Optimal control of vibronic population inversion with inclusion of molecular rotation

Abstract

This paper considers vibronic population inversion in the presence of molecular rotation. The objective is to invert the population of a vibronic level with populated rotational levels to a specific vibrational level in the excited electronic state regardless of the detailed population distribution in the final rotational levels. The control of the multilevel population inversion is achieved by design of a pump pulse through optimal control theory. The total energy fluence and the pulse peak intensity are imposed as physical constraints in the design cost functional. A model diatomic molecule is used as an example to investigate molecular rotational effects on the vibronic population inversion and the control properties at different target times. The numerical results indicate that the shape-optimized pulses can achieve nearly complete population inversion and largely overcome the difficulty that a rectangular pulse faces due to energy mismatches and multiple dipole transition moments.

Quantum control of I2 in the gas phase and in condensed phase solid Kr matrix

“…Although the thermal averaging over the initial population of vibrational states contributes to the delocalization of the LIF signal, the disagreement between simulation and experiment remains substantial if rotation is omitted from the calculations. 10,11,75,76 In Fig. 6, we show the comparison of gas phase I 2 experimental measurements ͑solid line͒ with exact quantum simulations ͑dashed line͒ which now include rotation, for the same positive and negative chirped pair of pump pulses as in Fig.…”

“…In this figure, the theoretical results are in excellent agreement with the experimental measurements, confirming the importance of rotational motion in wavepacket dynamics. 10,11,75,76 More detailed analysis shows that there are two important rotational effects. The first is the decay of the anisotropic orientational distribution induced by the polarized pump pulse and then sampled by the polarized probe pulse.…”

“…18 Here we extend this work and show that a one dimensional molecular model considering only vibrational dynamics cannot reproduce the longer time behavior of the LIF signals, because rotations start to play an important role after ϳ1 picosecond at room temperature. 10,11,75,76 One rotational effect, the evolution of the angular distribution of the excited sample, can be eliminated from the LIF signal by aligning the polarization axes of pump and probe beams at the ''magic angle.'' 77 However, the second rotational effect, the rotational-vibrational coupling, also plays an important role, producing a dispersion in evolution for each set of wavepackets belonging to a single vibrational state but having different total angular momentum.…”

Molecular “πPulse” for Total Inversion of Electronic State Population

“…In atoms [8] and in some spin systems (nuclear magnetic resonance), where two level approximations are reasonable, complete population inversion by pulses of electromagnetic radiation, where the entire population of one state is transferred to another state, is a long-established technique. The parallel solution for the electronic population of molecules, with their multiple rovibrational states, has not previously been found, although several theoretical calculations have been made [9][10][11][12]. In this Letter, we demonstrate that such a solution does exist for molecular systems and can be understood with simple physical models.…”

Molecular π pulses: Population inversion with positively chirped short pulses

“…Theoretical aspects of population inversion have been explored earlier along different lines. [20][21][22][23] Making use of displaced harmonic oscillator potentials, Somloi, Lorincz, and Rice 20,21 obtained the resonance condition for pulses much shorter than the time scale of vibrational motion and found that in this limit the displaced harmonic oscillator system responds to intense laser pulses as a two-level system. For relatively longer pulses, the concept of a pulse is not well defined and optimal control theory becomes the method of choice for maximizing population inversion.…”