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Journal of Chemical Physics / Volume 129 / Issue 19 / ARTICLES / Theoretical Methods and Algorithms
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J. Chem. Phys. 129, 194103 (2008); doi:10.1063/1.3010369 (9 pages)

Optimal alignment control of a nonpolar molecule through nonresonant multiphoton transitions

Kazuyuki Nakagami1, Yoshihiko Mizumoto1,2, and Yukiyoshi Ohtsuki1,2

1Department of Chemistry, Graduate School of Science, Tohoku University, Sendai 980-8578, Japan
2CREST, Japan Science and Technology Agency, 4-1-8 Honcho, Kawaguchi, Saitama 332-0012, Japan

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(Received 28 August 2008; accepted 10 October 2008; published online 17 November 2008)

Alignment control of an ensemble of nonpolar molecules is numerically studied by means of optimal control simulation. A nitrogen molecule that is modeled by a quantum rigid rotor is adopted. Controlled rotational wave packets are created through nonresonant optical transitions induced by polarizability coupling. Optimal pulses are designed to achieve the alignment control at a specified time in the absence/presence of external static fields in zero- and finite-temperature cases, as well as to maintain an aligned state. When maintaining an aligned state over a specified time interval is chosen as a target, the control mechanism is primarily attributed to a dynamical one. Multiple optimal solutions that lead to virtually the same control achievement are found, which are consistent with the topology of the quantum control landscape.

© 2008 American Institute of Physics

Article Outline

  1. INTRODUCTION
  2. OPTIMAL CONTROL SIMULATION
  3. RESULTS AND DISCUSSION
    1. Alignment control at a specified final time
    2. Maintaining alignment over a specified time interval
    3. Alignment control in the presence of a static electric field
  4. SUMMARY

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KEYWORDS and PACS

Keywords

molecule-photon collisions, multiphoton processes, nitrogen, optimal control, polarisability, rotational states, topology

PACS

  • 33.80.Wz

    Other multiphoton processes

  • 31.15.-p

    Calculations and mathematical techniques in atomic and molecular physics

  • 33.15.Mt

    Rotation, vibration, and vibration-rotation constants

  • 33.15.Kr

    Electric and magnetic moments (and derivatives), polarizability, and magnetic susceptibility

  • 33.15.Bh

    General molecular conformation and symmetry; stereochemistry

ARTICLE DATA

Permalink
http://link.aip.org/link/doi/10.1063/1.3010369

PUBLICATION DATA

ISSN:

0021-9606 (print)  
1089-7690 (online)

Publisher:

$abstract.society.value is a Member of CrossRef American Institute of Physics

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Figures (click on thumbnails to view enlargements)

FIG.1
(a) Optimal pulse, (b) target expectation value 〈cos2 θ〉(t), and (c) populations of rotational states as a function of time in the case of temperature T = 0 K. Time is measured in units of rotational period, Trot = h/2B (also see text). The control target is to maximize the degree of alignment at a specified final time, tf = 10Trot.

FIG.1 Download High Resolution Image (.zip file) | Export Figure to PowerPoint

FIG.2
Power spectrum of the optimal pulse in Fig. 1a. The intensity is normalized to its highest peak. The frequency is measured in units of rotational constant B. The inset shows the schematic illustration of optical transitions induced by the optimal pulse.

FIG.2 Download High Resolution Image (.zip file) | Export Figure to PowerPoint

FIG.3
(a) Optimal pulse, (b) target expectation value 〈cos2 θ〉(t), and (c) populations of rotational states as a function of time in the case of temperature T = 0 K. The control target is to maximize the degree of alignment at a specified final time, tf = 10Trot. The optimal pulse is obtained from a different initial trial field from that in Fig. 1.

FIG.3 Download High Resolution Image (.zip file) | Export Figure to PowerPoint

FIG.4
Power spectrum of the optimal pulse in Fig. 3a. The intensity is normalized to its highest peak. The frequency is measured in units of rotational constant B. The inset shows the schematic illustration of optical transitions induced by the optimal pulse.

FIG.4 Download High Resolution Image (.zip file) | Export Figure to PowerPoint

FIG.5
(a) Optimal pulse and (b) target expectation value 〈cos2 θ〉(t) as a function of time in the case of temperature T = 2 K. The optimal pulse is obtained from the same initial trial field as that used in Fig. 3. The control target is to maximize the degree of alignment at a specified final time, tf = 10Trot. The time evolution of the population of each rotational state is shown in (c), (d), and (e), in which the initial conditions are ρJ = 0,M = 00 = 0.8530, ρJ = 1,M = 00 = 0.0487, and ρJ = 1,M = ±10 = 0.0487, respectively.

FIG.5 Download High Resolution Image (.zip file) | Export Figure to PowerPoint

FIG.6
(a) Optimal pulse, (b) target expectation value 〈cos2 θ〉(t), and (c) populations of rotational states as a function of time in the case of temperature T = 0 K. The control target is to maintain the maximal degree of alignment over a specified time interval, t ∊ [2.5Trot,7.5Trot] (also see text).

FIG.6 Download High Resolution Image (.zip file) | Export Figure to PowerPoint

FIG.7
Power spectrum of the optimal pulse in Fig. 6a. The intensity is normalized to its highest peak. The frequency is measured in units of rotational constant B. The inset shows the schematic illustration of optical transitions induced by the optimal pulse.

FIG.7 Download High Resolution Image (.zip file) | Export Figure to PowerPoint

FIG.8
(a) Optimal pulse, (b) target expectation value 〈cos2 θ〉(t), and (c) populations of rotational states as a function of time in the case of temperature T = 0 K. The control target is to maximize the degree of alignment at a specified final time, tf = 10Trot, in the presence of a given static field, Eref = 1.69×10−3 a.u.

FIG.8 Download High Resolution Image (.zip file) | Export Figure to PowerPoint

FIG.9
Power spectrum of the optimal pulse in Fig. 8a. The intensity is normalized to its highest peak. The frequency is measured in units of rotational constant B. The inset shows the schematic illustration of optical transitions induced by the optimal pulse.

FIG.9 Download High Resolution Image (.zip file) | Export Figure to PowerPoint



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