This paper discusses different routes to gaining insight from closed loop learning control experiments. We focus on the role of the basis in which pulse shapes are encoded and the algorithmic search is performed. We demonstrate that a physically motivated, nonlinear basis change can reduce the dimensionality of the phase space to one or two degrees of freedom. The dependence of the control goal on the most important degrees of freedom can then be mapped out in detail, leading toward a better understanding of the control mechanism. We discuss simulations and experiments in selective molecular fragmentation using shaped ultrafast laser pulses.
Topics
Ultrafast lasers
REFERENCES
1.
2.
N. E.
Henriksen
, Chem. Soc. Rev.
31
, 37
(2002
), and references therein.3.
R. S.
Judson
and H.
Rabitz
, Phys. Rev. Lett.
68
, 1500
(1992
).4.
H. A.
Rabitz
, M. M.
Hsieh
, and C. M.
Rosenthal
, Science
303
, 1998
(2004
).5.
T.
Brixner
, N. H.
Damrauer
, G.
Krampert
, P.
Niklaus
, and G.
Gerber
, J. Opt. Soc. Am. B
20
, 878
(2003
).6.
M.
Dantus
and V. V.
Lozovoy
, Chem. Rev. (Washington, D.C.)
104
, 1813
(2004
).7.
C.
Daniel
, J.
Full
, L.
González
, C.
Lupulescu
, J.
Manz
, A.
Merli
, Š.
Vajda
, and L.
Wöste
, Science
299
, 536
(2003
).8.
R.
Bartels
, S.
Backus
, E.
Zeek
, L.
Misoguti
, G.
Vdovin
, I. P.
Christov
, M. M.
Murnane
, and H. C.
Kapteyn
, Nature (London)
406
, 164
(2000
).9.
B. J.
Pearson
and P. H.
Bucksbaum
, Phys. Rev. Lett.
92
, 243003
(2004
).10.
T.
Hornung
, R.
Meier
, and M.
Motzkus
, Chem. Phys. Lett.
326
, 445
(2000
).11.
J. M.
Geremia
and H.
Rabitz
, Phys. Rev. Lett.
89
, 263902
(2002
).12.
D.
Cardoza
, F.
Langhojer
, C.
Trallero
, O.
Monti
, and T. C.
Weinacht
, Phys. Rev. A
70
, 053406
(2004
).13.
J. L. White, B. J. Pearson, and P. H. Bucksbaum (unpublished).
14.
D. Cardoza, C. Trallero, F. Langhojer, H. Rabitz, and T. C. Weinacht (unpublished).
15.
S.
Backus
, C. G.
Durfee
, M. M.
Murnane
, and H. C.
Kapteyn
, Rev. Sci. Instrum.
69
, 1207
(1998
).16.
M. A.
Dugan
, J. X.
Tull
, and W. S.
Warren
, J. Opt. Soc. Am. B
14
, 2348
(1997
).17.
D.
Zeidler
, S.
Frey
, K. L.
Kompa
, and M.
Motzkus
, Phys. Rev. A
64
, 023420
(2001
).18.
B. J.
Pearson
, J. L.
White
, T. C.
Weinacht
, and P. H.
Bucksbaum
, Phys. Rev. A
63
, 063412
(2001
).19.
L. Davis, Handbook of Genetic Algorithms (Van Nostrand Reinhold, New York, 1991).
20.
J. M.
Geremia
, W.
Zhu
, and H.
Rabitz
, J. Chem. Phys.
113
, 10841
(2000
).21.
T. C.
Weinacht
, R.
Bartels
, S.
Backus
et al., Chem. Phys. Lett.
344
, 333
(2001
).22.
J. M.
Geremia
, E.
Weiss
, and H.
Rabitz
, Chem. Phys.
267
, 209
(2001
).23.
If the fitness can be separated in terms of a sum, i.e., the Hessian matrix of the fitness function is diagonal. If, however, the fitness function is separable in terms of a product, i.e., the Hessian matrix of the logarithm of the fitness function is diagonal.
24.
25.
S. A.
Malinovskaya
, P. H.
Bucksbaum
, and P. R.
Berman
, Phys. Rev. A
69
, 013801
(2004
).26.
R.
Trebino
, K. W.
DeLong
, D. N.
Fittinghoff
, J. N.
Sweetser
, M. A.
Krumbugel
, B. A.
Richman
, and D. J.
Kane
, Rev. Sci. Instrum.
68
, 3277
(1997
).27.
T.
Takayanagi
and A.
Yokoyama
, Bull. Chem. Soc. Jpn.
68
, 2225
(1995
).28.
D. G.
Abrashkevich
, M.
Shapiro
, and P.
Brumer
, J. Chem. Phys.
116
, 5584
(2002
).29.
L. J.
Butler
, E. J.
Hintsa
, S. F.
Shane
, and Y. T.
Lee
, J. Chem. Phys.
86
, 2051
(1987
).30.
N. H.
Damrauer
, C.
Dietl
, G.
Krampert
, S. H.
Lee
, K. H.
Jung
, and G.
Gerber
, Eur. Phys. J. D
20
, 71
(2002
).31.
32.
Note that the peak widths in the filter diagonalization are artificially narrow and do not reflect the strong damping on the modulations.
33.
S. M.
Hankin
, D. M.
Villeneuve
, P. B.
Corkum
, and D. M.
Rayner
, Phys. Rev. Lett.
84
, 5082
(2000
).34.
M. W.
Schmidt
, K. K.
Baldridge
, J. A.
Boatz
et al., J. Comput. Chem.
14
, 1347
(1993
).35.
S.
Anand
, M. M.
Zamari
, G.
Menkir
, R. J.
Levis
, and H. B.
Schlegel
, J. Phys. Chem. A
108
, 3162
(2004
).36.
X. P.
Tang
, S. F.
Wang
, M. E.
Elshakre
, L. R.
Gao
, Y. L
Wang
, H. F.
Wang
, and F. A.
Kong
, J. Phys. Chem. A
107
, 13
(2003
).37.
R.
Itakura
, K.
Yamanouchi
, T.
Tanabe
, T.
Okamoto
, and F.
Kannari
, J. Chem. Phys.
119
, 4179
(2003
).
This content is only available via PDF.
© 2005 American Institute of Physics.
2005
American Institute of Physics
You do not currently have access to this content.
