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Physical Review A

Control of population transfer in degenerate systems by nonresonant Stark shifts

François Légaré

Published Dec 10, 2003• 5 citations
Publisher

Abstract

Two simple schemes are presented for the selective population transfer in systems where the target state is degenerate with a second level. Both states are coupled with the ground state via a one photon resonance. The schemes use a combination of two laser pulses. The first pulse breaks the degeneracy of the levels by inducing a Stark shift. The second pulse is chirped across the new levels. The idea is illustrated by numerical simulations of the time-dependent Schr\"odinger equation for a four-level system. The efficient population transfer is explained using a dressed state representation. In conclusion, applications for molecules are suggested.

DOI
10.1103/physreva.68.063403

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Two simple schemes are presented for the selective population transfer in systems where the target state is degenerate with a second level. Both states are coupled with the ground state via a one photon resonance. The schemes use a combination of two laser pulses. The first pulse breaks the degeneracy of the levels by inducing a Stark shift. The second pulse is chirped across the new levels. The idea is illustrated by numerical simulations of the time-dependent Schr"odinger equation for a four-level system. The efficient population transfer is explained using a dressed state representation. In conclusion, applications for molecules are suggested.
Selective population transfer in electronic states of dissociative molecular systems is illustrated by adopting a control scheme based on Stark-chirped rapid adiabatic passage (SCRAP). In contrast to the discrete N-level system, dynamical Stark shift is induced in a more complex manner in the molecular electronic states. Wavepacket dynamics on the light-induced potentials, which are determined by the detuning of the pump pulse, can be controlled by additional Stark pulse in the SCRAP scheme. Complete population transfer can be achieved by either lowering the energy barrier along the adiabatic passage or placing the initial wavepacket on a well-defined dressed state suitable for the control. The determination of the pulse sequence is sufficient for controlling population transfer to the target state.
We demonstrate and analyze a novel scheme for complete transfer of atomic or molecular population between two bound states, by means of Stark-chirped rapid adiabatic passage (SCRAP). In this two-laser technique a delayed-pulse laser-induced Stark shift sweeps the transition frequency between two coupled states twice through resonance with the frequency of the population-transferring coupling laser. The delay of the Stark-shifting pulse with respect to the pulse of the coupling-laser Rabi frequency guarantees adiabatic passage of population at one of the two resonances while the evolution is diabatic at the other. The SCRAP method can give a population-transfer efficiency approaching unity. We discuss the general requirements on the intensity and timing of the pulses that produce the Rabi frequency and, independently, the Stark shift. We particularly stress extension to a double-SCRAP technique, a coherent variant of stimulated emission pumping in the limit of strong saturation. We demonstrate the success of the SCRAP method with experiments in metastable helium, where a two-photon transition provides the Rabi frequency.
The stark-chirped rapid adiabatic passage (SCRAP) is analyzed, which can give a complete transfer of atomic or molecular population between two bound states in the two level states and Λ(-three)-level state, by means of level-crossing technique and dressed states theory. SCRAP uses two laser pulses: a nearly-resonant pump laser pulse drives the population between a ground state and an excited state, and an intense far-off-resonance Stark laser pulse modifies the transition frequency and resonates with the Bohr transition frequency for two level crossings. A population-transfer maximal efficiency approaching unity is provided from the ground state to the excited state, when the delay of the Stark-shifting pulse with respect to the pulse of the coupling-laser frequency is appropriate and guarantees the pump pulse is strong at one of these crossings and is weak at second one.
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.
We propose a scheme for coherent control of population transfer and arbitrary superpositions of quantum states by a single-chirped laser pulse in a Λ-type excited-doublet four-level system. It is shown that selective, efficient, and robust population transfer from the initial state to the target states (excited or ground) can be achieved via chirped adiabatic passage when the pulse bandwidth is smaller than about 1/10 of the energy separations between the excited-doublet levels and between the ground states. Moreover, arbitrary coherent superpositions between the excited-doublet states, or between the higher ground state and either of the excited-doublet states, can be created by appropriately tuning the chirp rate and detuning the laser field. The proposed flexible method of coherent control of population transfer and arbitrary superpositions between the initially unpopulated states requires only a single pulse, and is robust against variations in the laser parameters, which has potential applications in quantum information processing.
We show that the technique of Stark-chirped rapid adiabatic passage (SCRAP), hitherto used for complete population transfer between two quantum states, offers a simple and robust method for complete population transfer amongst three states in atoms and molecules. In this case SCRAP uses three laser pulses: a strong far-off-resonant pulse modifies the transition frequencies by inducing dynamic Stark shifts and thereby creating time-dependent level crossings amongst the three diabatic states, while near-resonant and moderately strong pump and Stokes pulses, appropriately offset in time, drive the population between the initial and final states via adiabatic passage. The population transfer efficiency is robust to variations in the intensities of the lasers, as long as these intensities are sufficiently large to enforce adiabatic evolution. With suitable pulse timings the population in the (possibly decaying) intermediate state can be minimized, as with stimulated Raman adiabatic passage (STIRAP). This technique applies to one-photon as well as multiphoton transitions and it is also applicable to media exhibiting inhomogeneous broadening; these features represent clear advantages over STIRAP by overcoming the inevitable dynamical Stark shifts that accompany multiphoton transitions as well as unwanted detunings, e.g., induced by Doppler shifts.