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Tomsovic S, Urbina JD, Richter K. Controlling quantum chaos: Time-dependent kicked rotor. Phys Rev E 2023; 108:044202. [PMID: 37978592 DOI: 10.1103/physreve.108.044202] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/24/2023] [Accepted: 09/08/2023] [Indexed: 11/19/2023]
Abstract
One major objective of controlling classical chaotic dynamical systems is exploiting the system's extreme sensitivity to initial conditions in order to arrive at a predetermined target state. In a recent Letter [Phys. Rev. Lett. 130, 020201 (2023)0031-900710.1103/PhysRevLett.130.020201], a generalization of this targeting method to quantum systems was demonstrated using successive unitary transformations that counter the natural spreading of a quantum state. In this paper further details are given and an important quite general extension is established. In particular, an alternate approach to constructing the coherent control dynamics is given, which introduces a time-dependent, locally stable control Hamiltonian that continues to use the chaotic heteroclinic orbits previously introduced, but without the need of countering quantum state spreading. Implementing that extension for the quantum kicked rotor generates a much simpler approximate control technique than discussed in the Letter, which is a little less accurate, but far more easily realizable in experiments. The simpler method's error can still be made to vanish as ℏ→0.
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Affiliation(s)
- Steven Tomsovic
- Institut für Theoretische Physik, Universität Regensburg, D-93040 Regensburg, Germany
- Department of Physics and Astronomy, Washington State University, Pullman 99164-2814, Washington, USA
| | - Juan Diego Urbina
- Institut für Theoretische Physik, Universität Regensburg, D-93040 Regensburg, Germany
| | - Klaus Richter
- Institut für Theoretische Physik, Universität Regensburg, D-93040 Regensburg, Germany
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Tateno A, Masuzawa K, Nagashima H, Maeda K. Anisotropic and Coherent Control of Radical Pairs by Optimized RF Fields. Int J Mol Sci 2023; 24:ijms24119700. [PMID: 37298651 DOI: 10.3390/ijms24119700] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/30/2023] [Revised: 05/30/2023] [Accepted: 05/31/2023] [Indexed: 06/12/2023] Open
Abstract
Radical pair kinetics is determined by the coherent and incoherent spin dynamics of spin pair and spin-selective chemical reactions. In a previous paper, reaction control and nuclear spin state selection by designed radiofrequency (RF) magnetic resonance was proposed. Here, we present two novel types of reaction control calculated by the local optimization method. One is anisotropic reaction control and the other is coherent path control. In both cases, the weighting parameters for the target states play an important role in the optimizing of the RF field. In the anisotropic control of radical pairs, the weighting parameters play an important role in the selection of the sub-ensemble. In coherent control, one can set the parameters for the intermediate states, and it is possible to specify the path to reach a final state by adjusting the weighting parameters. The global optimization of the weighting parameters for coherent control has been studied. These manifest calculations show the possibility of controlling the chemical reactions of radical pair intermediates in different ways.
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Affiliation(s)
- Akihiro Tateno
- Department of Chemistry, Graduate School of Science and Engineering, Saitama University, 255 Shimo-okubo, Sakura-ku, Saitama 338-8570, Japan
| | - Kenta Masuzawa
- Department of Chemistry, Graduate School of Science and Engineering, Saitama University, 255 Shimo-okubo, Sakura-ku, Saitama 338-8570, Japan
| | - Hiroki Nagashima
- Department of Chemistry, Graduate School of Science and Engineering, Saitama University, 255 Shimo-okubo, Sakura-ku, Saitama 338-8570, Japan
| | - Kiminori Maeda
- Department of Chemistry, Graduate School of Science and Engineering, Saitama University, 255 Shimo-okubo, Sakura-ku, Saitama 338-8570, Japan
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Tomsovic S, Urbina JD, Richter K. Controlling Quantum Chaos: Optimal Coherent Targeting. PHYSICAL REVIEW LETTERS 2023; 130:020201. [PMID: 36706382 DOI: 10.1103/physrevlett.130.020201] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/15/2022] [Accepted: 12/20/2022] [Indexed: 06/18/2023]
Abstract
One of the principal goals of controlling classical chaotic dynamical systems is known as targeting, which is the very weakly perturbative process of using the system's extreme sensitivity to initial conditions in order to arrive at a predetermined target state. It is shown that a generalization to chaotic quantum systems is possible in the semiclassical regime, but requires tailored perturbations whose effects must undo the dynamical spreading of the evolving quantum state. The procedure described here is applied to initially minimum uncertainty wave packets in the quantum kicked rotor, a preeminent quantum chaotic paradigm, to illustrate the method, and investigate its accuracy. The method's error can be made to vanish as ℏ→0.
