We examine the conditions needed to accomplish stimulated Raman adiabatic passage (STIRAP) when the three levels (g, e and f ) are degenerate, with arbitrary couplings contributing to the pump-pulse interaction (g -e) and to the Stokes-pulse interaction (e-f ). We show that in general a sufficient condition for complete population removal from the g set of degenerate states for arbitrary, pure or mixed, initial state is that the degeneracies should not decrease along the sequence g, e and f . We show that when this condition holds it is possible to achieve the degenerate counterpart of conventional STIRAP, whereby adiabatic passage produces complete population transfer. Indeed, the system is equivalent to a set of independent three-state systems, in each of which a STIRAP procedure can be implemented. We describe a scheme of unitary transformations that produces this result. We also examine the cases when this degeneracy constraint does not hold, and show what can be accomplished in those cases. For example, for angular momentum states when the degeneracy of the g and f levels is less than that of the e level we show how a special choice for the pulse polarizations and phases can produce complete removal of population from the g set. Our scheme can be a powerful tool for coherent control in degenerate systems, because of its robustness when selective addressing of the states is not required or impossible. We illustrate the analysis with several analytically solvable examples, in which the degeneracies originate from angular momentum orientation, as expressed by magnetic sublevels.
We consider an adiabatic population transfer process that resembles the well established stimulated Raman adiabatic passage (STIRAP). In our system, the states have nonzero angular momentums J, therefore, the coupling laser fields induce transitions among the magnetic sublevels of the states. In particular, we discuss the possibility of creating coherent superposition states in a system with coupling pattern J = 0 ⇔ J = 1 and J = 1 ⇔ J = 2. Initially, the system is in the J = 0 state. We show that by two delayed, overlapping laser pulses it is possible to create any final superposition state of the magnetic sublevels |2, −2 , |2, 0 , |2, +2 . Moreover, we find that the relative phases of the applied pulses influence not only the phases of the final superposition state but the probability amplitudes as well. We show that if we fix the shape and the time-delay between the pulses, the final state space can be entirely covered by varying the polarizations and relative phases of the two pulses. Performing numerical simulations we find that our transfer process is nearly adiabatic for the whole parameter set.
A technique for creation of well-defined preselected coherent superpositions of multiple quantum states is proposed. It is based on an extension of the technique of stimulated Raman adiabatic passage ͑STIRAP͒ to degenerate levels. As an example, the nine-state system composed of the magnetic sublevels of three levels with angular momenta J g =0, J e = 1, and J f = 2 is studied in detail. Starting from the ͉J g =0, M g =0͘ state, STIRAP can create an arbitrary preselected coherent superposition between the five M f sublevels ͑M f =−2,−1,0, +1, +2͒ of the J f = 2 level with 100% efficiency in the adiabatic limit. The populations and the phases of the M f states in this superposition are determined entirely by the polarizations of the two laser fields. It is shown that this technique allows one to create any superposition of the five M f states, that is, to reach any point in the Hilbert space of the J f = 2 manifold, and the corresponding recipes for choosing the laser polarizations are presented.
A method is proposed for preparing any pure and wide class of mixed quantum states in the decoherence-free ground-state subspace of a degenerate multilevel lambda system. The scheme is a combination of optical pumping and a series of coherent excitation processes, and for a given pulse sequence the same final state is obtained regardless of the initial state of the system. The method is robust with respect to the fluctuation of the pulse areas, as in adiabatic methods; however, the field amplitude can be adjusted in a larger range.
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