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Soley MB, Markmann A, Batista VS. Classical Optimal Control for Energy Minimization Based On Diffeomorphic Modulation under Observable-Response-Preserving Homotopy. J Chem Theory Comput 2018; 14:3351-3362. [DOI: 10.1021/acs.jctc.8b00124] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Micheline B. Soley
- Department of Chemistry, Yale University, P.O.
Box 208107, New Haven, Connecticut 06520-8107, United States
- Energy Sciences Institute, Yale University, P.O.
Box 27394, West Haven, Connecticut 06516-7394, United States
| | - Andreas Markmann
- Department of Chemistry, Yale University, P.O.
Box 208107, New Haven, Connecticut 06520-8107, United States
- Energy Sciences Institute, Yale University, P.O.
Box 27394, West Haven, Connecticut 06516-7394, United States
| | - Victor S. Batista
- Department of Chemistry, Yale University, P.O.
Box 208107, New Haven, Connecticut 06520-8107, United States
- Energy Sciences Institute, Yale University, P.O.
Box 27394, West Haven, Connecticut 06516-7394, United States
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Chenel A, Meier C, Dive G, Desouter-Lecomte M. Optimal control of a Cope rearrangement by coupling the reaction path to a dissipative bath or a second active mode. J Chem Phys 2015; 142:024307. [DOI: 10.1063/1.4905200] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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Moore Tibbetts K, Rabitz H. Constrained control landscape for population transfer in a two-level system. Phys Chem Chem Phys 2015; 17:3164-78. [DOI: 10.1039/c4cp04792c] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Controlling population transfer in a two-level quantum system reveals a landscape with a rich structure containing highly connected optimal regions.
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Abstract
The broad success of optimally controlling quantum systems with external fields has been attributed to the favorable topology of the underlying control landscape, where the landscape is the physical observable as a function of the controls. The control landscape can be shown to contain no suboptimal trapping extrema upon satisfaction of reasonable physical assumptions, but this topological analysis does not hold when significant constraints are placed on the control resources. This work employs simulations to explore the topology and features of the control landscape for pure-state population transfer with a constrained class of control fields. The fields are parameterized in terms of a set of uniformly spaced spectral frequencies, with the associated phases acting as the controls. This restricted family of fields provides a simple illustration for assessing the impact of constraints upon seeking optimal control. Optimization results reveal that the minimum number of phase controls necessary to assure a high yield in the target state has a special dependence on the number of accessible energy levels in the quantum system, revealed from an analysis of the first- and second-order variation of the yield with respect to the controls. When an insufficient number of controls and/or a weak control fluence are employed, trapping extrema and saddle points are observed on the landscape. When the control resources are sufficiently flexible, solutions producing the globally maximal yield are found to form connected "level sets" of continuously variable control fields that preserve the yield. These optimal yield level sets are found to shrink to isolated points on the top of the landscape as the control field fluence is decreased, and further reduction of the fluence turns these points into suboptimal trapping extrema on the landscape. Although constrained control fields can come in many forms beyond the cases explored here, the behavior found in this paper is illustrative of the impacts that constraints can introduce.
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Affiliation(s)
- Katharine W Moore
- Department of Chemistry, Princeton University, Princeton, New Jersey 08544, USA
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Chenel A, Dive G, Meier C, Desouter-Lecomte M. Control in a Dissipative Environment: The Example of a Cope Rearrangement. J Phys Chem A 2012; 116:11273-82. [DOI: 10.1021/jp305274y] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- A. Chenel
- Laboratoire de Chimie
Physique, Université Paris-Sud and CNRS, UMR 8000, F-91405
Orsay, France
| | - G. Dive
- Centre d’Ingénierie
des Protéines, Université de Liège, Sart Tilman, B6, B-4000 Liège, Belgium
| | - C. Meier
- LCAR-IRSAMC, Université Paul Sabatier, 31062 Toulouse, France
| | - M. Desouter-Lecomte
- Laboratoire de Chimie
Physique, Université Paris-Sud and CNRS, UMR 8000, F-91405
Orsay, France
- Département de Chimie, Université de Liège, Sart Tilman, B6,
B-4000 Liège, Belgium
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Laser control in open quantum systems: preliminary analysis toward the Cope rearrangement control in methyl-cyclopentadienylcarboxylate dimer. Theor Chem Acc 2012. [DOI: 10.1007/s00214-012-1236-5] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/28/2022]
