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The Journal of Chemical Physics

Optical control of the singlet-triplet transition in Rb2

Jesús González‐Vázquez, Ignacio R. Solá, Jesús Santamarı́a, Vladimir S. Malinovsky

Published Sep 28, 2006• 26 citations
Publisher

Abstract

By controlling nonresonant dynamic Stark shifts it is possible to effectively decouple the intramolecular couplings of simple molecules. We have illustrated this effect in the 1 (1)Sigma(u)-->1 (3)Pi(u) transition in Rb(2). The laser scheme implies two important control knobs: the laser frequency, which must be chosen to avoid both single and multiphoton resonances and to select different electronic environments for the singlet and triplet states, and the pulse intensity, which must amplify the asymmetry in the dynamic polarizabilities that allows the decoupling, avoiding undesired strong-pulse effects. The mechanism of the scheme implies not only brute-force energy shifts but also light-induced reshaping of the potentials to avoid the undesired crossings. Quantitative aspects of the method are analyzed by using molecular models of increasing complexity for Rb(2).

DOI
10.1063/1.2355492

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APS•May 1, 2003•0 citations
By controlling nonresonant dynamic Stark shifts it is possible to effectively decouple the intramolecular couplings of simple molecules. We have illustrated this effect in the 1 (1)Sigma(u)-->1 (3)Pi(u) transition in Rb(2). The laser scheme implies two important control knobs: the laser frequency, which must be chosen to avoid both single and multiphoton resonances and to select different electronic environments for the singlet and triplet states, and the pulse intensity, which must amplify the asymmetry in the dynamic polarizabilities that allows the decoupling, avoiding undesired strong-pulse effects. The mechanism of the scheme implies not only brute-force energy shifts but also light-induced reshaping of the potentials to avoid the undesired crossings. Quantitative aspects of the method are analyzed by using molecular models of increasing complexity for Rb(2).
The energy levels of atoms and molecules exposed to intense, short, high-frequency laser pulses undergo time-dependent distortion known as dynamic Stark shift (DSS). These level shifts are induced by the coupling with nonresonant (nonessential) states and follow the temporal intensity profile of the laser pulse. Owing to the different DSSs of the individual atomic levels, transient resonance suppressions and enhancements significantly modify the multiphoton ionization pathway, leaving clear fingerprints (asymmetry, splitting, and shifting) in the energy spectrum of emitted photoelectrons. Here we investigate this phenomenon by solving the time-dependent Schr\"odinger equation of the valence electron of Na and Li in increasing levels of complexity: (i) developing minimal models for two-photon transition and (2+12+12+1)-photon ionization, (ii) applying a spectral method without continuum-continuum couplings, and (iii) propagating the electron wave packet on a large spatial grid accounting for all possible couplings. We show that appropriately detuned transform limited pulses provide a high level of control in strong-field excitation, when the atomic levels are dynamically shifted. Furthermore, we demonstrate the role of DSSs in the multipeak structure of the Autler-Townes doublet, found when several Rabi oscillations are induced during the strong-field resonant ionization.
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.
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 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.
We analyze the optically driven dynamics of a qubit implemented on a singlet-triplet subspace of two-electron states in a self-assembled quantum dot molecule. We study two possible control schemes based on the coupling to an excited (four-particle) state either by two spectrally separated laser pulses or by a single spectrally broad pulse. We quantitatively characterize the imperfections of the qubit operation resulting from nonadiabatic evolution and from limited spectral selectivity in a real system, as compared to the ideal adiabatic Raman transfer of occupation in the $\mathrm{\ensuremath{\Lambda}}$ system. Next, we study the effects of decoherence induced by the coupling to the phonons of the surrounding crystal lattice and by radiative recombination. As a result, we are able to identify the optimization trade-offs between different sources of errors and indicate the most favorable conditions for quantum control of the singlet-triplet qubit in the two optical control schemes.
A method to optically control a dark transition, for instance, the coupling between different spin states, is proposed. The control is achieved by manipulating the direction, amplitude, and duration of dynamic Stark shifts. Laser-driven spin switches can be prepared by conveniently generalizing different optical techniques, such as $\ensuremath{\pi}$-pulse schemes and adiabatic passage schemes. The efficiency and robustness of the schemes is analyzed for both two-level and multilevel systems, implying quantum state selective wave packet transfer between states of different multiplicity.
Compared to single-photon rates, multiphoton excitation rates of atoms and molecules are generally quite small, even at high laser intensities, at least in a 2-level system. Small multiphoton coupling strengths, large ac Stark shifts, and ionization all inhibit real population transfer between bound states. However, it has recently been shown that a 3-level system consisting of a ground state and a pair of nearly degenerate strongly coupled upper states greatly enhances the multiphoton coupling with the ground state, while also greatly reducing the ac Stark shift of the ground state. In this paper I will derive an analytic expression for the n-photon Rabi frequency, for this system, in the case of degenerate upper states, as well as an expression for the level shifts induced in the case of nondegenerate upper states. Numerical calculations based on the 3-level system are presented to verify the analytic results and to show that high-order {pi} pulses can be driven at moderate field strengths. To demonstrate the feasibility of this process in a real physical system, I will present fully correlated 2-electron calculations in a model one-dimensional molecular potential, including ionization that show a 12-photon {pi} pulse driven with near-infrared photons. In other words, amore » single excited state 18.6 eV above the ground state can be populated with over 90% efficiency with little ionization while the ground state is almost completely depopulated. Besides the possibility of producing an amplifying medium in the vacuum ultraviolet, this 3-level configuration may open the door to other strong field effects previously restricted to single-photon interactions, such as adiabatic passage and inner-shell ionization.« less