Alberto Castro , Umberto De Giovannini, Shunsuke A. Sato, Hannes Hübener , and Angel Rubio, Phys. Rev. Research 4, 033213 (2022)

We demonstrate that the electronic structure of a material can be deformed into Floquet pseudobands with arbitrarily tailored shapes. We achieve this goal with a combination of quantum optimal control theory and Floquet engineering. The power and versatility of this framework is demonstrated here by utilizing the independent-electron tight-binding description of the π electronic system of graphene. We show several prototype examples focusing on the region around the K (Dirac) point of the Brillouin zone: creation of a gap with opposing flat valence and conduction bands, creation of a gap with opposing concave symmetric valence and conduction bands (which would correspond to a material with an effective negative electron-hole mass), and closure of the gap when departing from a modified graphene model with a nonzero field-free gap. We employ time-periodic drives with several frequency components and polarizations, in contrast to the usual monochromatic fields, and use control theory to find the amplitudes of each component that optimize the shape of the bands as desired. In addition, we use quantum control methods to find realistic switch-on pulses that bring the materia into the predefined stationary Floquet band structure, i.e., into a state in which the desired Floquet modes of the target bands are fully occupied, so that they should remain stroboscopically stationary, with long lifetimes, when the weak periodic drives are started. Finally, we note that although we have focused on solid state materials, the technique that we propose could be equally used for the Floquet engineering of ultracold atoms in optical lattices and for other nonequilibrium dynamical and correlated systems.

Alberto Castro, Adrián García Carrizo, Sebastián Roca, David Zueco, and Fernando Luis, Phys. Rev. Appl. 17, 064028 (2022).

We demonstrate, numerically, the possibility of manipulating the spin states of molecular nanomagnets with shaped microwave pulses designed with quantum optimal control theory techniques. The state-to-state or full gate transformations can be performed in this way in shorter times than using simple monochromatic resonant pulses. This enhancement in the operation rates can therefore mitigate the effect of decoherence. The optimization protocols and their potential for practical implementations are illustrated by simulations performed for a simple molecular cluster hosting a single Gd3+ ion. Its eight accessible levels (corresponding to a total spin S = 7/2) allow encoding an eight-level qudit or a system of three coupled qubits. All necessary gates required for universal operation can be obtained with optimal pulses using the intrinsic couplings present in this system. The application of optimal control techniques can facilitate the implementation of quantum technologies based on molecular spin qudits.

J. L. Alonso, P. Bruscolini, A. Castro, J. Clemente-Gallardo, J. C. Cuchí, and J. A. Jover-Galtier, J. Chem. Theor. Comp. 14, 3975 (2018)

In previous works, we introduced a geometric route to define our Ehrenfest statistical dynamics (ESD) and we proved that, for a simple toy model, the resulting ESD does not preserve purity. We now take a step further: we investigate decoherence and pointer basis in the ESD model by considering some uncertainty in the degrees of freedom of a simple but realistic molecular model, consisting of two classical cores and one quantum electron. The Ehrenfest model is sometimes discarded as a valid approximation to nonadiabatic coupled quantum-classical dynamics because it does not describe the decoherence in the quantum subsystem. However, any rigorous statistical analysis of the Ehrenfest dynamics, such as the described ESD formalism, proves that decoherence exists. In this article, decoherence in ESD is studied by measuring the change in the quantum subsystem purity and by analyzing the appearance of the pointer basis to which the system decoheres, which for our example is composed of the eigenstates of the electronic Hamiltonian.

Alberto Castro, in Handbook of Materials Modeling : Methods: Theory and Modeling (Wanda Andreoni and Sidney Yip, eds.), 1-21 (Springer, Cham, 2018)

Optimal control theory (OCT) is a branch of mathematics that deals with the problem of finding optimal trajectories for dynamical systems. It can be used in combination with time dependent quantum mechanical methods that describe the evolution of the electronic and/or nuclear wave functions of atoms, molecules, or materials in the presence of external perturbations, such as electromagnetic fields. OCT may then find the optimal shape of those external perturbations: the optimal character is defined in terms of a functional of the behavior of the system. This chapter provides a brief description of the basic elements of the theory and an overview of its applications to quantum dynamics and electronic structure.

Adrián Gómez Pueyo, Miguel A. L. Marques, Angel Rubio, and Alberto Castro, J. Chem. Thelr. Comp. 14, 3040 (2018)

We examine various integration schemes for the time-dependent Kohn−Sham equations. Contrary to the time-dependent Schrödinger’s equation, this set of equations is nonlinear, due to the dependence of the Hamiltonian on the electronic density. We discuss some of their exact properties, and in particular their symplectic structure. Four different families of propagators are considered, specifically the linear multistep, Runge−Kutta, exponential Runge−Kutta, and the commutator-free Magnus schemes. These have been chosen because they have been largely ignored in the past for time-dependent electronic structure calculations. The performance is analyzed in terms of cost-versus-accuracy. The clear winner, in terms of robustness, simplicity, and efficiency is a simplified version of a fourth- order commutator-free Magnus integrator. However, in some specific cases, other propagators, such as some implicit versions of the multistep methods, may be useful.

