### Abstract

For most isolated molecules, the generation of a π-pulse which will create complete inversion of the population of two electronic states is impossible because the rotational contribution to the transition dipole moment is an explicit function of the projection of the total angular momentum along the electric field axis. It is, however, possible to obtain nearly complete inversion by use of phase- and amplitude-modulated pulses; we show examples of such inversion with scaled and swept hyperbolic secant pulses. We report the results of pulse shape calculations for model systems with one and eight transition dipole moments. The pulse shaping is based on optimal control theory, where both the time-dependent Schrödinger equation and the pulse energy are used as constraints and where the deviation of the pulse shape from a swept hyperbolic secant form is treated as a cost to be minimized. This use of a time-dependent penalty function is intended to bias the calculated optimal pulse shape in the direction of experimentally producible pulse shapes. The method is applied to a model system with two displaced potential energy surfaces which support harmonic vibrational motion.

Original language | English |
---|---|

Pages (from-to) | 6175-6183 |

Number of pages | 9 |

Journal | Journal of Physical Chemistry |

Volume | 97 |

Issue number | 23 |

Publication status | Published - 1993 |

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### ASJC Scopus subject areas

- Physical and Theoretical Chemistry

### Cite this

*Journal of Physical Chemistry*,

*97*(23), 6175-6183.

**Population inversion in a multilevel system : A model study.** / Amstrup, Bjarne; Lörincz, András; Rice, Stuart A.

Research output: Contribution to journal › Article

*Journal of Physical Chemistry*, vol. 97, no. 23, pp. 6175-6183.

}

TY - JOUR

T1 - Population inversion in a multilevel system

T2 - A model study

AU - Amstrup, Bjarne

AU - Lörincz, András

AU - Rice, Stuart A.

PY - 1993

Y1 - 1993

N2 - For most isolated molecules, the generation of a π-pulse which will create complete inversion of the population of two electronic states is impossible because the rotational contribution to the transition dipole moment is an explicit function of the projection of the total angular momentum along the electric field axis. It is, however, possible to obtain nearly complete inversion by use of phase- and amplitude-modulated pulses; we show examples of such inversion with scaled and swept hyperbolic secant pulses. We report the results of pulse shape calculations for model systems with one and eight transition dipole moments. The pulse shaping is based on optimal control theory, where both the time-dependent Schrödinger equation and the pulse energy are used as constraints and where the deviation of the pulse shape from a swept hyperbolic secant form is treated as a cost to be minimized. This use of a time-dependent penalty function is intended to bias the calculated optimal pulse shape in the direction of experimentally producible pulse shapes. The method is applied to a model system with two displaced potential energy surfaces which support harmonic vibrational motion.

AB - For most isolated molecules, the generation of a π-pulse which will create complete inversion of the population of two electronic states is impossible because the rotational contribution to the transition dipole moment is an explicit function of the projection of the total angular momentum along the electric field axis. It is, however, possible to obtain nearly complete inversion by use of phase- and amplitude-modulated pulses; we show examples of such inversion with scaled and swept hyperbolic secant pulses. We report the results of pulse shape calculations for model systems with one and eight transition dipole moments. The pulse shaping is based on optimal control theory, where both the time-dependent Schrödinger equation and the pulse energy are used as constraints and where the deviation of the pulse shape from a swept hyperbolic secant form is treated as a cost to be minimized. This use of a time-dependent penalty function is intended to bias the calculated optimal pulse shape in the direction of experimentally producible pulse shapes. The method is applied to a model system with two displaced potential energy surfaces which support harmonic vibrational motion.

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M3 - Article

AN - SCOPUS:0343471581

VL - 97

SP - 6175

EP - 6183

JO - Journal of Physical Chemistry

JF - Journal of Physical Chemistry

SN - 0022-3654

IS - 23

ER -