OPTIMALLY CONTROLLED VIBRATIONAL POPULATION TRANSFER IN A DIATOMIC QUANTUM SYSTEM

2009 ◽  
Vol 08 (01) ◽  
pp. 157-180 ◽  
Author(s):  
PRAVEEN KUMAR ◽  
SITANSH SHARMA ◽  
HARJINDER SINGH
Keyword(s):  
Iterative Method ◽  
Quantum System ◽  
Quantum Control ◽  
Vibrational Excitation ◽  
Transition Probability ◽  
Dipole Approximation ◽  
Time Dependent ◽  
Population Transfer ◽  
Initial State ◽  
Vibrational Population

A time-dependent formulation of quantum control is employed to investigate optimally controlled vibrational population transfer in a diatomic quantum system. The problem of finding the optimal laser field needed to achieve a specific quantum transition from an initial state to the desired target goal is formulated using an iterative method and the conjugate gradient method (CGM). The time-dependent Schrödinger equation is solved with interaction of laser radiation with matter included within a dipole approximation in the Hamiltonian. Appropriate boundary conditions are chosen for the evolution problem. The control objective is chosen as the value of transition probability from an initial state to a target state. A comparison is made between the results obtained using the iterative method and the CGM for optimization. Finally, quantum bits are encoded using the vibrational states of the diatomic in the regime of low-vibrational excitation.

Theoretical study of Zeno and anti-Zeno effects on photodissociation dynamics: A model approach

2016 ◽  
Vol 15 (08) ◽  
pp. 1650070 ◽  
Author(s):  
Bikram Nath ◽  
Chandan Kumar Mondal
Keyword(s):  
Repeated Measurements ◽  
Time Interval ◽  
Mathematical Tool ◽  
Population Transfer ◽  
Vibrational States ◽  
Initial State ◽  
Zeno Effect ◽  
Dissociation Dynamics ◽  
Vibrational Population

Zeno and anti-Zeno effects in the evolution of the multi-photonic dissociation dynamics of the diatomic molecule HBr[Formula: see text] owing to repeated measurements demand if the system in the initial state have been studied. The effects have been calculated numerically for the case of vibrational population transfer and dissociation dynamics of HBr[Formula: see text] taking it as a model. We use time-dependent Fourier grid Hamiltonian (TDFGH) method as a mathematical tool in presence of intense radiation field as perturbation. The effects have been explored through a probable mechanism of population transfer from the ground vibrational state to the different upper vibrational states which ultimately go to the dissociation continuum. The results show significant differences in the mechanism of population transfer and the significant role of time interval of measurement ([Formula: see text] in Zeno and anti-Zeno effects. In case of survival probability of ground vibrational states, there is Zeno effect when the frequency of the laser to which the molecule is submitted is near the vibrational [Formula: see text] to [Formula: see text] resonance, while there is anti-Zeno effect if it is far from this resonance.

scholarly journals Information Geometric Perspective on Off-Resonance Effects in Driven Two-Level Quantum Systems

2020 ◽  
Vol 2 (1) ◽  
pp. 166-188 ◽  
Author(s):  
Carlo Cafaro ◽  
Steven Gassner ◽  
Paul M. Alsing
Keyword(s):  
Resonance Condition ◽  
Transition Probability ◽  
Geometric Analysis ◽  
Quantum Systems ◽  
Time Dependent ◽  
Population Transfer ◽  
Resonance Effects ◽  
Hamiltonian Models ◽  
Exactly Solvable ◽  
Geodesic Paths

We present an information geometric analysis of off-resonance effects on classes of exactly solvable generalized semi-classical Rabi systems. Specifically, we consider population transfer performed by four distinct off-resonant driving schemes specified by su 2 ; ℂ time-dependent Hamiltonian models. For each scheme, we study the consequences of a departure from the on-resonance condition in terms of both geodesic paths and geodesic speeds on the corresponding manifold of transition probability vectors. In particular, we analyze the robustness of each driving scheme against off-resonance effects. Moreover, we report on a possible tradeoff between speed and robustness in the driving schemes being investigated. Finally, we discuss the emergence of a different relative ranking in terms of performance among the various driving schemes when transitioning from on-resonant to off-resonant scenarios.

scholarly journals One, Two and Three Photon Absorption in Atomic Hydrogen

2012 ◽  
Vol 12 ◽  
pp. 324-329
Author(s):  
Nilam Shrestha ◽  
Jeevan J Nakarmi
Keyword(s):  
Perturbation Theory ◽  
Matrix Element ◽  
Hydrogen Atom ◽  
Atomic Hydrogen ◽  
Transition Matrix ◽  
Dipole Approximation ◽  
Transition Matrix Element ◽  
Time Dependent ◽  
Photon Absorption ◽  
Initial State

Non relativistic, semi-classical in dipole approximation, based on time dependent Schrodinger equation under the framework of perturbation theory, three different absorption processes in hydrogen atom are studied and calculated transition matrix element from an initial state to final state.DOI: http://dx.doi.org/10.3126/njst.v12i0.6520 Nepal Journal of Science and Technology 12 (2011) 324-329 

Photoinduced Charge Transfer Dynamics in Carotenoid-Porphyrin-C60 Triad via the Linearized Semiclassical Nonequilibrium Fermi's Golden Rule

