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Physical Review A

Population transfer inN-level systems assisted by dressing fields

Takashi Nakajima

Published Jan 1, 1999• 19 citations
Publisher

Abstract

We analyze N-level systems for population transfer by counterintuitive pulse delay, in which $N\ensuremath{-}2$ intermediate states are strongly coupled by dressing laser fields. We have carried out specific analysis for the four- and five-level systems using a dressed-state picture, as representatives for even-N- and odd-N-level systems, respectively. We have found that the dynamics of the systems are essentially different for even-N- and odd-N-level systems, and that complete population transfer assisted by dressing fields is more restrictive for even-N-level systems than for odd-N-level systems.

DOI
10.1103/physreva.59.559

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We analyze N-level systems for population transfer by counterintuitive pulse delay, in which N\ensuremath−2N\ensuremath{-}2N\ensuremath−2 intermediate states are strongly coupled by dressing laser fields. We have carried out specific analysis for the four- and five-level systems using a dressed-state picture, as representatives for even-N- and odd-N-level systems, respectively. We have found that the dynamics of the systems are essentially different for even-N- and odd-N-level systems, and that complete population transfer assisted by dressing fields is more restrictive for even-N-level systems than for odd-N-level systems.
Even-N-level ladder system has been analyzed for population transfer by counterintuitive frequency-chirped laser pulse,in which N-2 intermediate states are strongly coupled by dressing laser field.The specific analysis for the four-level ladder system has been carried out by using a dressed-state picture,as representative for even-N-system.It is found that a well-controlled pulse area is required for complete population transfer from |1〉|4〉 if the dressing field is sufficiently strong and on resonance.And it is essential to detune the pump and Stokes laser so that one of the dressed intermediate states is on resonance,leading to the reduction of the whole system to the three-level system.
We present explicit analytic expressions for adiabatic dressed states which, in suitable limits, produce complete population transfer between initial and final states of a four-state excitation chain without ever placing appreciable population into intermediate states. The population-transfer scheme is a generalization of the three-state stimulated Raman adiabatic passage that makes use of counterintuitive pulse sequences. We demonstrate analytically and numerically that the four-state system differs in a very significant qualitative way from previously studied N-state systems with odd N. In particular, we find that the presence of modest detuning from single-photon resonance is critical to the success of population transfer.
We examine, both numerically and analytically, the limits of controllability and the dynamics of population transfer in systems with degenerate target states embedded in a finite manifold of states. An analysis of the dressed eigenstates of coupled field-matter systems is combined with the theory of the controllability of invariant systems on Lie groups to show the existence of a control scheme using a pair of shaped laser pulses acting upon a four-state system with intermediate degenerate states and a diamond-shaped array of transition moments $({\ensuremath{\mu}}_{12},{\ensuremath{\mu}}_{24},{\ensuremath{\mu}}_{13},{\ensuremath{\mu}}_{34}\ensuremath{\ne}0,{\ensuremath{\mu}}_{14},{\ensuremath{\mu}}_{23}=0).$ The limits of the controllability of these systems are linked to the symmetry of the transition dipole moments connecting the states. A broken symmetry of the transition dipole moments $({\ensuremath{\mu}}_{12}/{\ensuremath{\mu}}_{24}\ensuremath{\ne}{\ensuremath{\mu}}_{13}/{\ensuremath{\mu}}_{34})$ permits complete population transfer to one of the pair of degenerate states. Numerical simulations of the optimized population transfer to one of a pair of degenerate states in the system agree quantitatively with the analytically predicted limits of population transfer in different regimes in the joint material-field characteristics of the system. The applicability of the four-state model to selective population transfer in vibrationally mediated photodissociation experiments is discussed.
The effect of radiative decay and collisional damping on the delayed-field population transfer in the three-level system is investigated. The simple analytical steady-state solution of the three-level system, interacting with two intense delayed laser pulses in the dressed-state frame, is obtained and analyzed. The radiative relaxation transfers the system to the ``trapped state,'' which is shown to be stable relative to both radiative decay and collisional damping. The effect of an additional level \ensuremath{\Vert}m〉, situated close to the final level \ensuremath{\Vert}3〉, on the population-transfer process is considered. The field-induced relaxation rate from intermediate level \ensuremath{\Vert}2〉 to level \ensuremath{\Vert}3〉 is shown to be a very easily controllable parameter of the field intensities and their relative delay. This result leads to selective population transfer to the desired level and may prevent leaking out of the three-level system. Theoretical analysis corresponds entirely to recent experimental data [U. Gaubatz et al., J. Chem. Phys. 92, 1 (1990); 92, 5363 (1990)].
We investigate several configurations for complete population transfer on the basis of the dressed state picture in a three-level system. This picture allows us not only to confirm an atom staying in the only dark state all the time under the well-known stimulated Raman adiabatic passage but also to find the considerably different dynamics from the conventional adiabatic process in cases where the pulses are significantly overlapped or concurrent (optimal detuning method). We expand the concept of the adiabatic process in order to explain all these cases.