Stimulated Raman adiabatic passage among degenerate-level manifolds

Abstract

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.

Colloquium: Coherently controlled adiabatic passage

“…The transfer is executed in an adiabatic fashion, with the pump pulse, now linking ͉j͘ states and the ͉0͘ state, following the Stokes pulse, linking the final ͉kЈ͘ states with all ͉j͘ states. We note that using two separate steps, each including a transfer between a set of n degenerate states and a single nondegenerate level via n nondegenerate intermediate states, presents a different approach to the solution of the DQC problem suggested by others ͑Morris and Shore, 1983;Shore, 1990;Kis et al, 2004͒, where only one step is considered and degeneracy is allowed within each set of initial, final, and intermediate states.…”

Extension of the Morris-Shore transformation to multilevel ladders

“…For instance, it has been used to derive exact analytic solutions that extend known two-state solutions to degenerate two-state systems [4]. It has been used to design schemes for complete population transfer between degenerate states [5] and for creation of coherent superpositions of states [6]. The MS transformation has been also a crucial analytic method in creating recipes for efficient discrete quantum state tomography [7].…”

Physical realization of coupled Hilbert-space mirrors for quantum-state engineering

“…By utilizing three independent polarization directions of a laser pulse we can ensure three linkages with common time dependence. More general linkage patterns, still within the model described here, are also possible [10]. Physical realization of coupled Hilbert-space mirrors for quantum-state engineering 2241…”