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Optical Fiber Communication Conference

Multiphoton Control with Ultrafast Pulse Shaping

Debabrata Goswami, Syed Abbas Hosseini

Published Jan 1, 2001• 0 citations
Publisher

Abstract

A multiphoton density-matrix approach explores the effects of ultrafast shaped pulses for two-level systems that do not have a single photon resonance, and show that many multiphoton results are surprisingly similar to the single-photon results. These conditions thus allow extending the single-photon coherent control ideas to develop multiphoton coherent control.

DOI
10.1364/icqi.2001.pa29

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A multiphoton density-matrix approach explores the effects of ultrafast shaped pulses for two-level systems that do not have a single photon resonance, and show that many multiphoton results are surprisingly similar to the single-photon results. These conditions thus allow extending the single-photon coherent control ideas to develop multiphoton coherent control.
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.
In this thesis, we present work on coherent control of multilevelquantum systems in the strong field limit using shaped ultrafastlaser pulses. In recent years there have been numerous multiphotonabsorption experiments in two,three, and four-level atomic/molecularsystems and many are performed in the limit of weak fields whereperturbation theory is valid. Here, we describe a series ofexperiments aimed at exploring and understanding multiphotontransitions when the exciting field is strong and perturbationtheory breaks down. Our approach to strong field control utilizesboth parameterized scans of various pulse shapes and closed-looplearning control to identify a pulse shape that is optimal forpopulating a target quantum state. With this we will highlight thedifference between sequential population transfer and adiabaticrapid passage in multilevel systems with multiphoton couplingbetween levels. Additionally, we examine strong field control of afour-level atomic interferometer and show how interference in atarget state changes from resonant pathways in the frequency domainto time-domain interference via a singe path.Further, we use shaped femtosecond pulses to demonstrate aphenomenon in which a three-level atom becomes a modulator of anultrafast pulse. The results are based on a pump-probe scheme thatis very similar to Electromagnetically Induced Transparency (EIT).Important dynamics associated with a time-dependent coupling fieldare examined. Lastly, we extend previous work on two-photon drivensuperfluorescence from a shaped ultrafast drive laser and show howstimulated emission near threshold can turn modest coherent controlyields into essentially perfect discrimination between systems wherea control factor of about 104 is achieved between atomic andmolecular species.
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.
Coherent control of the atomic two-photon absorption with shaped single-cycle pulses is examined theoretically in the weak-field regime. The control over the stabilized carrier-envelope phase (CEP) of the pulses is determined as a key parameter allowing the full utilization of the ultrabroad pulse spectrum. This bandwidth is sufficient to provide besides the sequential two-photon pathways, additional Raman-type pathways coupling between the ground and the excited states. The interference between the different pathways is efficiently controlled via the control over the CEP. Simplified two-level model is analyzed in the frequency domain where the rational pulse shaping is applied. The developed intuition is applied to atomic Cs and verified by the exact numerical solution of time-dependent Schrodinger equation.
Control of multiphoton transitions is demonstrated for a multilevel system by generalizing the instantaneous phase of any chirped pulse as individual terms of a Taylor series expansion. In the case of a simple two-level system, all odd terms in the series lead to population inversion while the even terms lead to self-induced transparency. The results hold for multiphoton transitions that do not have any lower-order photon resonance or any intermediate virtual state dynamics within the laser pulse width.