Background states

The success of this extended STIRAP scheme can be traced to the fact that the basis of the subset of dressed eigenstates of the coupled matter-radiation field is a stationary state representation. In this representation, all couplings are already taken into account via the identity of and the locations of the energy levels. The contribution of the background states to the population transfer process is then limited to effects associated with nonresonant coupling to the field, and if these background states are far off resonance such effects are small. 

Figure 3.16 Schematic diagram of the vibrational spectrum of states used for the numerical simulations. The states selected for use in the successive STIRAP processes are represented with thick tines, and the background states are represented with thin dashed lines. (From Ref. 67).

The triads of states used by Kurkal and Rice have much larger energy separations than those used by Jakubetz and, except for (5, 0, 1), they lie in regions of the vibrational manifold with much smaller densities of states. Indeed, Kurkal and Rice found that the first STIRAP process in their sequential STIRAP scheme is robust with respect to interference arising from the presence of background states [62]. For that reason, we exploit a CDF only in the second STIRAP process. The CDF is derived in the same manner as in Section 3.4.2 using states 3), 4), and 5). 

As already noted, and as shown clearly in Figure 3.17, the first STIRAP in the sequential STIRAP process is robust with respect to interference from the background states [62]. For that reason, we assume that the population is... 

Note that rj defines the interval between the Stokes and pump pulses all of the above results correspond to t] = 1. The i -dependence of the efficiency in the STIRAP+CDF control for FWHM and 2 (5) given in Table 3.3 is shown in Figure 3.22. The efficiency for > 1 is higher than the efficiency (about 0.57) in the STIRAP control for = 1 and the same FWHM, 2 (5). The time dependences of the STIRAP + CDFs are shown for = 5 in Figure 3.23a, and the time dependences of the populations of 3), 4), and 5) in the STIRAP + CDF control are exhibited in Figure 3.23b. The time dependences of the populations of 3), 4), and 5) are similar to those found for adiabatic population transfer in a manifold without the background states. 

The calculations presented in the previous sections ignore the influence of molecular rotation on the efficiency of vibrational population transfer. This approximation defines useful models that permit qualitative investigation of the influence of background states on the efficiency of energy transfer within an embedded subset of states but is inadequate for the quantitative description of energy transfer in the corresponding real molecules. We expect the rotation... 

We now ask if the composite STIRAP protocol remains efficient in the presence of background states. To answer this question, we consider two examples population transfer between states of the thiophosgene molecule and between states of the HCN molecule. In the thiophosgene example, we consider transfer of population from state 1) to state 6) via state 5 ) embedded in a dense manifold... 

FWHM/(2Vln 2) these generate the population transfers shown in Figure 3.28. Note the very rapid oscillations in population and the very poor yields of the target state these phenomena are the consequence of the large transition moments between the background state and the intermediate state. 

We conclude that developing a protocol for efficient population transfer between a subset of states in a physical system requires a careful examination of the influence of background states. An analysis that is based only on the properties of a small subset of states may not be robust when those states are embedded in a dense manifold of other states. 

We examine the efficiency with which population transfer can be selectively directed by STIRAP -1- FFF control to one of a pair of nearly degenerate states in the presence of background states. The vehicle for our studies is a model of the vibrational spectrum of the nonrotating SCCI2 in Figure 3.6. 

M. Etinski, C. Uiberacker, and W. Jakubetz. Counterdiabatic suppression of background state population in resonance leaking by controlling intermediate branching. J. Chem. Phys., 124(12) 124110-124116(2006). 

V. Kurkal and S. A. Rice. Sensitivity of the extended STIRAP method of selective population transfer to coupling to background states. J. Phys. Chem. B, 105(28) 6488-6494(2001). 

T. Cheng, H. Darmawan, and A. Brown. Stimulated Raman adiabatic passage in molecules the effects of background states. Phys. Rev. A, 75(1) 013411-013421(2007). 

W. Jakubetz. Limitations of STIRAP-like population transfer in extended systems the three-level system embedded in a web of background states. J. Chem. Phys., 137(22) 224312-224327(2012). 

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