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Physical Review A

Quantum control via the dynamic Stark effect: Application to switched rotational wave packets and molecular axis alignment

Benjamin Sussman, Jonathan G. Underwood, Rune Lausten, Misha Ivanov, Albert Stolow

Published May 5, 2006• 80 citations
Publisher

Abstract

Nonperturbative quantum control schemes in the intermediate field strength (nonionizing) regime are investigated. We restrict the matter-field interaction to the nonresonant dynamic Stark effect (NRDSE) as induced by infrared laser fields, which we argue is a new and general tool for quantum control of atomic and molecular dynamics. For the case of Raman coupled matter states, an effective Hamiltionian may be constructed, and quantum control via NRDSE may be thought of as reversibly modifying the effective Hamiltonian during system propagation, thus leading to control over dynamic processes. As an illustration, the creation of field-free ``switched'' wave packets through the adiabatic turn on and sudden turn off of the NRDSE is considered and experimentally demonstrated. Wave packets generated through the switched NRDSE interaction may be very different in form and content than wave packets generated via resonant transitions with Gaussian optical pulses. In order to provide an example, we discuss the specific case of rotational wave packet dynamics where the NRDSE manifests itself as molecular axis alignment. This technique is applied to the creation of field-free molecular axis alignment using an intense switched $1.064\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{m}$ laser pulse. This switched laser pulse was generated via a plasma shuttering technique, giving a pulse with a rise time of $150\phantom{\rule{0.3em}{0ex}}\mathrm{ps}$ and a fall time of $170\phantom{\rule{0.3em}{0ex}}\mathrm{fs}$. The temporal evolution of the molecular axis alignment is probed via the optical Kerr effect. Field-free alignment via the switched NRDSE is demonstrated for both linear ($\mathrm{C}{\mathrm{O}}_{2}$, $\mathrm{C}{\mathrm{S}}_{2}$) and symmetric top (1,2-propadiene) polyatomic molecules.

