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Strong field control of multilevel quantum systems

Stephen D. Clow

Published Aug 1, 2010• 1 citation
OpenAlex

Abstract

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.

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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.
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.
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 $\ensuremath{\pi}$ 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.
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.
In this thesis, atomic coherence is used to enhance nonlinear optical processes in multi-level atoms. The multi-photon transitions are driven resonantly, and at the same time without absorptive losses, by using electromagnetically induced transparency (EIT), thereby allowing the study of χ(3) and χ(5) nonlinearities using weak driving fields. The coherently modified probe beam(s) and the atom-radiated signal fields arising from four- and six- wave- mixing (FWM and SWM) processes are measured in the spectral, temporal and spatial domains. In a three-level ladder-type atomic system, multiple peaks having spectral asymmetries are observed in the EIT window as well as in the FWM signal waveforms due to the diverse multiplicities of the participating atomic states. Using phase control tailored in the frequency domain, we demonstrate all-optical methods to control these spectral waveforms and discuss applications involving waveform-shaping and metrology. For the EIT study we demonstrate a switching of multiple dark peaks into bright peaks via phase-control of interferences in the underlying dark-states. In the FWM study we demonstrate all-optical spectral line shape symmetrization, linewidth narrowing and bandwidth switching. In a four-level inverted-Y-type atomic system, we drive and measure coexisting and phase-matched FWM and SWM signals. By using precision control of the relative phase and amplitude between these two processes of different nonlinear orders, we demonstrate phase coherence between them. First, a single-phase measurement is performed in the temporal and spatial domains, and the interferogram is used to measure the resonant frequency of the 5D5/2-5P3/2 atomic transition in 85Rb. Second, the method is extended to realize a capacity for two-phase measurement. In this case, the spectral bandwidth of the signal is modified in order to measure the phase-shift occurring in one Mach-Zehnder interferometer, while the intensity of the total signal waveform measures the phase-shift occurring in a second interferometer. Finally, we demonstrate phase-dependent spatial fusion between two ultra-weak optical fields by using a strong coupling field to first convert the weak fields into bosonic dark-state polaritons, which are then steered into a common all-optical waveguide mode arising due to the coupling field's intensity distribution and the resulting cross-Kerr refractive index gradient.
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 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.