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Affiliation(s)
- Steven Tomsovic
- Institut für Theoretische Physik, Universität Regensburg, D-93040 Regensburg, Germany
- Department of Physics and Astronomy, Washington State University, Pullman, Washington 99164, USA
| | - Juan Diego Urbina
- Institut für Theoretische Physik, Universität Regensburg, D-93040 Regensburg, Germany
| | - Klaus Richter
- Institut für Theoretische Physik, Universität Regensburg, D-93040 Regensburg, Germany
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Magann AB, Rudinger KM, Grace MD, Sarovar M. Feedback-Based Quantum Optimization. PHYSICAL REVIEW LETTERS 2022; 129:250502. [PMID: 36608235 DOI: 10.1103/physrevlett.129.250502] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/19/2021] [Revised: 08/08/2022] [Accepted: 09/23/2022] [Indexed: 06/17/2023]
Abstract
It is hoped that quantum computers will offer advantages over classical computers for combinatorial optimization. Here, we introduce a feedback-based strategy for quantum optimization, where the results of qubit measurements are used to constructively assign values to quantum circuit parameters. We show that this procedure results in an estimate of the combinatorial optimization problem solution that improves monotonically with the depth of the quantum circuit. Importantly, the measurement-based feedback enables approximate solutions to the combinatorial optimization problem without the need for any classical optimization effort, as would be required for the quantum approximate optimization algorithm. We demonstrate this feedback-based protocol on a superconducting quantum processor for the graph-partitioning problem MaxCut, and present a series of numerical analyses that further investigate the protocol's performance.
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Affiliation(s)
- Alicia B Magann
- Quantum Algorithms and Applications Collaboratory, Sandia National Laboratories, Livermore, California 94550, USA
- Quantum Algorithms and Applications Collaboratory, Sandia National Laboratories, Albuquerque, New Mexico 87185, USA
- Department of Chemical and Biological Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - Kenneth M Rudinger
- Quantum Algorithms and Applications Collaboratory, Sandia National Laboratories, Albuquerque, New Mexico 87185, USA
| | - Matthew D Grace
- Quantum Algorithms and Applications Collaboratory, Sandia National Laboratories, Livermore, California 94550, USA
| | - Mohan Sarovar
- Quantum Algorithms and Applications Collaboratory, Sandia National Laboratories, Livermore, California 94550, USA
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Masuzawa K, Sato M, Sugawara M, Maeda K. Quantum control of radical pair reactions by local optimization theory. J Chem Phys 2020; 152:014301. [DOI: 10.1063/1.5131557] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/24/2022] Open
Affiliation(s)
- Kenta Masuzawa
- Department of Chemistry, Graduate School of Science and Engineering, Saitama University, 255 Shimo-okubo, Sakura Ward, 338-8570 Saitama, Japan
| | - Masaya Sato
- Department of Chemistry, Graduate School of Science and Engineering, Saitama University, 255 Shimo-okubo, Sakura Ward, 338-8570 Saitama, Japan
| | - Michihiko Sugawara
- Keio Quantum Computing Center, Keio University, Kanagawa 223-8522, Japan
| | - Kiminori Maeda
- Department of Chemistry, Graduate School of Science and Engineering, Saitama University, 255 Shimo-okubo, Sakura Ward, 338-8570 Saitama, Japan
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Vranckx S, Loreau J, Vaeck N, Meier C, Desouter-Lecomte M. Photodissociation of the carbon monoxide dication in the 3Σ− manifold: Quantum control simulation towards the C2+ + O channel. J Chem Phys 2015; 143:164309. [DOI: 10.1063/1.4934233] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- S. Vranckx
- Service de Chimie Quantique et Photophysique, Université Libre de Bruxelles (ULB), CP 160/09, B-1050 Brussels, Belgium
- Laboratoire de Chimie Physique (UMR 8000), Université Paris-Sud, Orsay 91405, France
| | - J. Loreau
- Service de Chimie Quantique et Photophysique, Université Libre de Bruxelles (ULB), CP 160/09, B-1050 Brussels, Belgium
