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Physical Review A

Strong-field spatiotemporal ultrafast coherent control in three-level atoms

Barry D. Bruner, Haim Suchowski, Nikolay V. Vitanov, Yaron R. Silberberg

Published Jun 10, 2010• 24 citations
Publisher

Abstract

Simple analytical approaches for implementing strong field coherent control schemes are often elusive due to the complexity of the interaction between the intense excitation field and the system of interest. Here, we demonstrate control over multiphoton excitation in a three-level resonant system using simple, analytically derived ultrafast pulse shapes. We utilize a two-dimensional spatiotemporal control technique, in which temporal focusing produces a spatially dependent quadratic spectral phase, while a second, arbitrary phase parameter is scanned using a pulse shaper. In the current work, we demonstrate weak-to-strong field excitation of $^{85}\mathrm{Rb}$, with a $\ensuremath{\pi}$ phase step and the quadratic phase as the chosen control parameters. The intricate dependence of the multilevel dynamics on these parameters is exhibited by mapping the data onto a two-dimensional control landscape. Further insight is gained by simulating the complete landscape using a dressed-state, time-domain model, in which the influence of individual shaping parameters can be extracted using both exact and asymptotic time-domain representations of the dressed-state energies.

DOI
10.1103/physreva.81.063410

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Simple analytical approaches for implementing strong field coherent control schemes are often elusive due to the complexity of the interaction between the intense excitation field and the system of interest. Here, we demonstrate control over multiphoton excitation in a three-level resonant system using simple, analytically derived ultrafast pulse shapes. We utilize a two-dimensional spatiotemporal control technique, in which temporal focusing produces a spatially dependent quadratic spectral phase, while a second, arbitrary phase parameter is scanned using a pulse shaper. In the current work, we demonstrate weak-to-strong field excitation of 85Rb^{85}\mathrm{Rb}85Rb, with a \ensuremathπ\ensuremath{\pi}\ensuremathπ phase step and the quadratic phase as the chosen control parameters. The intricate dependence of the multilevel dynamics on these parameters is exhibited by mapping the data onto a two-dimensional control landscape. Further insight is gained by simulating the complete landscape using a dressed-state, time-domain model, in which the influence of individual shaping parameters can be extracted using both exact and asymptotic time-domain representations of the dressed-state energies.
Coherent control of resonant and non-resonant two-photon absorption processes was examined using a spatio-temporal pulse-shaping technique. By utilizing a combination of temporal focusing and femtosecond pulse-shaping techniques, we spatially control multiphoton absorption processes in a completely deterministic manner. Distinctive symmetry properties emerge through two-dimensional mapping of spatio-temporal data. These symmetries break down in the transition to strong fields, revealing details of strong-field effects such as power broadenings and dynamic Stark shifts. We also present demonstrations of chirp-dependent population transfer in atomic rubidium, as well as the spatial separation of resonant and non-resonant excitation pathways in atomic caesium.
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.
We demonstrate ultrafast coherent control of multiphoton absorption in a dynamically shifted energy level structure. In a three-level system that models optical interactions with sodium atoms, we control the quantum interference of sequential 2 + 1 photons and direct three-photon transitions. Dynamic change in energy levels predicts an enormous enhancement of |7p>-state excitation in the strong-field regime by a negatively chirped pulse. In addition, the |4s>-state excitation is enhanced symmetrically by nonzero linear chirp rates given as a function of laser peak intensity and laser detuning. Experiments performed by ultrafast shaped-pulse excitation of ground-state atomic sodium verifies the various strong-field contributions to |3s>-|7p> and |3s>-|4s> transitions. The result suggests that for systems of molecular level understanding adiabatic control approach with analytically shaped pulses becomes a more direct control than feedback-loop black-box approaches.
V-type three-level systems, where two excited states share a common ground state, serve as fundamental models for exploring coherent light-matter interactions in a range of quantum systems, from atomic gases to semiconductor nanostructures. In this work, we investigate the coherent evolution of such a system under strong femtosecond-pulse excitation by numerically solving the optical Bloch equations. Our analysis shows that the coherent evolution of a three-level system critically depends on the product of the excitation-pulse duration and energy separation between the excited states. Building on this understanding, we extend our analysis to simulate two-dimensional coherent spectra in a high-intensity regime. We demonstrate a control over the coherent pathway contributions to the nonlinear optical response of a V-type system by varying the intensity of the excitation pulses. This control is manifested through the ability to selectively turn individual spectral features on or off in the 2D spectra, each corresponding to distinct quantum pathways. Furthermore, the pulse intensities are varied to precisely adjust the phase of these peaks. Our approach provides a simple and robust framework for achieving control of coherent response of multilevel systems.
We show that coherent control of multiphoton transitions is possible in the strong field limit, even in the presence of large dynamic Stark shifts. By tailoring the phase of an ultrafast laser pulse, one can compensate for the dynamic Stark shift during the atom-field interaction to achieve efficient population transfer in two-photon absorption. Numerical simulations for atomic sodium reveal efficient population transfer from the $\ensuremath{\mid}3s⟩$ ground state to the $\ensuremath{\mid}4s⟩$ excited state using an appropriately shaped ultrafast laser pulse. The theory and simulations provide insight into coherent control of more complicated multiphoton processes.