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Kurosaki Y, Artamonov M, Ho TS, Rabitz H. Quantum optimal control of isomerization dynamics of a one-dimensional reaction-path model dominated by a competing dissociation channel. J Chem Phys 2009; 131:044306. [DOI: 10.1063/1.3185565] [Citation(s) in RCA: 25] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Igarashi A, Yamada H. Numerical study on dynamical behavior in oscillatory driven quantum double-well systems. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2008; 78:026213. [PMID: 18850927 DOI: 10.1103/physreve.78.026213] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/07/2007] [Revised: 05/07/2008] [Indexed: 05/26/2023]
Abstract
We numerically investigate quantum dynamics in a one-dimensional double-well system emphasizing influence of a parametrically polychromatic perturbation on the dynamics. It is found that time dependence of transition probability for an initially localized wave packet between the wells shows two types of motion, coherent and incoherent motion, depending on the perturbation parameters. As the strength and/or the number of frequency components of the perturbation increase, coherent motion changes into incoherent one. The former is related to coherent tunneling of the wave packet due to coherence; the latter is related to a delocalized state caused by decoherence. In coherent motion, by virtue of coherence of the dynamics, the expectation value and the standard deviation of a dynamical variable such as the energy of the system show oscillatory time dependence around the initial values. On the contrary in incoherent motion, because of the decoherence, the time dependence fluctuates irregularly around a certain value after a rapid increase due to the resonance. We find that negativity of the Wigner function also show similar time dependence in each type of motion. We compare the classification of the quantum dynamics based on regularity of the time dependence with the one of corresponding classical dynamics based on the Lyapunov exponent. The classifications of the quantum and classical dynamics overlap well in the parameter space. Furthermore, we confirm decoherence of quantum dynamics in a kicked double-well system.
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Affiliation(s)
- Akira Igarashi
- Graduate School of Science and Technology, Niigata University, Ikarashi 2-Nochou 8050, Niigata 950-2181, Japan.
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Moore K, Hsieh M, Rabitz H. On the relationship between quantum control landscape structure and optimization complexity. J Chem Phys 2008; 128:154117. [DOI: 10.1063/1.2907740] [Citation(s) in RCA: 39] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Dynamic simulation study on ultrafast excited-state torsional dynamics of 9,9′-bianthryl (BA) in gas phase: Real-time observation of novel oscillation behavior with the torsional coordinate. Chem Phys Lett 2008. [DOI: 10.1016/j.cplett.2008.01.015] [Citation(s) in RCA: 56] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/20/2022]
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de Vivie-Riedle R, Troppmann U. Femtosecond Lasers for Quantum Information Technology. Chem Rev 2007; 107:5082-100. [DOI: 10.1021/cr040094l] [Citation(s) in RCA: 77] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/15/2022]
Affiliation(s)
- Regina de Vivie-Riedle
- Department Chemie, Ludwig Maximilians Universität, Butenandtstrasse 11, 81377 München, Germany
| | - Ulrike Troppmann
- Department Chemie, Ludwig Maximilians Universität, Butenandtstrasse 11, 81377 München, Germany
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Zhao GJ, Han KL, Lei YB, Dou YS. Ultrafast excited-state dynamics of tetraphenylethylene studied by semiclassical simulation. J Chem Phys 2007; 127:094307. [PMID: 17824739 DOI: 10.1063/1.2768347] [Citation(s) in RCA: 88] [Impact Index Per Article: 5.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Detailed simulation study is reported for the excited-state dynamics of photoisomerization of cis-tetraphenylethylene (TPE) following excitation by a femtosecond laser pulse. The technique for this investigation is semiclassical dynamics simulation, which is described briefly in the paper. Upon photoexcitation by a femtosecond laser pulse, the stretching motion of the ethylenic bond of TPE is initially excited, leading to a significant lengthening of ethylenic bond in 300 fs. Twisting motion about the ethylenic bond is activated by the energy released from the relaxation of the stretching mode. The 90 degrees twisting about the ethylenic bond from an approximately planar geometry to nearly a perpendicular conformation in the electronically excited state is completed in 600 fs. The torsional dynamics of phenyl rings which is temporally lagging behind occurs at about 5 ps. Finally, the twisted TPE reverts to the initial conformation along the twisting coordinate through nonadiabatic transitions. The simulation results provide a basis for understanding several spectroscopic observations at molecular levels, including ultrafast dynamic Stokes shift, multicomponent fluorescence, viscosity dependence of the fluorescence lifetime, and radiationless decay from electronically excited state to the ground state along the isomerization coordinate.
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Affiliation(s)
- Guang-Jiu Zhao
- State Key Laboratory of Molecular Reaction Dynamics, Dalian Institute of Chemical Physics, Chinese Academy of Sciences, Dalian 116023, People's Republic of China
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