| | - N. Vaeck
- Service de Chimie Quantique et Photophysique, Université Libre de Bruxelles (ULB), CP 160/09, B-1050 Brussels, Belgium
| | - C. Meier
- Laboratoire Collisions Agrégats Réactivité, UMR 5589, IRSAMC, Université Toulouse III Paul Sabatier, Bât. 3R1b4, Toulouse, France
| | - M. Desouter-Lecomte
- Laboratoire de Chimie Physique (UMR 8000), Univ. Paris Sud, Université Paris-Saclay, Orsay 91405, France
- Département de Chimie, B6c Université de Liège, Sart Tilman, 4000 Liège, Belgium
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Controlling the shannon entropy of quantum systems. THESCIENTIFICWORLDJOURNAL 2013; 2013:381219. [PMID: 23818819 PMCID: PMC3683499 DOI: 10.1155/2013/381219] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 04/10/2013] [Accepted: 04/26/2013] [Indexed: 11/17/2022]
Abstract
This paper proposes a new quantum control method which controls the Shannon entropy of quantum systems. For both discrete and continuous entropies, controller design methods are proposed based on probability density function control, which can drive the quantum state to any target state. To drive the entropy to any target at any prespecified time, another discretization method is proposed for the discrete entropy case, and the conditions under which the entropy can be increased or decreased are discussed. Simulations are done on both two- and three-dimensional quantum systems, where division and prediction are used to achieve more accurate tracking.
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Suppression of Intramolecular Vibrational Energy Redistribution by Intense CW-Laser Fields. ADVANCES IN CHEMICAL PHYSICS 2011. [DOI: 10.1155/2011/584082] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
We present a quantum control scheme which realizes suppression of the intramolecular vibrational energy redistribution (IVR). In this scheme, we utilize effective decomposition brought by intense CW-laser fields, which enables to exclude
the doorway state coupled to background manifolds. In doing so, we introduce a helper state and make it optically coupled with the doorway state through the intense CW-laser field. We have applied the present scheme to both the Bixon-Jortner model and the
SCCl2 model system.
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Bomble L, Chenel A, Meier C, Desouter-Lecomte M. Local control of non-adiabatic dissociation dynamics. J Chem Phys 2011; 134:204112. [DOI: 10.1063/1.3589911] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Ho TS, Rabitz H. Accelerated monotonic convergence of optimal control over quantum dynamics. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2010; 82:026703. [PMID: 20866936 DOI: 10.1103/physreve.82.026703] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/22/2009] [Revised: 05/21/2010] [Indexed: 05/29/2023]
Abstract
The control of quantum dynamics is often concerned with finding time-dependent optimal control fields that can take a system from an initial state to a final state to attain the desired value of an observable. This paper presents a general method for formulating monotonically convergent algorithms to iteratively improve control fields. The formulation is based on a two-point boundary-value quantum control paradigm (TBQCP) expressed as a nonlinear integral equation of the first kind arising from dynamical invariant tracking control. TBQCP is shown to be related to various existing techniques, including local control theory, the Krotov method, and optimal control theory. Several accelerated monotonic convergence schemes for iteratively computing control fields are derived based on TBQCP. Numerical simulations are compared with the Krotov method showing that the new TBQCP schemes are efficient and remain monotonically convergent over a wide range of the iteration step parameters and the control pulse lengths, which is attributable to the trap-free character of the transition probability quantum dynamics control landscape.
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Affiliation(s)
- Tak-San Ho
- Department of Chemistry, Princeton University, Princeton, NJ 08544, USA.
