Bichromatic control

As an example of this approach we consider control over the relative probability of forming 2P3/2 vs. 2Pl /,2 atomic iodine, denoted I and I, in the dissociation of methyl iodide in the regime of 266 nm, 

This reaction is an example of electronic branching of photodissociation products. The results reported below are for a nonrotating two-dimensional collinear model [49, 50] in which the H3 center of mass, the C, and the I atoms are assumed to lie on a line. Results for a rotating collinear model are discussed in the next section. 

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The role of the laser phase in controlling molecular dynamics was clear in the examples shown in Chapter 3, For example, in the one- vs. three-photon scenario the relative laser phase (3 — 3c/>,) enters directly into the interference term [see, e.g., Eq. (3.53)], as does the relative phase ((frl — (j>2) in the bichromatic control scenario [Eq. (3.19)]. These residts embody two useful general rules about the contribution of the laser phase to coherent control scenarios. The first is that the interference term contains the difference between the laser phase imparted to the molecule by one route, and that imparted to the molecule by an alternate route. Second, the phase imparted to the state Em) by a light field of the form ... 

The first panel of Figure 5.12 shows the bichromatic control scenario. The sec panel shows the simplest path to the continuum, consisting of one-photon absorpt of CO]. The subsequent panels show the three-photon process to the contir (absorption of a> followed by stimulated emission and reabsorption of coj, ctc ... 

Figure 5.12 Interfering pathways from Et) to the continuum associated with the scenario in Figure 5.11. The frequency and phase of the lasers are co, and (a) Bichromatic control, (b) One-photon absorption, (c) Three-photon process in which initially unpopulated state Ej) is coupled to the continuum at energy E and interferes with one-photon absorption from state ] ,). (d) Same as in (c) but for a five-photon process. Notice that in processes depicted in (c) and (d) the phase

Photodissociation is but one of many processes that are amenable to control. A host of other processes that have been studied are discussed later in this book, such as > asymmetric synthesis, control of bimolecular reactions, strong-field effects, and so forth. Also of interest is control of nonlinear optical properties of materials [203],i particularly for device applications. In this section we describe an application of thfrj bichromatic control scenario discussed in Section 3.1.1) to the control of refractive indices. riff... 

Here we show that an application of bichromatic control (Section 3.1.1) allows us to control both the real and imaginary parts of the refractive index. In doing so we consider isolated molecules [213, 214], or molecules in a very dilute gas, where collisional effects can be ignored and time scales over which radiative decay occurs can be ignored. 

Consider then the case of bichromatic control where a system prepared in a. superposition of bound Hamiltonian eigenstates IE,),... 

Examination of Eq. (6.21) shows that y(a>) is comprised of two terms that are proportional to c, 2 and that are associated with the traditional contribution to the susceptibility from state 11 ) and E2) independently, plus two field-dependent terms, proportional to a -j = c cje co /eia), which results front the coherent excitation of both II ) and E2) to the same total energy E = Ex + to) = E2+ to2. As a consequence, changing au alters the interference between excitation routes and allows for coherent control over the susceptibility. As in all bichromatic control scenarios, this control is achieved by altering the parameters in the state preparation in order to affect c1,c2 and/or by varying the relative intensities of the two laser fields. Note that control over y(ciy) is expected to be substantial if e(a>j)/e(cOj) is large. However, under these circumstances control over yfro,) is minimal since the corresponding interference term is proportional to e(a>t)/e(cQj). Hence, effective control over the refractive index is possible only at one of co( or >2. 

For zero detuning, however, the two frequencies thus emitted cannot be reab jl sorbed. That is, contrary to the emission process, the reabsorption process would lead to the same final state [ )), and there would be no way we can tell which pathway was chosen by the system (see Fig. 9.9). Thus, the resultant can cell atiprfj of reabsorption of the two emitted frequencies in the LWI case is seen to be a specia case of the bichromatic control scenario (Section 3.1.1). 

Thus, we obtain a form, which is correct (within the range of validity of the SVC A) for strong fields, that resembles the weak-field bichromatic control result of Eq. (3.12). The only difference is that instead of the Fourier transform of the electric field of the pulse, Eq. (10.19) depends on the Fourier transform of the product of the pulse electric field and the decaying factor exp[—(n/fyA Ei) J,oo /(OI2 dt ], which describes the depletion of the initial state(s) due to the action of the pulse. 

In essence, bichromatic control can be used to change the sign of a [Pg.286]

Since the classical treatment has its restrictions and the applicability of the quantum OCT is limited to low-dimensional systems due to its formidable computational cost, it would be very desirable to incorporate the semiclassical method of wavepacket propagation like the Herman-Kluk method [20,21] into the OCT. Recently, semiclassical bichromatic coherent control has been demonstrated for a large molecule [22] by directly calculating the percent reactant as a function of laser parameters. This approach, however, is not an optimal control. 

The bichromatic off-resonance LIP obeys the same general relation to the field as does the monochromatic LIP, namely, AW(y) = —dind E(y, f). All that one need do is calculate the dipole induced in the material superposition state by the bichro- matic field. Following our discussion of the control of refractive indices in Section, 6.2, the induced dipole is given by... 

The pump-probe pulses are obtained by splitting a femtosecond pulse into two equal pulses for one-color experiments, or by frequency converting a part of the output to the ultraviolet region for bichromatic measurements. The relative time delay of the two pulses is adjusted by a computer-controlled stepping motor. Petek and coworkers have developed interferometric time-resolved 2PPE spectroscopy in which the delay time of the pulses is controlled by a piezo stage with a resolution of 50 attoseconds [14]. This set-up made it possible to probe decoherence times of electronic excitations at solid surfaces. 

Alternatively, new perspective method of coherent manipulation can be implemented by the bichromatic optical excitation of strained samples of diamonds with an additional external control parameter - electric field (see [34]). 

Here we extend the simple three-level EIT system to mote complicated and versatile configurations in a multi-level atomic system coupled by multiple laser fields. We show that with multiple excitation paths provided by different laser fields, phase-dependent quantum interference is induced either constractive or destractive interfereiKe can be realized by varying the relative phases among the laser fields. Two specific examples are discussed. One is a three-level system coupled by bichromatic coupling and probe fields, in which the phase dependent interference between the resonant two-photon Raman transitions can be initiated and controlled. Another is a four-level system coupled by two coupling fields and two probe fields, in which a double-EIT confignration is created by the phase-dependent interference between three-photon and one-photon excitation processes. We analyze the coherently coupled multi-level atomic system and discuss the control parameters for the onset of constructive or destructive quantum interference. We describe two experiments performed with cold Rb atoms that can be approximately treated as the coherently coupled three-level and four-level atomic systems respectively. The experimental results show the phase-dependent quantum coherence and interference in the multi-level Rb atomic system, and agree with the theoretical calculations based on the coherently coupled three-level or four-level model system. 

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