Coherent states STIRAP

Coherent excitation of quantum systems by external fields is a versatile and powerful tool for application in quantum control. In particular, adiabatic evolution has been widely used to produce population transfer between discrete quantum states. Eor two states the control is by means of a varying detuning (a chirp), while for three states the change is induced, for example, by a pair of pulses, offset in time, that implement stimulated Raman adiabatic passage (STIRAP) [1-3]. STIRAP produces complete population transfer between the two end states 11) and 3) of a chain linked by two fields. In the adiabatic limit, the process places no temporary population in the middle state 2), even though the two driving fields - pump and Stokes-may be on exact resonance with their respective transitions, 1) 2)and... 

FIGURE 23 Illustration of the STIRAP technique used for coherent population transfer. Shown are the time evolution of (a) the Rabi frequencies of the pump and Stokes lasers, (b) the mixing angle, (c) the dressed-state eigenvalues, and (d) the populations of the initial and final levels. [Reproduced with permission from Bergmann, K., Theuer, H., and Shore, B. W. (1998) Rev. Mod. Phys. 70, 1003.]... 

The first experimental demonstration of coherent population transfer by STIRAP via continuum states was reported recently [237]. It was realized, as shown in the left panel of Figure 3.15, by transferring population from the 2s So metastable state of He to its 4s So excited state by a Raman-type... 

With a coherent stimulated Raman process (STIRAP) (see Sect. 7.3), nearly the whole initial population Ni may be transferred into the final level If) [1048]. Here no exact resonance with the intermediate excited level ) is wanted in order to avoid transfer losses by spontaneous emission from level ). The population transfer can be explained by an adiabatic passage between dressed states (that is, states of the molecule plus the radiation field) [1049, 1050]. 

Starting with very weakly bound molecules produced by MA, coherent transfer to more deeply bound levels has been achieved in both Rb2 [134] and KRb [135]. The stimulated Raman adiabatic passage (STIRAP) process, incorporating pump and dump pulses in the counterintuitive order (see Figure 5.29), enabled high transfer efficiency. Pulses of cw laser light were used in order for the process to be phase coherent. In this initial work, the final states were not very deeply bound, 600 MHz for Rb2 and 10 GHz for KRb. In more recent work, very deeply bound states have been reached. In Cs2, levels bound by >1000cm have been populated... 

The STIRAP method has attracted considerable interest as a highly efficient way to coherently transfer atom pairs or Feshbach molecules into a more deeply bound state [85]. The method offers a high transfer efficiency without heating of the molecular... 

The basic idea of STIRAP to transfer population between two quantum states relies on a particularly clever implementation of a coherent two-photon Raman transition, involving a dark state during the transfer. For a detailed description of its principles and an overview of early applications, the reader may refer to Ref. [86]. 

To demonstrate the time evolution proeess of the atomic coherence, we solve the time-dependent density-matrix equation, and the results are shown in Fig. 23. In Fig. 23, Step-1 prepares the coherence by a F-STIRAP process [52], The system state vector could be written as ... 

If the pulses dJi and CO2 have the same time back edge, the maximal atomic coherence between l) and 12) is reached. In step-2, we apply a STIRAP process among states 2, 3 and 14, the pulse sequences are shown in the right side of Fig. 23 (al). By simulation, we imd that the component of state 12 in the state vector is fully transferred to state 13 as shown in the right side of Fig. 23 (a2) and the coherence between l)- 2 is fully transferred to the coherence between l - 3 as shown in Fig. 23 (a3). Because the states 2 and 3 are not coupled with state 4 in the STIRAP process, it does not arouse the stimulated emission [53] from state 4 to l) when the pulse CO2 is applied. 

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