Alberto Castro

University of Zaragoza | UNIZAR

Non-equilibrium steady states are created when a periodically driven quantum system is also incoherently interacting with an environment - as it is the case in most realistic situations. The notion of Floquet engineering refers to the manipulation of the properties of systems under periodic perturbations. Although it more frequently refers to the c...

Floquet engineering consists in the modification of physical systems by the application of periodic time-dependent perturbations. The search for the shape of the periodic perturbation that best modifies the properties of a system in order to achieve some predefined metastable target behavior can be formulated as an optimal control problem. We discu...

Non-equilibrium steady states are created when a periodically driven quantum system is also incoherently interacting with an environment -- as it is the case in most realistic situations. The notion of Floquet engineering refers to the manipulation of the properties of systems under periodic perturbations. Although it more frequently refers to the...

First-principle calculations are employed to investigate the ultrafast isomerization of the acetylene cation and dication. We use the time-dependent density functional theory together with the Ehrenfest dynamics to track the coupled electron-nuclear dynamics. For both the acetylene cation and the dication, we observe nonadiabatic behaviors during t...

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...

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...

We demonstrate that the electronic structure of a material can be deformed into Floquet pseudo-bands with arbitrarily tailored shapes. We achieve this goal with a novel 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-b...

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...

Molecular or condensed matter systems are often well approximated by hybrid quantum-classical models: the electrons retain their quantum character, whereas the ions are considered to be classical particles. We discuss various alternative approaches for the computation of equilibrium (canonical) ensemble averages for observables of these hybrid quan...

Molecular or condensed matter systems are often well approximated by hybrid quantum-classical models: the electrons retain their quantum character, whereas the ions are considered to be classical particles. We discuss various alternative approaches for the computation of equilibrium (canonical) ensemble averages for observables of these hybrid quan...

We calculate the charge-transfer cross sections for the Ne2++He collision. To this end, we employ Ehrenfest molecular dynamics with time-dependent density-functional theory. The active electrons of the projectile are handled by applying an initial velocity to the Kohn-Sham orbitals via a Galilean boost. The dynamical calculations are performed in a...

In this work we generalize and combine Gibbs and von Neumann approaches to build, for the first time, a rigorous definition of entropy for hybrid quantum-classical systems. The resulting function coincides with the two cases above when the suitable limits are considered. Then, we apply the MaxEnt principle for this hybrid entropy function and obtai...

We generalize von Neumann entropy function to hybrid quantum-classical systems by considering the principle of exclusivity of hybrid events. For non-interacting quantum and classical subsystems, this entropy function separates into the sum of the usual classical (Gibbs) and quantum (von Neumann) entropies, whereas if the two parts do interact, it c...

Hybrid quantum‐classical systems combine both classical and quantum degrees of freedom. Typically, in Chemistry, Molecular Physics or Materials Science, the classical degrees of freedom describe atomic nuclei (or cations with frozen core electrons), whereas the quantum particles are the electrons. Although many possible hybrid dynamical models exis...

Over the last few years, extraordinary advances in experimental and theoretical tools have allowed us to monitor and control matter at short time and atomic scales with a high degree of precision. An appealing and challenging route toward engineering materials with tailored properties is to find ways to design or selectively manipulate materials, e...

We consider the numerical propagation of models that combine both quantum and classical degrees of freedom -- usually, electrons and nuclei, respectively. We focus, in our computational examples, on the case in which the quantum electrons are modeled with time-dependent density-functional theory, although the methods discussed below can be used wit...

Over the last years extraordinary advances in experimental and theoretical tools have allowed us to monitor and control matter at short time and atomic scales with a high-degree of precision. An appealing and challenging route towards engineering materials with tailored properties is to find ways to design or selectively manipulate materials, espec...

In conventional quantum optimal control theory, the parameters that determine an external field are optimised to maximise some predefined function of the trajectory, or of the final state, of a matter system. The situation changes in the case of quantum electrodynamics, where the degrees of freedom of the radiation field are now part of the system....

