Demos.OptMorseOscillator.AMO
Optimal control of bond length in a Morse oscillator (using Gaussian AMO)
In their seminal work on a rapid monotonically convergent iteration algorithm for quantum optimal control over the expectation value of a positive definite operator, Zhu and Rabitz presented an efficient approach to optimal control in quantum dynamics. Here we repeat some of their calculations where a Gaussian function (additional multiplicative operator, aka AMO) is used as a model for the optimal control of a bond length.
Results of optimization (in state space)
Here we are showing only the first 30 iteration steps, during which the target functional increases. Also the cost functional (laser fluence) increases, but still the total functional is monotonically growing, as required by theory.
However, it is not quite clear why the increase begins only after 20 steps.
Note also that beyond 32 or 33 iteration steps, the calculation suddenly becomes unstable, with very strong spikes occurring in the control field. Hence, we had to stop the calculation even though the functionals apparently have not reached saturation yet.
| 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 | |
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View the resulting dynamics (in coordinate space)
Now we use the result for the time dependence of the optimized control field and use it for a propagation in coordinate space. The results show that at final time (T=3.17ps) the resultig wavefunction indeed looks (more or less) like a Gaussian packet. Its center, however, is not found at R=2.5 which would have been the control target, but rather at 2.34 only. Perhaps because the optimization is not fully converged yet ?!?
