Dressed potential

S. A. Rice The coupled matter-radiation system considered in the control schemes can, indeed, be studied from the point of view of dressed potential-energy surfaces, as suggested by the remark by Prof. Quack. We find it more convenient to use the equivalent point of view of continuous transfer of amplitude back and forth between the undressed potential-energy surfaces, because the formalism we have developed calculates the temporally and spectrally shaped field for that dynamical representation. 

Fig. 1.1. Schematic view of the Coulomb explosion imaging of nuclear dynamics. Molecules exposed to an intense laser field undergo structural deformation in response to the formation of light-dressed potential energy surfaces, and decompose into fragment ions after multiple ionization. Since the momentum vectors of fragment ions sensitively reflect the geometrical structure just before the Coulomb explosion, the ultrafast nuclear dynamics of a molecule in an intense laser field can be elucidated through measurements of the momenta of fragment ions...

It is convenient to treat intense electromagnetic field problems in the dressed molecular states picture (see review by Giusti-Suzor, et al, (1995)). This picture allows one to think about intense field problems in a framework that closely resembles the weak field, diabatic or adiabatic states picture that is the primary focus of this book. In the dressed states picture the photon energy is added to, or subtracted from, the field-free potential energy curves. One obtains field-dressed potential curves. 

Each field free potential curve, V (R), generates a family of field-dressed potentials, Vj>n(iJ), with the result that many intersections between potential curves occur that are not present in the field-free case. The spectroscopic and dynamical consequences of these field-dressed curve crossings are understood using exactly the same methods presented in this book for field-free intersecting potentials. 

Figure 3.12 Field-dressed potential energy curves for HJ interacting with a 532nm laser field. The field-dressed diabatic curves are shown as full lines. The field-dressed adiabatic curves, shown as dotted and dashed curves, correspond respectively to laser intensities of 1 x 1013 W/cm2 and 4 x 1013 W/cm2 (from Giusti-Suzor, et al., 1995).

Figure 2.1 Field-dressed potential energy curves of Hj (X = 532 nm), in the diabatic (solid lines) and adiabatic (broken lines for / = 10 W/cm and dotted lines for / = 5 x 10 W/cm ) frames. Curve-crossing regions are outlined by rectangular boxes XI, X2, and X3. The energies of the v = 2,4, 5 vibrational levels are indicated by thin horizontal lines.

Considering the diagonal terms in Equation 7.17, such that = x(f fp). it is also convenient to define time-dependent dressed potentials. 

After the pulse, there is also population of the two upper vibrational levels of the lower state, v" = 52 and v" = 53 (see Figure 7.4b) stable molecules are thus formed in a one-color scheme, because the time-dependent frequency of the pulse is sweeping an optical Feshbach resonance. In the dressed potential picture, the initial continuum level of the ground potential Vg R, t) is at resonance with a bound level of the excited potential Ve(R, t). Note the efficiency of the process the number of molecules formed in these two levels of the lower state is equivalent to the number of photoassociated molecules in 15 levels in the excited state. The efficiency of various PA pulses for this population transfer has been discussed in Ref [19]. The levels v" = 53 and v = 52 are respectively bound by 5 x 10 and 0.042 cm to be compared with the resonance window of 1.74 cm in the excited state. Due to the very small value of the binding energy, these molecules are halo molecules, as defined by Koehler and colleagues [8] their creation as a byproduct of the PA process should be further investigated. Recently, Kallush and Kosloff [28] have discussed the nonperturbative character of the PA process, where the conservation of the total population requires a... 

To compute the dressed potential surface, it is convenient to introduce the projector which projects on the subset of electronic states g. Introducing... 

In analogy to Sec. 3.1, we may neglect in many cases to a good approximation the difference between the naked and the dressed potential matrices... 

In other words, the group-Born-Oppenheimer is a gauge invariant approximation. In the above equation, the dressed potential transforms as... 

A similar analysis can be performed for the dressed potential energy surfaces. Combining Eqs. (7.4), (7.16) and (7.18), the elements of the dressed diabatic potential energy matrix corresponding to the excited states can be written as... 

One can see that the dressed potential energy matrix elements of Eq. (7.24) have the same form than the field-free diabatic potential energy matrix elements of Eq. (7.4). Thus, analytical expressions for the positions and energies of the minima of the dressed upper adiabatic PES and MECI can be obtained by replacing Ej by... 

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