described above in Table 7.1 and in Figure 7.2. Two other pulses will also be considered in the discussion of Section 7.6. We give in Table 7.2 the parameters for the various pulses, as well as the associated PA windows. Another characteristic timescale associated with the radiation is the Rabi period, discussed in detail in Ref. [18], which is larger than 20 psec for the chirped pulses considered here. 

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