Quantum control of nuclear wave packets by locally designed optimal pulses

An implicit split-operator algorithm for the nonlinear time-dependent Schrödinger equation

The explicit split-operator algorithm is often used for solving the linear and nonlinear time-dependent Schrödinger equations. However, when applied to certain nonlinear time-dependent Schrödinger equations, this algorithm loses time reversibility and second-order accuracy, which makes it very inefficient. Here, we propose to overcome the limitations of the explicit split-operator algorithm by abandoning its explicit nature. We describe a family of high-order implicit split-operator algorithms that are norm-conserving, time-reversible, and very efficient. The geometric properties of the integrators are proven analytically and demonstrated numerically on the local control of a two-dimensional model of retinal. Although they are only applicable to separable Hamiltonians, the implicit split-operator algorithms are, in this setting, more efficient than the recently proposed integrators based on the implicit midpoint method.

Locally optimized control pulses with nonlinear interactions

The local control theory has been extended to deal with nonlinear interactions, such as polarizability interaction, as well as a combination of dipole and polarizability interactions. We explain herein how to implement the developed pulse-design algorithm in a standard computer code that numerically integrates the Liouville equation and/or the Schrödinger equation without incurring additional high computational cost. Through a case study of the rotational dynamics control of crystalline orbital molecules, the effectiveness of the locally optimized control pulses is demonstrated by adopting four types of control objectives, namely, two types of state-selective excitation, alignment, and orientation control.

d'Alembert-Schrödinger hybrid simulation for laser-induced multiquantum state transitions in a three-dimensional artificial atom

In this Letter, a d'Alembert-Schrödinger hybrid method is proposed to analyze the transient interaction between the incident electromagnetic control pulse and the electron. This hybrid method is based on the d'Alembert equation, which describes the propagation of the electromagnetic field and the time-dependent Schrödinger equation, which describes the action of the electron. Moreover, the finite-difference time-domain method is used to solve those equations. In our simulation, using the presented hybrid equations and the control equation of the quantum state, a scheme is presented to design laser pulses to control discrete quantum states in a three-dimensional artificial atom model. Excitingly, the laser pulses have been successfully designed for the perfect four quantum states' transition for the first time. With that, the spatiotemporal distribution for the probability density of an electron wave packet is showed in detail to describe the laser-induced transition process of quantum states.

Multiple solutions in the tracking control of quantum systems

This paper demonstrates the existence of multiple solutions at each time point in tracking control of quantum systems. These solutions are shown to arise from the nonlinear dependence of the short-time propagators U(t + delta t,t) on the control field. The multiplicity of solutions depends on the parameters of the controlled system and the nature of the imposed track. Multiple solutions necessitate that a choice be made at each time point, resulting in an exponentially expanding space of distinct control fields that maintain the prescribed track. This behavior is illustrated by application to a small model system. The presence of multiple tracking control fields is consistent with behavior observed from quantum control landscape theory.

Topology of the quantum control landscape for observables

A broad class of quantum control problems entails optimizing the expectation value of an observable operator through tailored unitary propagation of the system density matrix. Such optimization processes can be viewed as a directed search over a quantum control landscape. The attainment of the global extrema of this landscape is the goal of quantum control. Local optima will generally exist, and their enumeration is shown to scale factorially with the system's effective Hilbert space dimension. A Hessian analysis reveals that these local optima have saddlepoint topology and cannot behave as suboptimal extrema traps. The implications of the landscape topology for practical quantum control efforts are discussed, including in the context of nonideal operating conditions.

A new quantum control scheme for multilevel systems based on effective decomposition by intense laser fields

A new quantum control scheme for general multilevel systems using intense laser fields is proposed. In the present scheme, the target subspace consisting of several quantum levels is effectively isolated by applying intense cw lasers with specific conditions. The formulation is carried out using the Green function with the help of projection operator method. Dynamics of the isolated target subspace is governed by an effective Hamiltonian. The developed scheme is applied to the quantum control of dissipative four- and five-level systems. It is clarified that the present method makes it possible not only to manipulate the coherent population dynamics but also to suppress the dissipative dynamics.

Concatenated toolkit for quantum optimal control wave-function propagation

Numerical propagation of the Schrödinger equation is the bottleneck in many quantum optimal control computations. For a quantum system of N states with an electric-field-dipole interaction, the use of a propagation toolkit introduced in a prior work yields an O(N) reduction in floating-point operations per wave function propagation. A concatenation scheme for the toolkit method is introduced, and a scaling analysis shows a significant additional reduction in computational cost. The method exploits the fact that the same sequences of discretized control field values are often repeated many times in a control simulation. The concatenated toolkit is benchmarked against the standard toolkit in a numerical simulation.

Reference trajectory tracking for locally designed coherent quantum controls

Local time control methods are used in the simulation of quantum control phenomena because they conveniently ensure an increase of a predefined performance index and also avoid singularities associated with tracking procedures. However, the drawback of the existing implementations is that they only take into account one-photon, direct transitions and may stop at nonoptimal values of the index. We propose in this paper a modification of the currently used algorithms that addresses this issue and explain how the convergence is improved. Furthermore, when iterations are required, we show that this approach can be inserted into a monotonically convergent algorithm.

Optimal control landscapes for quantum observables

The optimal control of quantum systems provides the means to achieve the best outcome from redirecting dynamical behavior. Quantum systems for optimal control are characterized by an evolving density matrix and a Hermitian operator associated with the observable of interest. The optimal control landscape is the observable as a functional of the control field. The features of interest over this control landscape consist of the extremum values and their topological character. For controllable finite dimensional quantum systems with no constraints placed on the controls, it is shown that there is only a finite number of distinct values for the extrema, dependent on the spectral degeneracy of the initial and target density matrices. The consequences of these findings for the practical discovery of effective quantum controls in the laboratory is discussed.

Local control of the quantum dynamics in multiple potential wells

The driven wave-packet dynamics in potentials exhibiting several potential wells is investigated. Therefore, local-control strategies are employed where the control field is constructed from the system's dynamics at any instant of time. It is shown that particles can be moved successively between various potential minima. Furthermore, results presented indicate that the intuitive local-control scheme allows for the initiation of a clockwise or counterclockwise rotational motion of a model molecular motor.

Quantum dynamics driven by continuous laser fields under measurements: Towards measurement-assisted quantum dynamics control

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.

Laser control of vibrational excitation in carboxyhemoglobin: A quantum wave packet study

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.

Quantum Control of a Chiral Molecular Motor Driven by Laser Pulses

"Molecular motors or machines" are one of the hot subjects in chemistry because they play an important role in molecular devices. We have theoretically demonstrated that unidirectional rotations of a chiral molecular motor can be driven by using tailored linearly polarized laser pulses. The findings obtained here serve as a theoretical basis for control of functions such as gearing or acceleration of molecular motors.