DOI
10.1103/physreva.73.053403

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Nonperturbative quantum control schemes in the intermediate field strength (nonionizing) regime are investigated. We restrict the matter-field interaction to the nonresonant dynamic Stark effect (NRDSE) as induced by infrared laser fields, which we argue is a new and general tool for quantum control of atomic and molecular dynamics. For the case of Raman coupled matter states, an effective Hamiltionian may be constructed, and quantum control via NRDSE may be thought of as reversibly modifying the effective Hamiltonian during system propagation, thus leading to control over dynamic processes. As an illustration, the creation of field-free ``switched'' wave packets through the adiabatic turn on and sudden turn off of the NRDSE is considered and experimentally demonstrated. Wave packets generated through the switched NRDSE interaction may be very different in form and content than wave packets generated via resonant transitions with Gaussian optical pulses. In order to provide an example, we discuss the specific case of rotational wave packet dynamics where the NRDSE manifests itself as molecular axis alignment. This technique is applied to the creation of field-free molecular axis alignment using an intense switched 1.064\ensuremathμm1.064\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{m}1.064\ensuremathμm laser pulse. This switched laser pulse was generated via a plasma shuttering technique, giving a pulse with a rise time of 150ps150\phantom{\rule{0.3em}{0ex}}\mathrm{ps}150ps and a fall time of 170fs170\phantom{\rule{0.3em}{0ex}}\mathrm{fs}170fs. The temporal evolution of the molecular axis alignment is probed via the optical Kerr effect. Field-free alignment via the switched NRDSE is demonstrated for both linear (CO2\mathrm{C}{\mathrm{O}}_{2}CO2​, CS2\mathrm{C}{\mathrm{S}}_{2}CS2​) and symmetric top (1,2-propadiene) polyatomic molecules.
The dynamic Stark effect due to a strong nonresonant but nonionizing laser field provides a route to quantum control via the creation of novel superposition states. We consider the creation of a field-free "switched" wave packet through adiabatic turn-on and sudden turn-off of a strong dynamic Stark interaction. There are two limiting cases for such wave packets. The first is a Raman-type coupling, illustrated by the creation of field-free molecular axis alignment. An experimental demonstration is given. The second case is that of dipole-type coupling, illustrated by the creation of charge localization in an array of quantum wells.
We discuss an approach to quantum control based on initial adiabatic tuning of the field-free Hamiltonian by a strong laser field to optimize the system for the desired transitions induced by the control laser pulse. As an illustration, we describe single-qubit, two-qubit, and some qudit logical gates within rotational and vibrational states of a diatomic molecule. Gate operations use resonant Raman transitions, and the prior adjustment of the Hamiltonian is done by a strong nonresonant aligning field.
The application of nonresonant lasers to quantum systems can modify energy levels in a general way. This approach, using the nonresonant dynamic Stark effect, is an effective mechanism for modifying chemical dynamics. These molecular techniques have analogous implementations in quantum technologies. Applications include controlling vacuum fluctuations to create molecular alignment and broadband light sources, photonic catalysis, quantum memories in atomic vapours, and photonics in bulk diamond phonons. The links between these different applications are investigated.
Based on the idea of reverse engineering, we design an optimal laser pulse to control strong-field multiphoton atomic transitions. Starting from the time-dependent Schr\"odinger equation of the full system, we adiabatically eliminate the nonessential states and apply the rotating-wave approximation to arrive at an effective two-state representation that involves dynamic Stark shifts and multiphoton coupling. Solving this equation inversely for the field, we obtain an analytical laser pulse shape that is expected to induce the full system's evolution according to user-defined quantum pathways. In our procedure, the amplitude and phase of the laser pulse are engineered such that the dynamically shifted electronic states are resonantly coupled during the action of the pulse at each moment of time. As a result, the driven system evolves from an arbitrary initial population distribution to any desired final quantum state superposition at a predefined rate. The proposed scheme is demonstrated using the example of the $3s\ensuremath{\rightarrow}4s$ two-photon transition of atomic sodium. By solving the time-dependent Schr\"odinger equation of the single-active electron with two different methods, either propagating time-dependent coefficients of many field-free states or directly propagating the three-dimensional electronic wave packet on a grid, we demonstrate the robustness as well as the limitations of the presented reverse engineering scheme.
The four-wave mixing produced with two ultrashort phase-locked !-3! laser pulses propagating coherently in a two-level system in the infrared spectral region is shown to depend on the pulses relative phase. The Maxwell-Bloch equations are solved beyond the rotating-wave approximation to account for field frequencies which are largely detuned from the atomic resonance. The relative phase dominating the efficiency of the coupling to the 5! anti-Stokes Raman component is determined by sign of the total ac Stark shift induced in the system, in such a way that the phase influence disappears precisely where the ac Stark effect due to both pulses is compensated. This fundamental quantum interference effect can be the basis for nonlinear ultrafast optical spectroscopy techniques. Phenomena arising from the coherent control of nonlinear interactions are of importance in fields as diverse as optoelectronics and materials research, in high harmonic generation, in photoionization or molecular dissociation, and in biological applications such as spectroscopy and imaging, among others [1, 2, 3, 4, 5, 6, 7]. Optical quantum coherent control is based on the fact that the phases of interfering transition amplitudes in light-matter interactions can be controlled through the optical phase of coherent light sources that drive the interaction, in such a way that the transition rates to final states and the dynamics at various stages of the process can be modified [1]. In a recent paper [8], a theoretical investigation on the quantum coherent control of the optical transient four-wave mixing of two intense phase-locked femtosecond laser pulses of central angular frequencies ω and 3ω propagating in a two-level atom (TLA) was reported. It was shown how the nonlinear (χ (3) ) coupling to the antiStokes Raman field at frequency 5ω depends critically on the initial relative phase φ of the propagating pulses. In Ref. [8], the study was centered to intense pulses in the visible and ultraviolet spectral regions, with frequencies at resonance or lower than the atomic transition. The phenomena observed in [8], however, can be scaled to various laser and material parameters. In the infrared spectral range, for instance, experiments on ultrafast molecular dynamics are frequently performed by help of twocolor pump probe nonlinear spectroscopy techniques. In this type of studies, due to the high intensities inherent to ultrashort (subpicosecond) pulses, nonlinear effects such as stimulated Raman processes may become important and are often utilized as a complementary tool to gain information [9]. In this Letter, we address the conditions for quantum coherent control of transient four-wave mixing interactions with two phase-locked ω-3ω femtosecond laser pulses in the mid-IR spectral region. Our purpose is to reveal the basic physics for a strict two-level medium and to this end the Maxwell-Bloch TLA will be considered. We will study pulses with a duration of 300 fs (with a w 5w
Wave-mechanical phenomena such as resonance and interference, in both light and matter, are central to the principles of quantum coherent control over molecular processes. Focusing on the dynamical aspects, this dissertation is a compilation of studies on the interaction physics involving wave packets in molecules, the driving light field, and the underlying coherence and control. In each work, we will demonstrate interesting correlations between the properties of a carefully designed excitation light field and desirable outcomes of the molecules quantum dynamics. We will analyze the dynamical effect of a Feshbach resonance in the adiabatic Raman photoassociation for ultracold diatomic molecule formation from ultracold atoms. A narrow resonance is shown to be able to increase the effective number of collisions, in an ultracold atomic gas, that are available for photoassociation. This results in an optimal resonance width much smaller than the atomic collision energy bandwidth, due to the balance between the effective collision rate and single-collision transfer probability. Next, we demonstrate the linear molecular response to high-intensity, broadband, shaped optical fields. We show that this originates from interferences based on intra-pulse Raman excitations, and thus response linearity is not unique to the first-order perturbative limit and can not be used to infer the strength of the field. In the last study, we simulate the stochastic vibrational wave packet and dissociation-flux dynamics in a molecule excited by light with temporal and spectral incoherent properties. Between this case and that using a coherent pulse with the same spectral profile, we compare the vibrational wave functions and the loss of electronic and vibrational coherence, and demonstrate the qualitative difference between coherently and incoherently driven dynamics in molecules.