Attosecond science is a new and rapidly developing research area in which molecular dynamics are studied at the timescale of a few attoseconds. Within the past decade, attosecond pump–probe spectroscopy has emerged as a powerful experimental technique that permits electron dynamics to be followed on their natural timescales. With the development of...

In conventional quantum optimal control theory, the parameters that determine an external field are optimised to maximise some predefined function of the trajectory, or of the final state, of a matter system. The situation changes in the case of quantum electrodynamics, where the degrees of freedom of the radiation field are now part of the system....

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 Ehrenfest Statistical Dynamics (ESD) model by considering some uncertainty in th...

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 e...

We examine various integration schemes for the time-dependent Kohn-Sham equations. Contrary to the time-dependent Schr\"odinger's equation, this set of equations is non-linear, 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 f...

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 m...

We present an implementation of optimal control theory for the first-principles non-adiabatic 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 combination of the non-adiabatic Ehrenfest-path molecular dynamics (EMD) based on time-dependent density-functional theory (TDDFT), and the quantum optimal control formalism (QOCT) is used to optimize the shape of ultra-short laser pulses in order to achieve the photo-dissociation of the Hydrogen molecule and the trihydrogen cation H$_3^+$. Thi...

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, a...

We use quantum optimal control theory algorithms to design external electric fields that drive the coupled spin and orbital dynamics of an electron in a double quantum dot, subject to the spin-orbit coupling and Zeeman magnetic fields. We obtain time profiles of multifrequency electric field pulses which increase the rate of spin-flip transitions b...

We use quantum optimal control theory algorithms to design external electric fields that drive the coupled spin and orbital dynamics of an electron in a double quantum dot, subject to the spin-orbit interaction and Zeeman magnetic fields. We obtain time-profiles of multi-frequency electric pulses which increase the rate of spin-flip transitions by...

Schrödinger suggested that thermodynamical functions cannot be based on the gratuitous allegation that quantum-mechanical levels (typically the orthogonal eigenstates of the Hamiltonian operator) are the only allowed states for a quantum system [E. Schrödinger, Statistical Thermodynamics (Courier Dover, Mineola, 1967)]. Different authors have inter...

Real-space grids are a powerful alternative for the simulation of electronic systems. One of the main advantages of the approach is the flexibility and simplicity of working directly in real space where the different fields are discretized on a grid, combined with competitive numerical performance and great potential for parallelization. These prop...

We have studied theoretically the possibility of ultra-fast manipulation of a single electron spin in 2D semiconductor quantum dots, by means of high-frequency time-dependent electric fields. The electron spin degree of freedom is excited through spin-orbit coupling, and the procedure may be enhanced by the presence of a static magnetic field. We u...

High harmonic generation (HHG) provides a flexible framework for the development of coherent light sources in the extreme-ultraviolet and soft x-ray regimes. However it suffers from low conversion efficiencies as the control of the HHG spectral and temporal characteristics requires manipulating electron trajectories on attosecond time scale. The ph...

At the core of attosecond science lies the ability to generate laser pulses of sub-femtosecond duration. In tabletop devices the process relies on high-harmonic generation, where a major challenge is to obtain high yields and high cutoff energies required for the generation of attosecond pulses. We develop a computational method that can simultaneo...

In a note to the second edition of his book on statistical thermodynamics, Schr\"odinger suggests that thermodynamical functions cannot be based on the gratuitous allegation that quantum-mechanical levels (typically the orthogonal eigenstates of the Hamiltonian operator) are the only allowed states for the quantum system. Different authors have int...

We derive the fundamental equations of an optimal control theory for systems containing both quantum electrons and classical ions. The system is modeled with Ehrenfest dynamics, a non-adiabatic variant of molecular dynamics. The general formulation, that needs the fully correlated many-electron wave function, can be simplified by making use of time...

Molecular absorption and photoelectron spectra can be efficiently predicted with real-time time-dependent density functional theory. We show herein how these techniques can be easily extended to study time-resolved pump-probe experiments, in which a system response (absorption or electron emission) to a probe pulse is measured in an excited state....

