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Physical Review A

Temporal analysis of nonresonant two-photon coherent control involving bound and dissociative molecular states

Jing Su, Shaohao Chen, Agnieszka Jaroń-Becker, Andreas Becker

Published Dec 8, 2011• 0 citations
Publisher

Abstract

We theoretically study the control of two-photon excitation to bound and dissociative states in a molecule induced by trains of laser pulses, which are equivalent to certain sets of spectral phase modulated pulses. To this end, we solve the time-dependent Schr\"odinger equation for the interaction of molecular model systems with an external intense laser field. Our numerical results for the temporal evolution of the population in the excited states show that, in the case of an excited dissociative state, control schemes, previously validated for the atomic case, fail due to the coupling of electronic and nuclear motion. In contrast, for excitation to bound states the two-photon excitation probability is controlled via the time delay and the carrier-envelope phase difference between two consecutive pulses in the train.

DOI
10.1103/physreva.84.065402

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We theoretically study the control of two-photon excitation to bound and dissociative states in a molecule induced by trains of laser pulses, which are equivalent to certain sets of spectral phase modulated pulses. To this end, we solve the time-dependent Schr"odinger equation for the interaction of molecular model systems with an external intense laser field. Our numerical results for the temporal evolution of the population in the excited states show that, in the case of an excited dissociative state, control schemes, previously validated for the atomic case, fail due to the coupling of electronic and nuclear motion. In contrast, for excitation to bound states the two-photon excitation probability is controlled via the time delay and the carrier-envelope phase difference between two consecutive pulses in the train.
We investigate the coherent control of nonresonant two-photon excitation and (2+12+12+1) photon ionization processes from the time-dependent perspective. To this end, we have solved the time-dependent Schr\"odinger equation for a hydrogen atom interacting with an ultraviolet laser field. Results are obtained for symmetric and antisymmetric phase distributions leading to dark and bright pulses, for which the temporal field distributions consist of many subpulses. For the two-photon excitation process, it is found that at intermediate time between the subpulses, the population in the excited state can exceed the final state population and, in particular, is nonzero for dark pulses. The results for the (2+12+12+1) photon ionization closely follow those for the excitation process, which shows that the ionization of the electron proceeds as a resonant process via the excited state in all cases considered.
A coherent control scheme for the population distribution in the vibrational states of nonpolar molecules is proposed. Our theoretical analysis and results of numerical simulations for the interaction of the hydrogen molecular ion in its electronic ground state with an infrared laser pulse reveal a selective two-photon transition between the vibrational states via a coupling with the first excited dissociative state. We demonstrate that for a given temporal intensity profile the population transfer between vibrational states, or a superposition of vibrational states, can be made complete for a single chirped pulse or a train of chirped pulses, which accounts for the accumulated phase difference due to the ac Stark effect. Effects of a spatial intensity (or focal) averaging are discussed.
In this paper, we theoretically investigate the control of the non-resonant two-photon absorption induced by two time-delayed laser pulses, and an analytical solution for the dependence of the two-photon transition probability on the time delay and relative carrier-envelope phase of the two laser pulses is achieved. We show that the two-photon absorption can be significantly enhanced or completely suppressed by varying the time delay between the two laser pulses or their relative carrier-envelope phase. We also show that the two-photon absorption can be selectively excited when two excited states are simultaneously excited. Furthermore, we discuss the two-photon absorption control in the molecular system and analyze the effect of the absorption bandwidth on the control efficiency of the two-photon absorption.
Temporal phase control over the multi-photoionization of NO is investigated experimentally. The coherent excitation of the molecular system is achieved by a sequence of two phase-related non-Fourier-transform-limited laser pulses delivered by a nanosecond dye laser. The phase-locked pulses are produced by making use of an actively stabilized interferometer with a tunable path-length difference. As the coherence time of the laser is comparable with the inhomogenous dephasing time of the medium, the measurements are performed with temporally overlapped pulses. In order to avoid the modulation of the ionic signal coming from optical interference, the linear polarizations of the two pulses are crossed. The quantum modulation of the signal versus the time delay between the two pulses is observed for the three following distinct processes: (a) two-photon resonant four-photon ionization of the ground vibronic state; (b) two-photon absorption of the A-X transition followed by ionization; and (c) two-photon ionization of the electronically excited state A. As a result, temporal phase control over bound-bound and bound-free transitions is demonstrated. The efficiency of the control process is shown to be limited by the presence of uncoupled excitation channels inherent to the method employed. The advantage in using a sequence of cross-polarized pulses for the controlling processes is discussed.
We present an analytic scheme for designing laser pulses to manipulate the field-free molecular alignment of a homonuclear diatomic molecule. The scheme is based on the use of a generalized pulse-area theorem and makes use of pulses constructed around two-photon resonant frequencies. In the proposed scheme, the populations and relative phases of the rovibrational states of the molecule are independently controlled utilizing changes in the laser intensity and in the carrier-envelope phase difference, respectively. This allows us to create the correct coherent superposition of rovibrational states needed to achieve optimal molecular alignment. The validity and efficiency of the scheme are demonstrated by explicit application to the H(2) molecule. The analytically designed laser pulses are tested by exact numerical solutions of the time-dependent Schrodinger equation including laser-molecule interactions to all orders of the field strength. The design of a sequence of pulses to further enhance molecular alignment is also discussed and tested. It is found that the rotating wave approximation used in the analytic design of the laser pulses leads to small errors in the prediction of the relative phase of the rotational states. It is further shown how these errors may be easily corrected.
We present and experimentally demonstrate for the first time the observation and femtosecond coherent control over the temporal evolution of a transient population that is excited via nonresonant two-photon absorption. Based on symmetry properties of the two-photon absorption process, the exciting femtosecond pulses are phase-shaped to photoinduce different evolutions of the transient excited population for a given final excited population. As a study case, we focus here on the attractive case of two-photon dark pulses that, although inducing zero final population (hence, the terminology of "dark pulses"), they induce a transient excited population during the pulse irradiation that can significantly deviate from zero. This nonzero transient population can be viewed as the bright side of such dark pulses. The symmetry-based coherent control is demonstrated first with dark pulses that we shape to induce transient excited population that at all times is kept below different target levels. Then, it is further demonstrated with pairs of dark pulses where one is rationally shaped to induce temporal evolution of the transient excited population that is the inverse of the evolution induced by the other. The work is conducted in the weak-field regime with the sodium atom as the model system. The approach developed here is general, conceptually simple, and very effective.