Quantum optimal control of molecular isomerization in the presence of a competing dissociation channel

Constrained control landscape for population transfer in a two-level system

Controlling population transfer in a two-level quantum system reveals a landscape with a rich structure containing highly connected optimal regions.

Exploring constrained quantum control landscapes

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.

Numerical study on dynamical behavior in oscillatory driven quantum double-well systems

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.

Ultrafast excited-state dynamics of tetraphenylethylene studied by semiclassical simulation

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.