2020 ◽  
Author(s):  
Zhengqing Tong ◽  
Margaret S. Cheung ◽  
Barry D. Dunietz ◽  
Eitan Geva ◽  
Xiang Sun
Keyword(s):  
Charge Transfer ◽  
Golden Rule ◽  
Time Dependent ◽  
Rate Coefficients ◽  
Initial State ◽  
Photoinduced Charge Transfer ◽  
Transfer Rates ◽  
Fermi's Golden Rule ◽  
Photoinduced Charge ◽  
Fermi’S Golden Rule

The nonequilibrium Fermi’s golden rule (NE-FGR) describes the time-dependent rate coefficient for electronic transitions, when the nuclear degrees of freedom start out in a <i>nonequilibrium</i> state. In this letter, the linearized semiclassical (LSC) approximation of the NE-FGR is used to calculate the photoinduced charge transfer rates in the carotenoid-porphyrin-C<sub>60</sub> molecular triad dissolved in explicit tetrahydrofuran. The initial nonequilibrium state corresponds to impulsive photoexcitation from the equilibrated ground-state to the ππ* state, and the porphyrin-to-C<sub>60</sub> and the carotenoid-to-C<sub>60</sub> charge transfer rates are calculated. Our results show that accounting for the nonequilibrium nature of the initial state significantly enhances the transition rate of the porphyrin-to-C<sub>60</sub> CT process. We also derive the instantaneous Marcus theory (IMT) from LSC NE-FGR, which casts the CT rate coefficients in terms of a Marcus-like expression, with explicitly time-dependent reorganization energy and reaction free energy. IMT is found to reproduce the CT rates in the system under consideration remarkably well.

scholarly journals Equivalence between Redfield- and master-equation approaches for a time-dependent quantum system and coherence control

2011 ◽  
Vol 83 (6) ◽  
Author(s):  
D. O. Soares-Pinto ◽  
M. H. Y. Moussa ◽  
J. Maziero ◽  
E. R. deAzevedo ◽  
T. J. Bonagamba ◽  
...  
Keyword(s):  
Master Equation ◽  
Quantum System ◽  
Time Dependent

A new modified group explicit iterative method for the numerical solution of time dependent viscous Burgers' equation

2014 ◽  
Vol 05 (02) ◽  
pp. 1350029 ◽  
Author(s):  
Jyoti Talwar ◽  
R. K. Mohanty
Keyword(s):  
Iterative Method ◽  
Numerical Solution ◽  
Convergence Analysis ◽  
Iterative Methods ◽  
Iteration Method ◽  
Burgers Equation ◽  
Time Dependent ◽  
Alternating Group ◽  
Explicit Method ◽  
Rectangular Coordinates

In this article, we discuss a new smart alternating group explicit method based on off-step discretization for the solution of time dependent viscous Burgers' equation in rectangular coordinates. The convergence analysis for the new iteration method is discussed in details. We compared the results of Burgers' equation obtained by using the proposed iterative method with the results obtained by other iterative methods to demonstrate computationally the efficiency of the proposed method.

Quantum universality by state distillationIndirect quantum control for finite-dimensional coupled systems

2010 ◽  
Vol 10 (1&2) ◽  
pp. 87-96
Author(s):  
J. Nie ◽  
H.C. Fu ◽  
X.X. Yi
Keyword(s):  
Quantum System ◽  
Quantum Control ◽  
Coherent Control ◽  
Coupled Systems ◽  
Preparation Technology ◽  
State Preparation ◽  
Finite Dimensional ◽  
State Dependent ◽  
Control Scheme ◽  
Initial States

We present a new analysis on the quantum control for a quantum system coupled to a quantum probe. This analysis is based on the coherent control for the quantum system and a hypothesis that the probe can be prepared in specified initial states. The results show that a quantum system can be manipulated by probe state-dependent coherent control. In this sense, the present analysis provides a new control scheme which combines the coherent control and state preparation technology.

On the optimality of optical pumping for a closed Λ-system with large decay rates of the intermediate excited state

2021 ◽  
Author(s):  
Dionisis Stefanatos ◽  
Emmanuel Paspalakis
Keyword(s):  
Optimal Control ◽  
Excited State ◽  
Decay Rate ◽  
Optimal Control Theory ◽  
Optical Pumping ◽  
Quantum Information Processing ◽  
Decay Rates ◽  
Population Transfer ◽  
Initial State ◽  
Weakly Coupled

Abstract We use optimal control theory to show that for a closed Λ-system where the excited intermediate level decays to the lower levels with a common large rate, the optimal scheme for population transfer between the lower levels is actually optical pumping. In order to obtain this result we exploit the large decay rate to eliminate adiabatically the weakly coupled excited state, then perform a transformation to the basis comprised of the dark and bright states, and finally apply optimal control to this transformed system. Subsequently, we confirm the optimality of the optical pumping scheme for the original closed Λ-system using numerical optimal control. We also demonstrate numerically that optical pumping remains optimal when the decay rate to the target state is larger than that to the initial state or the two rates are not very different from each other. The present work is expected to find application in various tasks of quantum information processing, where such systems are encountered

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