We design optimal harmonic-trap trajectories to transport cold atoms without final excitation, combining an inverse engineering technique based on Lewis-Riesenfeld invariants with optimal control theory. Since actual traps are not really harmonic, we keep the relative displacement between the center of mass of the transport modes and the trap center bounded. Under this constraint, optimal protocols are found according to different physical criteria. The minimum time solution has a "bang-bang" form, and the minimum displacement solution is of "bang-off-bang" form. The optimal trajectories for minimizing the transient energy are also discussed.

In this article we formulate frictionless atom cooling in harmonic traps as a time-optimal control problem, permitting imaginary values of the trap frequency for transient time intervals during which the trap becomes an expulsive parabolic potential. We show that the minimum time solution has a "bang-bang" form, where the frequency jumps suddenly at certain instants and then remains constant, and calculate estimates of the minimum cooling time for various numbers of such jumps. A numerical optimization method based on pseudospectral approximations is used to obtain suboptimal realistic solutions without discontinuities, which may be implemented experimentally.

Frictionless atom cooling in harmonic traps is formulated as a time-optimal control problem and a synthesis of optimal controlled trajectories is obtained.

In this paper, we develop methods for optimal manipulation of coupled spin dynamics in the presence of relaxation. These methods are used to compute analytical bounds for the optimal efficiency of coherence transfer between coupled nuclear spins in presence of longitudinal and transverse relaxation. We derive relaxation optimized pulse sequences which achieve these bounds and maximize the sensitivity of the experiments in spectroscopic applications. This paper is a continuation of our previous work. Here, we take into account both the longitudinal and the transverse relaxation mechanisms, thus generalizing our previous results, where the former had been neglected.

In this paper, we present a unified computational method based on pseudospectral approximations for the design of optimal pulse sequences in open quantum systems. The proposed method transforms the problem of optimal pulse design, which is formulated as a continuous-time optimal control problem, to a finite-dimensional constrained nonlinear programming problem. This resulting optimization problem can then be solved using existing numerical optimization suites. We apply the Legendre pseudospectral method to a series of optimal control problems on open quantum systems that arise in nuclear magnetic resonance spectroscopy in liquids. These problems have been well studied in previous literature and analytical optimal controls have been found. We find an excellent agreement between the maximum transfer efficiency produced by our computational method and the analytical expressions. Moreover, our method permits us to extend the analysis and address practical concerns, including smoothing discontinuous controls as well as deriving minimum-energy and time-optimal controls. The method is not restricted to the systems studied in this article and is applicable to optimal manipulation of both closed and open quantum systems.