Detuning frequency

Adopting the rotating-wave approximation (RWA) and introducing the detuning frequency Ao= Ujk-yjk and the Rabi frequency Mjk -we find... 

In Eqs (10.180) the terms that depend explicitly on time originate from cos((yZ)e " = (1/2)(1 + exp( 2z(z /)) and oscillate with frequency 2(7>. The other rates in the problem are the detuning frequency and the thennal rates (population relaxation and dephasing). For optical transitions these rates are usually much smaller than a>, for example typical room temperature vibrational relaxation rates are of order lO s while vibrational frequencies are in the range IO s . The effect of the fast tenns, exp( 2zrotating wave approximation (RWA)." Under this approximation Eqs (10.180) become... 

E is the radiative lifetime of the molecule added phenomenologically to describe spontaneous emission, 2 = —d -EJh is the Rabi frequency, and the detuning frequency is defined by... 

Both in the strong (Fig. 4.6) and the weak (Fig. 4.7) eases, we find Q(co = 0) 0, which is expected in the slow modulation case eonsidered here. Physically, when the laser detuning frequency is exactly in the middle of two frequency shifts, + v, the rate of photon emissions is identical whether the molecule is in the up state ( + v) or in the down state (—v). Therefore, the effect of bath fluctuation on the photon counting statistics is negligible, which leads to Poissonian counting statistics at o)f = 0. 

Figure 8. Fluorescence excitation spectra for pentacene in/j-terphenyl at 1.5 K measured with a tunable dye laser of linewidth 3 MHz. The laser detuning frequency is referenced to the line center at 592.321 nm. (a) Broad scan of the inhomogeneously broadened line all the sharp features are repeatable structure, (b) Expansion of 2 GHz spectral range showing several single molecules, (c) Low-power scan of a single molecule at 592.407 nm showing the lifetime-limited width of 7.8 MHz and a Lorentzian fit. After Ref. 7.

We will explore the effect of three parameters 2 -and < )> that is, the time delay between the pulses, the tuning or detuning of the carrier frequency from resonance with an excited-state vibrational transition and the relative phase of the two pulses. We follow closely the development of [22]. Using equation (Al.6.73). 

One of the most interesting features of the Raman spectmm is its dependence on tire incident light frequency, coj. When Wj is on resonance with the excited electronic state, the scattering process closely resembles a process of absorption followed by emission. However, as Uj is detuned from resonance there are no longer... 

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... 

We assume that tlie light field is detuned to tlie red of tire J —> J atomic resonance frequency. 

The use of a reactor in series with the ctipacitors w ill reduce the harmonic effects in a power network, as well as their effect on other circuits in the vicinity, such as a telecommunication network (see also Section 23.1 1 and Example 23.4). The choice of reactance should be such that it W ill provide the required detuning by resonating below the required harmonic, to provide a least impedance path for that harmonic and filter it out from the circuit. The basic idea of a filter circuit is to make it respond to the current of one frequency and reject all other frequency components. At power frequency, the circuit should act as a capacitive load and improve the p.f. of the system. For the fifth harmonic, for instance, it should resonate below X 50 Hz for a 50 Hz system, say at around 200-220 Hz, to avoid excessive charging voltages w hich may lead to... 

Fig. 40. Flole-burning spectra of thioindigo in benzoic acid crystal at 1.35 K. The scanning laser frequency cu is measured with respect to the burning laser frequency cUb is detuning of the burning laser frequency relative to the center of absorption line.

If the uncertainty in the deadtime is 0.01 min. Fig, 16.11 shows that its magnitude becomes significant (magnitude greater than -20 dB, that is, 10 percent) at frequencies above 10 radians per minute. Therefore this much uncertainty would not require controller detuning for deadtimes greater than 0.2, but the 0.1 deadtime may have to be detuned somewhat to maintain stability despite the uncertainty. 

FIGURE 5.5 (a) Components of the CARS signal. The last three terms in Equation 5.1 are plotted versus detuning A = C0p-co -O. O is the center frequency of a homogeneously broadened Raman line with linewidth F. The curves are calculated with an assumption that2 R = 1.2 = 0)- (b) Schematic of the FM CARS process. Solid curve, sum of the contribu-... 

In Fig. 9 the ion current calculated as described above is shown as a function of the detunings of the pump-and-dump laser frequency in a two-dimensional plot. 

Figure 9. Calculated ion current spectra for different detunings of the pump laser and the dump laser frequency. The two-dimensional plot includes REMP1 spectra as well as CIS spectra.

An upper limit to the required Rabi frequency is found by requiring that it be equal to the detuning. Using this requirement with Eq. (10.31) Christiansen-... 

Sr = f2r — (wp — ujs) is the detuning from the Raman resonance at frequency f2r with a half width at half maximum (HWHM) of Tr. N is the number density of Raman-active scatterers and C is a proportionality constant. 

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