The technique of stimulated Raman adiabatic passage (STIRAP) has become an established procedure for producing complete population inversion in atoms or molecules via application of Stokes and pump pulses in a counterintuitive sequence. Previously we reported on numerical and analytical investigations showing some of the additional and important phenomena that arise when some of the levels involved have nonzero angular momentum, the field polarization directions have no simplifying symmetries, and Zeeman splitting lifts the magnetic sublevel degeneracy. Here we verify our theoretical findings using the metastable neon system:
3P0?3P1?3P2 with the corresponding angular momentum sequence J=0?J=1?J=2. In particular, we demonstrate that it is possible to transfer all population from the single initial state to any single selectable final magnetic sublevel M. Selectivity can be achieved either by choosing special laser polarization angles or, for fixed polarizations, by tuning the two lasers into two-photon resonance between the initial and desired final state. The complete control of magnetic sublevel population enabled by this procedure extends the customary experimental methods for producing oriented or aligned beams of atoms. In addition, we demonstrate very clearly the previous prediction that population transfer may fail for certain sets of parameters (detunings, Rabi frequencies, and polarization angles). \textcopyright{} 1996 The American Physical Society.
The technique of stimulated Raman adiabatic passage has become an established procedure for producing complete population inversion in atoms or molecules via application of Stokes and pump pulses in a counterintuitive sequence. We discuss here some of the new and important phenomena that arise when some of the states involved have nonzero angular momentum, the field polarization directions have no simplifying symmetries, and Zeeman splitting lifts the magnetic sublevel degeneracy. We consider the effects of the linkage structure of the Hamiltonian, the effects of various polarization directions, and the effects of various choices for carrier frequencies, as expressed by detunings from single-photon resonance. In particular, we consider an example with angular momentum J=0\ensuremath{\leftrightarrows}J=1\ensuremath{\leftrightarrows}J=2 in which nine magnetic sublevels occur. We show that under suitable conditions it is possible, simply through the appropriate tuning of pump and Stokes carrier frequencies, to place the entire population into any specified single magnetic sublevel.
We consider an adiabatic population transfer process that resembles the well-established stimulated Raman adiabatic passage. In our system, the states have nonzero angular momentums J , therefore, the coupling laser fields induce transitions between 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 ⇔ 1 and 1 ⇔ 2. Initially, the system is in the J = 0 state. We show that by, applying 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 also the probability amplitudes. 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.
We examine the conditions needed to accomplish stimulated Raman adiabatic passage (STIRAP) when the three levels (ground
g, excited
e, and final
f) are degenerate, with arbitrary couplings contributing to the pump-pulse interaction $(g\text{\ensuremath{-}}e)$ and to the Stokes-pulse interaction $(e\text{\ensuremath{-}}f)$. 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. Using a sequence of unitary transformations we demonstrate 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 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.
Ongoing work aimed at developing highly efficient methods of populating a chosen sublevel of an energy level highlights the need to understand off-resonant effects in coherent excitation. This motivated us to re-examine some aspects of the theory of coherent excitation in a three-state system with a view to obtaining algebraic expressions for off-resonant eigenvalues and eigenvectors. Earlier work gives simple closed-form expressions for the eigenvalues this system, expressions applying even when the system is not on two-photon resonance. We present here expressions of similar simplicity for the components of the normalised eigenvectors. The analytic properties of these components explain the observed sensitivity of the stimulated-Raman-adiabatic-passage process (STIRAP) to the condition of two-photon resonance. None of the eigenstates is ‘trapped’ or ‘dark’ unless the system is on two-photon resonance; off resonance, all states have nonzero projections on the unperturbed intermediate state. A simple argument shows that no dressed state can be adiabatically connected to both the unperturbed initial and final states when the system is off two-photon resonance. That is, adiabatic transfer from initial to final state requires that these be degenerate before and after the STIRAP pulse sequence, and this implies zero two-photon detuning. However, substantial transfer probabilities are observed experimentally for very small two-photon detunings. We show that such systems are characterised by very sharp avoided crossings of two eigenvalues, and that the observed population transfer can be understood as an effect of non adiabatic transitions occurring at the avoided crossings.
It introduced several methods to transfer population,including two-level system and three-level system, and gave some comparisons on transfer efficiency and transfer velocity of them in theory. It is shown that population transfer by coherent pulse sequence is better than incoherence one. Numerical simulation results showed that when using Stimulated Raman Adiabatic Rapid Passage (STIRAP), in which the pump laser pulse fully overlaps the Stokes pulse with the Stokes preceding the pump, population can be transferred completely and rapidly. Robust control of population transfer among Zeeman sublevels in the ground states of three-level system is investigated using adiabatic rapid passage in theory. The laser pulse widths are supposed to be short compared to the lifetime of the excited level, which means adiabatic. We demonstrated that techniques of STIRAP can be found to optimize population transfer in the ground states of three-level Λ system.