The combination of time-dependent density functional theory and quantum optimal control formalism is used to optimize the shape of ultra-short laser pulses in order to achieve the photodissociation of the hydrogen molecule. The very short pulse durations used in this work (a few femtoseconds) do not allow for significant nuclear movement during irr...

At non-zero temperature and when a system has low-lying excited electronic states, the ground-state Born-Oppenheimer approximation breaks down and the low-lying electronic states are involved in any chemical process. In this work, we use a temperature-dependent effective potential for the nuclei which can accommodate the influence of an arbitrary n...

Quantum optimal control theory (QOCT) provides the necessary tools to theoretically design driving fields capable of controlling a quantum system towards a given state or along a prescribed path in Hilbert space. This theory must be complemented with a suitable model for describing the dynamics of the quantum system. Here, we are concerned with man...

Octopus is a general-purpose density-functional theory (DFT) code, with a particular emphasis on the time-dependent version of DFT (TDDFT). In this paper we present the ongoing efforts to achieve the parallelization of octopus. We focus on the real-time variant of TDDFT, where the time-dependent Kohn-Sham equations are directly propagated in time....

All applications of time-dependent density-functional theory (TDDFT) until now have attempted to describe the response of many-electron systems to external fields. Given its success in this task, it seems timely, therefore, to address the inverse problem: given a prescribed goal (e.g., the transfer of electronic charge to a given region in space, o...

Ionization and excitation of water molecules in intense laser pulses is studied theoretically by solving the three-dimensional time-dependent electronic Schr\"odinger equation within the single-active-electron approximation. The possibility to image orbital densities by measurement of the orientation-dependent ionization of H2O in few-cycle, 800nm...

Quantum optimal control theory (QOCT) aims at finding an external field that drives a quantum system in such a way that optimally achieves some predefined target. In practice this normally means optimizing the value of some observable, a so called merit function. In consequence, a key part of the theory is a set of equations, which provides the gra...

Quantum dynamics (i.e., the Schr\"odinger equation) and classical dynamics (i.e., Hamilton equations) can both be formulated in equal geometric terms: a Poisson bracket defined on a manifold. In this paper we first show that the hybrid quantum-classical dynamics prescribed by the Ehrenfest equations can also be formulated within this general framew...

We present some approaches to the computation of ultra-fast laser pulses capable of selectively breaking molecular bonds. The calculations are based on a mixed quantum-classical description: The electrons are treated quantum mechanically (making use of time-dependent density-functional theory), whereas the nuclei are treated classically. The tempor...

In principle, we should not need the time-dependent extension of density-functional theory (TDDFT) for excitations, and in particular not for Molecular Dynamics (MD) studies: the theorem by Hohenberg and Kohn teaches us that for any observable that we wish to look at (including dynamical properties or observables dependent on excited states) there...

Quantum optimal control theory is a powerful tool for engineering quantum systems subject to external fields such as the ones created by intense lasers. The formulation relies on a suitable definition for a target functional, that translates the intended physical objective to a mathematical form. We propose the use of target functionals defined in...

Quantum dynamics (e.g., the Schr\"odinger equation) and classical dynamics (e.g., Hamilton equations) can both be formulated in equal geometric terms: a Poisson bracket defined on a manifold. The difference between both worlds is due to the presence of extra structure in the quantum case, that leads to the appearance of the probabilistic nature of...

We prove that for a combined system of classical and quantum particles, it is possible to write a dynamics for the classical particles that incorporates in a natural way the Boltzmann equilibrium population for the quantum subsystem. In addition, these molecular dynamics do not need to assume that the electrons immediately follow the nuclear motion...

The ionization probability of N2, O2, and CO2 in intense laser fields is studied theoretically as a function of the alignment angle by solving the time-dependent Schrödinger equation numerically assuming only the single-active-electron approximation. The results are compared to recent experimental data [D. Pavicić, Phys. Rev. Lett. 98, 243001 (2007...

The ionization probability of N$_2$, O$_2$, and CO$_2$ in intense laser fields is studied theoretically as a function of the alignment angle by solving the time-dependent Schr\"odinger equation numerically assuming only the single-active-electron approximation. The results are compared to recent experimental data [D.~Pavi{\v{c}}i{\'c} et al., Phys....

