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Physical Review A

Coherent quantum control of multiphoton transitions by shaped ultrashort optical pulses

Doron Meshulach, Yaron R. Silberberg

Published Aug 1, 1999• 366 citations
Publisher

Abstract

Multiphoton transitions can be reached by many routes through a continuum of virtual levels. We show that the transition probability of two-photon and multiphoton processes can be controlled by tailoring the shape of an ultrashort excitation pulse, so that the many paths leading to the final state interfere to give a desired probability amplitude. We analyze the effect of pulse shapes on N-photon absorption as well as on Raman transitions. We show theoretically that certain tailored dark pulses do not excite the system at all, while other shaped pulses induce transitions as effectively as transform limited pulses, even when their peak amplitudes are greatly reduced. These results are confirmed experimentally for two-photon transitions in atomic cesium.

DOI
10.1103/physreva.60.1287

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Multiphoton transitions can be reached by many routes through a continuum of virtual levels. We show that the transition probability of two-photon and multiphoton processes can be controlled by tailoring the shape of an ultrashort excitation pulse, so that the many paths leading to the final state interfere to give a desired probability amplitude. We analyze the effect of pulse shapes on N-photon absorption as well as on Raman transitions. We show theoretically that certain tailored dark pulses do not excite the system at all, while other shaped pulses induce transitions as effectively as transform limited pulses, even when their peak amplitudes are greatly reduced. These results are confirmed experimentally for two-photon transitions in atomic cesium.
Multiphoton transition probability can be manipulated by tailoring the ultrashort laser pulses. In this paper, we theoretically and experimentally investigate the influence of the absorption bandwidth and line shape on the coherent control of two-photon transitions in two-level system by manipulating the femtosecond laser pulse with the $\ensuremath{\pi}$ spectral phase step. A coherent feature with a coherent peak and two coherent dips can be achieved if the absorption bandwidth is less than twice of the laser spectral bandwidth. The absorption bandwidth decides the coherent peak or dip intensity, and the absorption line shape affects the symmetry of the two coherent dips.
We investigate the excitation of an atom or molecule via two-photon absorption induced by an ultrashort laser pulse in the perturbative intensity regime. We show that the probability for a resonant transition, i.e., with an intermediate state within the spectral width of the pulse, can be reduced to zero by pulses having a $\ensuremath{\theta}$-phase step at a certain detuning $\ensuremath{\delta}\ensuremath{\omega}$ from the central frequency. Our theoretical predictions are confirmed by numerical calculations for the $4s\ensuremath{\rightarrow}4d$ transition in the potassium atom.
Selective multiphoton excitations can be achieved by tailoring the driving pulses to manipulate the outcome of the light-matter interaction. While single-photon transitions of single atoms driven by ultrashort pulses, dependent mainly on the resonant frequency component, and thus possesses no optical selectivity no matter how the excitation pulse shapes [1]. Interestingly, when an ultrashort pulse interacts with an optically dense medium, quantum controllable optical selectivity can be achieved in a single-photon process.
Multiphoton transitions can be manipulated by tailoring the ultrashort laser pulse. In this paper, we propose two schemes for achieving precise control of the selective excitation between two excited states in stimulated Raman-scattering process. We theoretically demonstrate that by properly designing the spectral phase distribution, the stimulated Raman transition probability for one excited state is kept at zero or a maximal value, while that for the other excited state can be continuously tuned over a wide range. Furthermore, the influence of the spectral bandwidth on the tunable range by the two schemes is discussed. We conclude that these schemes have significant application to the selective excitation of femtosecond coherent anti-Stokes Raman scattering.
Weak-field coherent phase control of atomic non-resonant multiphoton excitation induced by shaped femtosecond pulses is studied theoretically in the single-cycle regime. The carrier-envelope phase (CEP) of the pulse, which in the multi-cycle regime does not play any control role, is shown here to be a new effective control parameter that its effect is highly sensitive to the spectral position of the ultrabroad spectrum. Rationally chosen position of the ultrabroadband spectrum coherently induces several groups of multiphoton transitions from the ground state to the excited state of the system: transitions involving only absorbed photons as well as Raman transitions involving both absorbed and emitted photons. The intra-group interference is controlled by the relative spectral phase of the different frequency components of the pulse, while the inter-group interference is controlled jointly by the CEP and the relative spectral phase. Specifically, non-resonant two- and three-photon excitation is studied in a simple model system within the perturbative frequency-domain framework. The developed intuition is then applied to weak-field multiphoton excitation of atomic cesium (Cs), where the simplified model is verified by non-perturbative numerical solution of the time-dependent Schrödinger equation. We expect this work to serve as a basis for a new line of femtosecond coherent control experiments.