Adrián Gómez Pueyo and Alberto Castro, Eur. Phsy. J B 91, 105 (2018)

We investigate, numerically, the possibility of associating to each approximation to the exchange-and-correlation functional in density-functional theory (DFT), an optimal electron-electron interaction potential for which it performs best. The fundamental theorems of density-functional theory (DFT) make no assumption about the precise form of the electron–electron interaction: to each possible electron–electron interaction corresponds an exchange-and-correlation functional. This fact suggests the opposite question: given some functional of the density, is there any electron–electron interaction for which it is the exact exchange-and-correlation functional? And, if not, what is the interaction for which the functional produces the best results? Within the context of lattice DFT, we study these questions by working on the one-dimensional Hubbard chain. The idea of associating an optimal interaction potential to each approximation to the exchange and correlation functionals suggests, finally, a procedure to optimise parameterised families of functionals: find that one whose associated interaction most closely resembles the real one.

David Kammerlander, Alberto Castro, and Miguel A. L. Marques, Eur. Phys. J. B 90, 91 (2017)

How fast can a laser pulse ionize an atom? We address this question by considering pulses that carry a fixed time-integrated energy per-area, and finding those that achieve the double requirement of maximizing the ionization that they induce, while having the shortest duration. We formulate this double-objective quantum optimal control problem by making use of the Pareto approach to multi-objective optimization, and the differential evolution genetic algorithm. The goal is to find out how a precise time-profiling of ultra-fast, large-bandwidth pulses may speed up the ionization process. We work on a simple one-dimensional model of hydrogen-like atoms (the Poschl-Teller potential) that allows to tune the number of bound states that play a role in the ionization dynamics. We show how the detailed shape of the pulse accelerates the ionization, and how the presence or absence of bound states influences the velocity of the process.

Adrián Gómez Pueyo, Jorge A. Budagosky M., and Alberto Castro, Phys. Rev. A. 94, 063421 (2016)

We present an implementation of optimal control theory for the first-principles nonadiabatic Ehrenfest molecular dynamics model, which describes a condensed matter system by considering classical point-particle nuclei, and quantum electrons, handled in our case with time-dependent density-functional theory. The scheme is demonstrated by optimizing the Coulomb explosion of small sodium clusters: the algorithm is set to find the optimal femtosecond laser pulses that disintegrate the clusters, for a given total duration, fluence, and cutoff frequency. We describe the numerical details and difficulties of the method.

Jessica Walkenhorst, Umberto De Giovannini, Alberto Castro, and Angel Rubio, Eur. Phys. J. B 89, 128 (2016)

Recent advances in laser technology allow us to follow electronic motion at its natural time-scale with ultra-fast time resolution, leading the way towards attosecond physics experiments of extreme precision. In this work, we assess the use of tailored pumps in order to enhance (or reduce) some given features of the probe absorption (for example, absorption in the visible range of otherwise transparent samples). This type of manipulation of the system response could be helpful for its full characterization, since it would allow us to visualize transitions that are dark when using unshaped pulses. In order to investigate these possibilities, we perform first a theoretical analysis of the non-equilibrium response function in this context, aided by one simple numerical model of the hydrogen atom. Then, we proceed to investigate the feasibility of using time-dependent density-functional theory as a means to implement, theoretically, this absorption-optimization idea, for more complex atoms or molecules. We conclude that the proposed idea could in principle be brought to the laboratory: tailored pump pulses can excite systems into light-absorbing states. However, we also highlight the severe numerical and theoretical difficulties posed by the problem: large-scale non-equilibrium quantum dynamics are cumbersome, even with TDDFT, and the shortcomings of state-of-the-art TDDFT functionals may still be serious for these out-of-equilibrium situations.

Alberto Castro, ChemPhysChem 17, 1601 (2016)

The combination of nonadiabatic Ehrenfest-path molecular dynamics (EMD) based on time-dependent density functional theory (TDDFT) and quantum optimal control formalism (QOCT) was used to optimize the shape of ultra-short laser pulses to achieve photodissociation of a hydrogen molecule and the trihydrogen cation H3 + . This work completes a previous one [A. Castro, ChemPhysChem, 2013, 14, 1488–1495], in which the same objective was achieved by demonstrating the combination of QOCT and TDDFT for many-electron systems on static nuclear potentials. The optimization model, therefore, did not include the nuclear movement and the obtained dissociation mechanism could only be sequential: fast laser-assisted electronic excitation to nonbonding states (during which the nuclei are considered to be static), followed by field-free dissociation. Here, in contrast, the optimization was performed with the QOCT constructed on top of the full dynamic model comprised of both electrons and nuclei, as described within EMD based on TDDFT. This is the first numerical demonstration of an optimal control formalism for a hybrid quantum–classical model, that is, a molecular dynamics method.