A new method for solving the electronic three-dimensional time-dependent Schrödinger equation (TDSE) for molecules in ultrashort intense laser fields was developed. In this method the molecules are described within the single-active-electron (SAE) approximation using density-functional theory (DFT). The method and its implementation is tested for H...

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The suitability of the time-dependent density-functional theory (TDDFT) approach for the theoretical study of the optical properties of biomolecules is demonstrated by several examples. We critically discuss the limitations of available TDDFT implementations to address some of the present open questions in the description of the excited-state dynam...

We report linear response properties of the recently proposed boron fullerenes [N. Gonzalez Szwacki et al., Phys. Rev. Lett., 2007, 98, 166804]: magnetic susceptibilities, static dipole polarizabilities and dynamical polarizabilities (i.e. optical and near ultraviolet absorption spectra), calculated from first principles within the (time-dependent)...

We demonstrate how the shape of femtosecond laser pulses can be tailored in order to obtain maximal ionization of atoms or molecules. For that purpose, we have overlayed a direct-optimization scheme on top of a fully unconstrained computation of the three-dimensional time-dependent Schrodinger equation. The procedure looks for pulses that maintain...

We propose the use of mixing strategies to accelerate the convergence of the common iterative algorithms utilized in quantum optimal control theory (QOCT). We show how the nonlinear equations of QOCT can be viewed as a "fixed-point" nonlinear problem. The iterative algorithms for this class of problems may benefit from mixing strategies, as it happ...

We present a reciprocal space technique for the calculation of the Coulomb integral in two dimensions in systems with reduced periodicity, i.e., finite systems, or systems that are periodic only in one dimension. The technique consists in cutting off the long-range part of the interaction by modifying the expression for the Coulomb operator in reci...

Atoms and molecules react in complex manners when they are irradiated with high-intensity electromagnetic pulses: multi-photon, tunnelling and over-the-barrier ionisation, laser driven photo-induced isomerisations or fragmentations, and high harmonic generation are some of the non-linear effects that are observed. The so-called pulse shaping techni...

The quest for more efficient optoelectronic devices requires a thorough understanding of the intrinsic properties of the metallic nanostructures such as the optical spectra. Many optoelectronic devices are based upon gold nanostructures but even though, there is a large set of experimental studies, little is known theoretically. Between the concern...

We present in detail the recently derived ab-initio molecular dynamics (AIMD) formalism [Phys. Rev. Lett. 101 096403 (2008)], which due to its numerical properties, is ideal for simulating the dynamics of systems containing thousands of atoms. A major drawback of traditional AIMD methods is the necessity to enforce the orthogonalization of the wave...

By first-principles time-dependent density-functional calculations, we show the relevance of relativistic effects to shape the photoabsorption cross section of small gold clusters (Au(n), n < or = 8, and n = 20) and small nanowires (n < or = 7). The relativistic effects not only dictate the stabilization of planar geometries (as it has already been...

The polarizability measures how the system responds to an applied electrical field. Computationally, there are many different ways to evaluate this tensorial quantity, some of which rely on the explicit use of the external perturbation and require several individual calculations to obtain the full tensor. In this work, we present some consideration...

We present fully ab-initio calculations of van der Waals coefficients for two different situations: i) the interaction between hydrogenated silicon clusters; and ii) the interactions between these nanostructures and a non metallic surface (a silicon or a silicon carbide surface). The methods used are very efficient, and allow the calculation of sys...

A numerical approach that allows for the solution of the time-dependent Schrödinger equation (TDSE) describing molecules exposed to intense short laser pulses was developed. The molecular response to the strong field is described within the single-active electron approximation (SAE). The method is applied in the fixed-nuclei approximation to molecu...

The concept of the electron localization function (ELF) is extended to two-dimensional (2D) electron systems. We show that the topological properties of the ELF in two dimensions are considerably simpler than in molecules studied previously. We compute the ELF and demonstrate its usefulness for various physical 2D systems focusing on semiconductor...

