Wusheng Zhu

Rapidly convergent iteration methods for quantum optimal control of population

A family of new iteration methods is presented for designing quantum optimal controls to manipulate the transition probability. Theoretical analysis shows that these new methods exhibit quadratic and monotonic convergence. Numerical calculations verify that for these new methods, within very few steps, the optimized objective functional comes close to its convergent limit.

A rapid monotonically convergent iteration algorithm for quantum optimal control over the expectation value of a positive definite operator

A new iteration method is presented for achieving quantum optimal control over the expectation value of a positive definite operator. Theoretical analysis shows that this new algorithm exhibits quadratic and monotonic convergence. Numerical calculations verify that for this new algorithm, within a few steps, the optimized objective functional comes close to its converged limit.

MONOTONICALLY CONVERGENT ALGORITHM FOR QUANTUM OPTIMAL CONTROL WITH DISSIPATION

This paper extends a monotonically convergent algorithm for quantum optimal control to treat systems with dissipation. The algorithm working with the density matrix is proved to exhibit quadratic and monotonic convergence. Several numerical tests are implemented in three-level model systems. The algorithm is exploited to control various targets, including the expectation value of a Hermitian operator, the modulus square of the expectation value of a non-Hermitian operator, and off-diagonal elements of the density matrix.

Incorporating physical implementation concerns into closed loop quantum control experiments

In quantum control experiments, it is desirable to build features into the field that address physical concerns such as simplicity, robustness, dynamical coherence, power expenditure, etc. With a judicious choice for the cost functional, it is possible to incorporate such secondary features into the field, often without altering the experimental procedure or apparatus. Through simulated closed-loop population transfer experiments, we demonstrate the benefit of carefully designed cost functionals. As specific examples, we address two common physical concerns: removing extraneous structure from the control pulse and finding robust fields. Removing unnecessary field components is critical if information about the mechanism is to be interpreted from the structure of the optimal pulse. Robust fields produce a stable outcome despite noise in the field and, perhaps, environmental inhomogeneities in the quantum system as is typical of condensed phase experiments.

Quantum control design via adaptive tracking

An adaptive tracking algorithm is developed to achieve quantum system control field designs. The adaptive algorithm has the advantage of operating noniteratively to efficiently find desirable controls, and has the feature of high stability by suppressing the influence of disturbances from tracking singularities. The core of the adaptive tracking control algorithm is a self-learning track switch technique which is triggered by monitoring of the evolving system trajectory. The adaptive tracking algorithm is successfully tested for population transfer.

Quantum optimal control of multiple targets: Development of a monotonically convergent algorithm and application to intramolecular vibrational energy redistribution control

An optimal control procedure is presented to design a field that transfers a molecule into an objective state that is specified by the expectation values of multiple target operators. This procedure explicitly includes constraints on the time behavior of specified operators during the control period. To calculate the optimal control field, we develop a new monotonically and quadratically convergent algorithm by introducing a quadruple space that consists of a direct product of the double (Liouville) space. In the absence of the time-dependent constraints, the algorithm represented in the quadruple-space notation reduces to that of the double-space notation. This simplified formulation is applied to a two dimensional system which models intramolecular vibrational energy redistribution (IVR) processes in polyatomic molecules. An optimal pulse is calculated that exploits IVR to transfer a specific amount of population to an optically inactive state, while the other portion of the population remains in the initial state at a control time. Using trajectory plots in quantum-number space, we numerically analyze how the control pathway changes depending on the amount of the excited population.

Quantum optimal control of wave packet dynamics under the influence of dissipation

Optimal control within the density matrix formalism is applied to the production of desired non-equilibrium distributions in condensed phases. The time evolution of a molecular system modeled by a displaced harmonic oscillator is assumed to be described by the Markoffian master equation with phenomenological relaxation parameters. The physical objectives of concern are the creation of a specified vibronic state, population inversion and wave packet shaping. The effects of an initial thermal distribution and dissipation on these targets are examined. In order to transfer a large amount of population (i.e., the strong-field regime) to a target wave packet in an electronic excited state, it is shown that creating a shaped packet in the ground state is often required to achieve high yield. This control pathway cannot be taken into account within the weak-field approximation, and is especially important when the target state includes vibrational states that are weakly accessible from the initial state or that have preferential indirect excitation paths from the initial state. Although relaxation effects usually reduce the control efficiency, under certain conditions, the bath-induced dynamics can help to create an objective state.

Closed loop learning control to suppress the effects of quantum decoherence

This paper explores the use of laboratory closed loop learning control to suppress the effects of decoherence in quantum dynamics. Simulations of the process are performed in multilevel quantum systems strongly interacting with the environment. A genetic algorithm is used to find an optimal control field which seeks out transition pathways to achieve a minimum influence of decoherence upon the system at a target time. The simulations suggest that decoherence may be optimally managed in the laboratory through closed loop operations with a suitable cost that is sensitive to the coherence of the dynamics. The case studies of dimension N=4 and N=10 with strong system–environment coupling indicate that the additional complexity with increasing system dimension can make it more difficult to manage decoherence.

Managing singular behavior in the tracking control of quantum dynamical observables

Singularities can arise in the external field obtained by tracking control of quantum mechanical systems. Whether or not the trajectory is disturbed by the presence of a singular point is shown to mainly depend on the average momentum along the trajectory at the moment of passing the singular point. If the singularity occurs on a turning point, the tracking will be quite unstable since the direction taken by the trajectory is very sensitive to field errors. The theoretical analysis of these situations yields detailed conclusions about the impact of field singularities in quantum tracking control. A rank index is defined to characterize nontrivial singularities, and the rank is shown to play an important role in determining the tracking quality while passing over a singular turning point where the field has a unique solution. A special class of nontrivial singularities is identified by the ability to remove the singularity under a proper limiting process. These insights into the nature and influence of singularities in tracking control of quantum systems are beneficial for developing numerical schemes and for designing controls.

Noniterative algorithms for finding quantum optimal controls

Iterative methods are generally necessary for solving the design equations to identify optimal quantum controls. Since iteration can be computationally intensive, it is significant to develop good approximate noniterative methods. In this paper we present noniterative techniques for achieving quantum optimal control over the expectation value of positive semidefinite operators. The noniterative methods are characterized by an order index. Zeroth-order methods involving no feedback from the objective are generally found to be inadequate. A proposed first-order noniterative algorithm is expected to often be a good approximation. Numerical tests verify the noniterative capabilities of the algorithm.