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Neves JL, Heitmann B, Khaneja N, Glaser SJ. Heteronuclear decoupling by optimal tracking. JOURNAL OF MAGNETIC RESONANCE (SAN DIEGO, CALIF. : 1997) 2009; 201:7-17. [PMID: 19695913 DOI: 10.1016/j.jmr.2009.07.024] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/10/2009] [Revised: 07/19/2009] [Accepted: 07/25/2009] [Indexed: 05/28/2023]
Abstract
The problem to design efficient heteronuclear decoupling sequences is studied using optimal control methods. A generalized version of the gradient ascent engineering (GRAPE) algorithm is presented that makes it possible to design complex non-periodic decoupling sequences which are characterized by tens of thousands of pulse sequence parameters. In contrast to conventional approaches based on average Hamiltonian theory, the concept of optimal tracking is used: a pulse sequence is designed that steers the evolution of an ensemble of spin systems such that at a series of time points, a specified trajectory of the density operator is tracked as closely as possible. The approach is demonstrated for the case of low-power heteronuclear decoupling in the liquid state for in vivo applications. Compared to conventional sequences, significant gains in decoupling efficiency and robustness with respect to offset and inhomogeneity of the radio-frequency field were found in simulations and experiments.
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Affiliation(s)
- Jorge L Neves
- Department of Chemistry, Technische Universität München, 85747 Garching, Germany
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14
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Local Control Theory: Recent Applications to Energy and Particle Transfer Processes in Molecules. ADVANCES IN CHEMICAL PHYSICS 2009. [DOI: 10.1002/9780470431917.ch2] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/04/2023]
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15
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Beyvers S, Saalfrank P. A hybrid local/global optimal control algorithm for dissipative systems with time-dependent targets: Formulation and application to relaxing adsorbates. J Chem Phys 2008; 128:074104. [DOI: 10.1063/1.2830709] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/24/2022] Open
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Pezeshki S, Schreiber M, Kleinekathöfer U. Shaping femtosecond coherent anti-Stokes Raman spectra using optimal control theory. Phys Chem Chem Phys 2008; 10:2058-66. [DOI: 10.1039/b714268d] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/15/2023]
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17
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Sugawara M, Tamaki M, Yabushita S. A new control scheme of multilevel quantum system based on effective decomposition by intense CW lasers. J Phys Chem A 2007; 111:9446-53. [PMID: 17718547 DOI: 10.1021/jp073268m] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/25/2023]
Abstract
We propose a new scheme for quantum dynamics control of multilevel system using intense lasers. To do so, we apply intense CW lasers to create a strongly coupled subsystem with which one can make the complementary space effectively isolated, and we apply the established control schemes to the isolated subsystem. We have also obtained an effective Hamiltonian for the target subsystem with the help of the second-order perturbation theory. Numerical demonstrations on model systems show that the present decomposition scheme effectively works for population dynamics control. It is also found that relaxation processes can be suppressed under the proposed scheme.
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Affiliation(s)
- M Sugawara
- Department of Fundamental Science and Technology, Graduate School of Science and Technology, Keio University, 3-14-1 Hiyoshi, Yokohama 223-8522, Japan.
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18
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Sugawara M. Measurement-assisted quantum dynamics control of 5-level system using intense CW-laser fields. Chem Phys Lett 2006. [DOI: 10.1016/j.cplett.2006.07.069] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
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Salomon J, Turinici G. On the relationship between the local tracking procedures and monotonic schemes in quantum optimal control. J Chem Phys 2006; 124:74102. [PMID: 16497025 DOI: 10.1063/1.2170085] [Citation(s) in RCA: 14] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Numerical simulations of (bilinear) quantum control often rely on either monotonically convergent algorithms or tracking schemes. However, despite their mathematical simplicity, very limited intuitive understanding exists at this time to explain the former type of algorithms. Departing from the usual mathematical formalization, we present in this paper an interpretation of the monotonic algorithms as finite horizon, local in time, tracking schemes. Our purpose is not to present a new class of procedures but rather to introduce the necessary rigorous framework that supports this interpretation. As a by-product we show that at each instant, estimates of the future quality of the current control field are available and used in the optimization. When the target is expressed as reaching a prescribed final state, we also present an intuitive geometrical interpretation as the minimization of the distance between two correlated trajectories: one starting from the given initial state and the other backward in time from the target state. As an illustration, a stochastic monotonic algorithm is introduced. Numerical discretizations of the two procedures are also presented.
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Affiliation(s)
- Julien Salomon
- Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie, Paris, France.
