# Fast-kick-off monotonically convergent algorithm for searching optimal control fields

## Abstract

This Rapid Communication presents a fast-kick-off search algorithm for quickly finding optimal control fields in the state-to-state transition probability control problems, especially those with poorly chosen initial control fields. The algorithm is based on a recently formulated monotonically convergent scheme [T.-S. Ho and H. Rabitz, Phys. Rev. E 82, 026703 (2010)]. Specifically, the local temporal refinement of the control field at each iteration is weighted by a fractional inverse power of the instantaneous overlap of the backward-propagating wave function, associated with the target state and the control field from the previous iteration, and the forward-propagating wave function, associated with the initial state and the concurrently refining control field. Extensive numerical simulations for controls of vibrational transitions and ultrafast electron tunneling show that the new algorithm not only greatly improves the search efficiency but also is able to attain good monotonic convergence quality when further frequency constraints are required. The algorithm is particularly effective when the corresponding control dynamics involves a large number of energy levels or ultrashort control pulses.

- Authors:

- Center for Quantum Science and Engineering and Department of Physics, National Taiwan University, Taipei 10617, Taiwan (China)
- Department of Chemistry, Princeton University, Princeton, New Jersey 08544 (United States)
- (United States)

- Publication Date:

- OSTI Identifier:
- 22068612

- Resource Type:
- Journal Article

- Journal Name:
- Physical Review. A

- Additional Journal Information:
- Journal Volume: 84; Journal Issue: 3; Other Information: (c) 2011 American Institute of Physics; Country of input: Syrian Arab Republic; Journal ID: ISSN 1050-2947

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ALGORITHMS; COMPUTERIZED SIMULATION; CONVERGENCE; EFFICIENCY; ELECTRONS; ENERGY LEVELS; OPTIMAL CONTROL; PROBABILITY; PULSES; TUNNEL EFFECT; WAVE FUNCTIONS

### Citation Formats

```
Liao, Sheng-Lun, Ho, Tak-San, Rabitz, Herschel, Chu, Shih-I, and Department of Chemistry, University of Kansas, Lawrence, Kansas 66045.
```*Fast-kick-off monotonically convergent algorithm for searching optimal control fields*. United States: N. p., 2011.
Web. doi:10.1103/PHYSREVA.84.031401.

```
Liao, Sheng-Lun, Ho, Tak-San, Rabitz, Herschel, Chu, Shih-I, & Department of Chemistry, University of Kansas, Lawrence, Kansas 66045.
```*Fast-kick-off monotonically convergent algorithm for searching optimal control fields*. United States. doi:10.1103/PHYSREVA.84.031401.

```
Liao, Sheng-Lun, Ho, Tak-San, Rabitz, Herschel, Chu, Shih-I, and Department of Chemistry, University of Kansas, Lawrence, Kansas 66045. Thu .
"Fast-kick-off monotonically convergent algorithm for searching optimal control fields". United States. doi:10.1103/PHYSREVA.84.031401.
```

```
@article{osti_22068612,
```

title = {Fast-kick-off monotonically convergent algorithm for searching optimal control fields},

author = {Liao, Sheng-Lun and Ho, Tak-San and Rabitz, Herschel and Chu, Shih-I and Department of Chemistry, University of Kansas, Lawrence, Kansas 66045},

abstractNote = {This Rapid Communication presents a fast-kick-off search algorithm for quickly finding optimal control fields in the state-to-state transition probability control problems, especially those with poorly chosen initial control fields. The algorithm is based on a recently formulated monotonically convergent scheme [T.-S. Ho and H. Rabitz, Phys. Rev. E 82, 026703 (2010)]. Specifically, the local temporal refinement of the control field at each iteration is weighted by a fractional inverse power of the instantaneous overlap of the backward-propagating wave function, associated with the target state and the control field from the previous iteration, and the forward-propagating wave function, associated with the initial state and the concurrently refining control field. Extensive numerical simulations for controls of vibrational transitions and ultrafast electron tunneling show that the new algorithm not only greatly improves the search efficiency but also is able to attain good monotonic convergence quality when further frequency constraints are required. The algorithm is particularly effective when the corresponding control dynamics involves a large number of energy levels or ultrashort control pulses.},

doi = {10.1103/PHYSREVA.84.031401},

journal = {Physical Review. A},

issn = {1050-2947},

number = 3,

volume = 84,

place = {United States},

year = {2011},

month = {9}

}