Demos.OptMorseOscillator.OVL

Optimal control of population dynamics in a Morse oscillator (using overlaps)

In their seminal work on a rapidly convergent iteration methods for quantum optimal control of population, Zhu, Botina, and Rabitz showed how to speed up optimal control simulations for the special case of populations which are described as square moduli of overlaps. Here we repeat some of their calculations for the v=0→1 transition of a Morse oscillator and extend them toward prescribed pulse shapes.

Note that - in general - the convergence of the target functional is much faster than for simulations where populations are calculated from overlaps.

Arbitrary pulse shape

Already after the first iteration, the target state population exceeds 99 %. This goes at the cost of a relatively high laser fluence which, however, is reduced substantially in the further course of the iteration.Nevertheless, the target state population stay well above 98%.

After 50 iteration steps, we arrive at a quasi-monochromatic pulse. Not too surpringly, its frequency is very close to the Bohr frequency ω₀₁=0.01724 whereas the amplitude is close the prediction from the Rabi-formula E₀=0.002957 for a pulse duration of 1 ps and for a transition dipole moment of μ₀₁=0.0257.

Time dependence	Iteration convergence	FROG spectra of u(t)
Control field u(t)	Target functional
State vector x(t)	Cost functional
Observables y(t)	Difference

• Animated iteration
• Input data file
• Run script
• Logfile output

Prescribed pulse shape

The pulse found in the above simulation cannot be realized in experiment because of the sudden switch-on and switch-off (rectangular envelope). In order to be more realistic, we modify the optimal control algorithm as suggested in work by Sundermann and de Vivie-Riedle: In this approach, optimization is not for arbitrary pulse shape but requiring that the envelope should have a special shape, for example sin² .

Again, we reach a population transfer of more than 99% already after the first iteration. However this is reduced down to about 95.7% when minimizing the laser fluence.

Time dependence	Iteration convergence	FROG spectra of u(t)

• Animated iteration
• Input data file
• Run script
• Logfile output