Detuning parameter

The / factor is a detuning parameter that prevents large changes in the manipulated variables. The larger the value of /, the less underdamped and the more robust the dosedloop system will be. 

Figure 2. Resonance diagram (steady-state amplitude v as a function of the detuning parameter (1 — > )/( fi.)) for 3 different values F (F0t < Fo2 <...

The ability of CPT to separate two enantiomers also depends on the individual detuning parameters Ay and on the related dynamical phase 2 2 r. At resonance Ay = 0 and

population transfer from state 1) to a combination of states 2) and 3). In that case, the p2/p3 branching ratio of the final populations is given, as in the double STIRAP case [98,99], by the IfWfinl2 ratio, and no enantiomeric selectivity is then possible. 

Figure 3.20 The calculated transducer response, sin(X)/X, vs the detuning parameter, ...

The initial stage of the evolution of Jf (x) does not depend on the detuning parameter y, since the principal term of the expansion of (58) with respect to x yields... 

Note that the expressions (81)—(83) are valid for j = 0, too. In this case they coincide with the formulas obtained in the preceding section. Formulas (81)-(83) immediately give the short-time behavior of the Bogoliubov coefficients at x —> 0 it is sufficient to put k pi, k, 1 and to replace the hypergeometric functions by 1. In this limit the detuning parameter y drops out of the expressions (in the leading terms of the Taylor expansions). 

We see that the U variances are always less than at the initial stage, but the degree of their squeezing rapidly decreases with increase of the number m. Note that the dependence on the detuning parameter y in the short-time limit appears only in terms of the order of x2m+3 (and higher). 

According to (185), the initial stage of the evolution does not depend on the detuning parameter y for all states that yield Im( ) = 0, since at x > 0 one has... 

To continue we define a detuning parameter, A = co - cOq. If A then exp(-i(co - cOpjO is slowly varying... 

The detuning parameter F is increased from one until the biggest log-modulus reaches a specified value. The biggest log modulus is a measure of how far the closed-loop system is from being unstable (Luyben, 1986). 

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). 

Note that negative Acoj (red detuning) produces a force attracting the atom to the intensity maximum while positive (blue detuning) repels the atom away from the intensity maximum. The spontaneous force or cooling force can also be written in tenns of the saturation parameter and the spontaneous emission rate. 

Since the only angle dependence conies from 0 , and the actions /, L are constant. From this point onwards we concentrate on motion under the reduced Hamiltonian which depends, apart from the scaling parameter y, only on the values of scaled coupling parameter p and the scaled detuning term p. In other words, we investigate the monodromy only in a fixed J (or polyad number N = 2J) section of the three-dimensional quanmm number space. 

We anticipate that, regardless of the detuning from an optical resonance used, the parameters f, g, and h will always be determinable from measurements of SHG as a function of the rotation angle of a quarter waveplate used to set the polarization state of the incident fundamental light. The amount of SHG-CD can be calculated from the parameters or, of course, read directly... 

The realization of SPODS via PL, that is, impulsive excitation and discrete temporal phase variations, benefits from high peak intensities inherent to short laser pulses. In view of multistate excitation scenarios, this enables highly efficient population transfer to the target states (see Section 6.3.3). Furthermore, PL can be implemented on very short timescales, which is desirable in order to outperform rapid intramolecular energy redistribution or decoherence processes. On the other hand, since PL is an impulsive scenario, it is sensitive to pulse parameters such as detuning and intensity [44]. A robust realization of SPODS is achieved by the use of adiabatic techniques. The underlying physical mechanism will be discussed next. 

Figure 9.10 EIT for highly structured continuum Yq = 72 = 0 05 with no detuning S2 = 0. The other parameters are as in Figure 9.8. Reprinted figure by permission from Ref. [36]. Copyright 2007 by the American Physical Society.

Most of the data are acquired in the same way as described above. K atoms are excited to the 29s and 27d states by the laser excitation, 4s —> 4p — 29s, 27d. The atoms are allowed to collide for 1 //s, after which a rapidly rising detuning pulse is applied, followed by the more slowly rising field ionization pulse. Atoms which have made the transition to the 29p state are selectively ionized by the field ionization pulse and detected. This signal is monitored as the small static tuning field is scanned. The amplitude and phase of the rf field are changed as parameters. 

It is possible to design multipath control schemes in which the laser phase cancels out of the interference term. One possibility is a diamond path configuration, co + 0)2 vs 0)2 + o), with a resonance near o) contributing a phase to the first path and a resonance near 0)2 contributing a phase to the second path. As before, the total probability is the square of the sum of the amplitudes for each path, but here the phases of the two laser beams appear in both paths and cancel in the cross term. In this case the control parameters are the laser frequencies, which determine the detuning from the resonances. This technique was used by Daniel Elliott and coworkers to control the differential cross sections for the ionization of Ba and NO. 

Thus, the crw coefficients do not contribute after the pulse is over they are pure transients. By contrast, the rw coefficients c+(f) can be nonzero after the pulse is over, with magnitude depending, as shown below, on the detuning com l - co0. Equation (2.22) thus gives a criterion, for the Gaussian pulse, as to the time required to establish the resonance condition [Eq. (2.12)]. It follows from Eq. (2.22) that the relevant parameter is the pulse duration 1/T. This quantity can, in principle, be shorter than a single optical cycle, but the resonance condition still holds. 

Fig. 8.14 Control over dimethylallene enantiomer populations as a function of the detuning A] for various laser powers. First column corresponds to probabilities of L (dot-dash curves) and D (solid curves) after a single laser pulse, assuming that the initial state is all L. Second column is similar, but for an initial state that is all D. Rightmost column corresponds to the . probabilities L and D after repeated excitation-relaxation cycles, as described in the text. First fqw corresponds to control using laser parameters on the extreme right, in which there is no internal conversion second row uses the same laser parameters as does the first row, but with internal conversion time of 10 ps bottom row shows results for an internal conversion time mf 10ps, but with modified laser parameters shown.

As reported earlier (18), the QRLPP effect is a threshold process, requiring sufficiently high atomic density N and laser intensity I. The threshold values depend on various parameters like laser detuning and bandwidth, focusing optics, and the particular excited state involved also, the threshold N and threshold I values are correlated, with the increase of one allowing a decrease of the other. Typical threshold values in Cs are N=10i cm and I=10 W cm when a 6010A laser is used to excite the 5(803 2) state. Threshold values when other states are excited or when other alkali vapors are used can be quite different for example, Stwalley and co-workers (19) have reported that the threshold values in a sodium vapor are N lQt cm and I 10 W cm when a focused cw dye laser at 5688 or S683A is used to excite the Na(4D) state. 

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