3 pages, 3 figures.-- PACS nrs.: 78.67.−n; 73.23.Ra; 78.20.Bh.-- Printed version published on Mar 2008. We present two models of coherent quantum switches constructed from a single-electron quantum ring and a double quantum dot, respectively. The systems are driven by picosecond laser pulses obtained using quantum optimal control theory. The optimi...

The success of density functional theory (DFT) is clearly demonstrated by the overwhelming amount of research articles describing results obtained within DFT that were published in the last decades. There is also a fair number of books reviewing the basics of the theory and its extensions (e.g., the present volume, [1] and [2]). These works fall ma...

Coherent single-electron control in a realistic semiconductor double quantum dot is studied theoretically. Using optimal-control theory we show that the energy spectrum of a two-dimensional double quantum dot has a fully controllable transition line. We find that optimized picosecond laser pulses generate population transfer at significantly higher...

The van der Waals dispersion coefficients of a set of polycyclic aromatic hydrocarbons, ranging in size from the single-cycle benzene to circumovalene (C(66)H(20)), are calculated with a real-time propagation approach to time-dependent density functional theory (TDDFT). In the nonretarded regime, the Casimir-Polder integral is employed to obtain C(...

Complete control of single-electron states in a two-dimensional semiconductor quantum-ring model is established, opening a path into coherent laser-driven single-gate qubits. The control scheme is developed in the framework of optimal-control theory for laser pulses of two-component polarization. In terms of pulse lengths and target-state occupatio...

In light matter interaction a ‘strong’ laser field will be defined differently depending on the process under investigation. In the context of this chapter a laser field is considered to be strong if the potential energy surfaces of the irradiated molecule or cluster are altered considerably.

The reactivity between lithium and the Al-{13} cluster is studied using the density functional theory and the local density approximation (LDA) for exchange and correlation. The effects caused by the addition of two Li atoms on the structural and electronic properties of the Al cluster are analyzed by calculating equilibrium geometries, binding ene...

We have calculated the optical absorption spectrum of four isomers of the ionized Vanadium tetramer V-4(+) using the time-dependent density functional theory, with the adiabatic local density approximation for the exchange and correlation potential. The computational scheme is based on a real-time propagation of the time-dependent Kohn-Sham equatio...

The photoabsorption spectra of several of the most stable isomers of the Ti8C12 metallocarbohedryne are calculated using time-dependent density functional theory. Several ground-state magnitudes have been also calculated, such as cohesive energies, electronic gaps between the highest occupied and lowest unoccupied molecular orbitals, and static pol...

The main practical result of the Runge-Gross theorem are the time-dependent Kohn-Sham (TDKS) equations: a set of coupled one-particle Schrödinger-like equations with the form (atomic units are used hereafter)

An extensive study of the optical absorption spectra of the blue fluorescent protein (BFP) is presented. We investigate different protonation states of the chromophore (neutral, anionic, and cationic) and analyze the role of the protein environment and of thermal fluctuations. The role of the environment is 2-fold: (i) it induces structural modific...

The optical absorption spectrum of the Ti8C12, and V8C12 Met-Cars is calculated using time-dependent density functional theory within a real-space, real-time scheme. Other ground-state quantities are also calculated, such as the ionization potential and the electronic affinity. The broad absorption features of the calculated absorption spectrum are...

We review the time-dependent density functional theory (TDDFT) and its use to investigate excited states of nanostructures. These excited states are routinely probed using electromagnetic elds. In this case, two different regimes are usually distinguished: i) If the electromagnetic eld is ìweakî ñ as in optical absorption of light ñ it is sufcient...

In this paper we address the problem of the numerical integration of the time-dependent Schrodinger equation i partial differential (t)phi=Hphi. In particular, we are concerned with the important case where H is the self-consistent Kohn-Sham Hamiltonian that stems from time-dependent functional theory. As the Kohn-Sham potential depends parametrica...

We performed first-principles calculations of the optical response of the green fluorescent protein (GFP) within a combined quantum-mechanical molecular-mechanics and time-dependent density-functional theory approach. The computed spectra are in excellent agreement with experiments assuming the presence of two, protonated and deprotonated, forms of...