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Sugawara M. Quantum dynamics driven by continuous laser fields under measurements: Towards measurement-assisted quantum dynamics control. J Chem Phys 2005; 123:204115. [PMID: 16351248 DOI: 10.1063/1.2132275] [Citation(s) in RCA: 17] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We study quantum system dynamics driven by continuous laser fields under the measurement process. In order to take into account the system transition due to the measurement, we define the superoperator which eliminates the coherence relevant to the measured quantum states. We clarify that the dynamics of the measured states is frozen in the frequent measurement limit, while the space spanned by unmeasured states is isolated from the original system. We also derive the effective Liouvillian which governs incoherent population dynamics under the condition, in which measurements are frequently applied. We apply the formulation to two-level and Lambda-type three-level systems and clarify how the quantum measurements hinder the coherent population dynamics driven by the continuous laser fields in practical examples. Analysis on the laser field amplitude dependency of the final distribution in the t-->infinity limit suggests the possibility of the measurement-assisted quantum control.
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Affiliation(s)
- M Sugawara
- Department of Fundamental Science and Technology, Graduate School of Science and Technology, Keio University, 3-14-1 Hiyoshi, Kohoku-ku, Yokohama 223-8522, Japan.
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Abstract
This paper presents a new tracking method where the target observable O(s,T) at the final dynamical time T follows a predefined track P(s) with respect to a homotopy tracking variable s>or=0. The procedure calculates the series of control fields E(s,t) required to accomplish observable homotopy tracking by solving a first-order differential equation in s for the evolution of the control field. Controls produced by this technique render the desired track for all s without encountering field singularities. This paper also extends the technique to the case where the field-free Hamiltonian and dipole moment operator change with s in order to explore the control of new physical systems along the track. Several simulations are presented illustrating the various uses for this quantum tracking control technique.
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Affiliation(s)
- Adam Rothman
- Department of Chemistry, Princeton University, Princeton, New Jersey 08544-1009, USA.
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Meier C, Heitz MC. Laser control of vibrational excitation in carboxyhemoglobin: A quantum wave packet study. J Chem Phys 2005; 123:044504. [PMID: 16095366 DOI: 10.1063/1.1946737] [Citation(s) in RCA: 32] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/12/2022] Open
Abstract
A coherent control algorithm is applied to obtain complex-shaped infrared laser pulses for the selective vibrational excitation of carbon monoxide at the active site of carbonmonoxyhemoglobin, modeled by the six-coordinated iron-porphyrin-imidazole-CO complex. The influence of the distal histidine is taken into account by an additional imidazole molecule. Density-functional theory is employed to calculate a multidimensional ground-state potential energy surface, and the vibrational dynamics as well as the laser interaction is described by quantum wave-packet calculations. At each instant in time, the optimal electric field is calculated and used for the subsequent quantum dynamics. The results presented show that the control scheme is applicable to complex systems and that it yields laser pulses with complex time-frequency structures, which, nevertheless, have a clear physical interpretation.
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Affiliation(s)
- Christoph Meier
- Laboratoire Collisions, Agrégats et Réactivité, UMR 5589, Institut de Recherche sur les Systèmes Atomiques et Moléculaires Complexes, Université Paul Sabatier, 118 Route de Narbonne, 31062 Toulouse, France.
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Lan BL, Vrábel I, Jakubetz W. Pulse-pair control of resonance leaking in molecular multiphoton transitions. J Chem Phys 2004; 121:10401-10. [PMID: 15549920 DOI: 10.1063/1.1812531] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We use model five-level systems to study resonance leaking of pi-pulse-induced multiphoton (MP) transitions along a strongly coupled anharmonic ladder. We demonstrate that the presence of a weakly bound background state attached to the ladder either in linear or Lambda configuration can have very pronounced effects on resonant MP ladder transitions, including essentially complete quenching of the primary transition. We also develop control strategies for the elimination of background state population based on phase-adjusted Gaussian pulse pairs and discuss the underlying control mechanisms. Finally we show that these strategies are effective in realistic molecular many-level systems. In particular, we demonstrate efficient pulse-pair control of resonance leaking in a 165-level system modeling vibrational excitation in HCN.
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Affiliation(s)
- Boon-Leong Lan
- School of Engineering and Science, Monash University, Bandar Sunway, 46150 Petaling Jaya, Selangor, Malaysia.
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