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Working with trapped atoms at close distance to each other, we show that one can implement entangling gates based on non-independent qubits using a single pulse per qubit, or a single structured pulse. The optimal parameters depend on approximate solutions of Diophantine equations, causing the fidelity to never be exactly perfect, even under ideal conditions, although the errors can be made arbitrarily smaller at the cost of stronger fields. We fully characterize the mechanism by which the gates operate, and show that the main source of error in realistic implementations comes from fluctuations in the peak intensity, which especially damages the fidelity of the gates that use stronger fields. Working with two-pulse sequences, instead of one, enables the use of a plethora of mechanisms and a broad range of optimal parameters to choose from, to achieve high-fidelity gates., Comment: 10 pages, 7 figures

In this study, we present a revision of the Quantum Optimal Control Theory (QOCT) originally proposed by Rabitz et al (Phys. Rev. A 37, 49504964 (1988)), which has broad applications in physical and chemical physics. First, we identify the QOCT equations as the Euler-Lagrange equations of the functional associated to the control scheme. In this framework we prove that the extremal functions found by Rabitz are not continuous, as it was claimed in previous works. Indeed, we show that the costate is discontinuous and vanishes after the measurement time. In contrast, we demonstrate that the driving field is continuous. We also identify a new set of continuous solutions to the QOCT. Overall, our work provides a significant contribution to the QOCT theory, promoting a better understanding of the mathematical solutions and offering potential new directions for optimal control strategies., Comment: 18 pages, 2 figures

We use a novel optimization procedure that includes the temporal and spatial parameters of the pulses acting on arrays of trapped neutral atoms, to prepare entangling gates in N-qubits systems. The spatio-temporal control allows treating a denser array of atoms, where each pulse acts on a subset of the qubits, potentially allowing to speed the gate operation by two orders of magnitude by boosting the dipole-blockade between the Rydberg states. Studying the rate of success of the algorithm under different constraints, we evaluate the impact of the proximity of the atoms and, indirectly, the role of the geometry of the arrays in 3 and 4-qubit systems, as well as the minimal energy requirements and how this energy is used among the different qubits. Finally, we characterize and classify all optimal protocols according to the mechanism of the gate, using a quantum pathways analysis., Comment: 10 pages, 8 figures

By controlling the temporal and spatial features of light, we propose a novel protocol to prepare two-qubit entangling gates on atoms trapped at close distance, which could potentially speed up the operation of the gate from the sub-micro to the nanosecond scale. The protocol is robust to variations in the pulse areas and the position of the atoms, by virtue of the coherent properties of a dark state, which is used to drive the population through Rydberg states. From the time-domain perspective, the protocol generalizes the one proposed by Jaksch and coworkers [Jaksch et al., Phys. Rev. Lett. 85, 2208 (2000)], with three pulses that operate symmetrically in time, but with different pulse areas. From the spatial-domain perspective, it uses structured light. We analyze the map of the gate fidelity, which forms rotated and distorted lattices in the solution space. Finally, we study the effect of an additional qubit to the gate performance and propose generalizations that operate with multi-pulse sequences., Comment: 9 pages, 7 figures

We characterize the set of optimal protocols for two-qubit entangling gates through a mechanism analysis based on quantum pathways, which allows us to compare and rank the different solutions. As an example of a flexible platform with a rich landscape of protocols, we consider trapped neutral atoms excited to Rydberg states by different pulse sequences that extend over several atomic sites, optimizing both the temporal and the spatial features of the pulses. Studying the rate of success of the algorithm under different constraints, we analyze the impact of the proximity of the atoms on the nature and quality of the optimal protocols. We characterize in detail the features of the solutions in parameter space, showing some striking correlations among the set of parameters. Together with the mechanism analysis, the spatio-temporal control allows us to select protocols that operate under mechanisms by design, like finding needles in the haystack., Comment: 12 pages, 9 figures

We predict anti-alignment dynamics in the excited state of H2+ or related homonuclear dimers in the presence of a strong field. This effect is a general indirect outcome of the strong transition dipole and large polarizabilities typically used to control or to induce alignment in the ground state. In the excited state, however, the polarizabilities have the opposite sign than in the ground state, generating a torque that aligns the molecule perpendicular to the field, deeming any laser-control strategy impossible., Comment: 4 figures

The two-dimensional electron-nuclear Schr\"odinger equation using soft-core Coulomb potentials has been a cornerstone for modeling and predicting the behavior of one-active-electron diatomic molecules, particularly for processes where both bound and continuum states are important. The model, however, is computationally expensive to extend to more electron or nuclear coordinates. Here we propose to use the Ehrenfest approach to treat the nuclear motion, while the electronic motion is still solved by quantum propagation on a grid. In this work we present results for a one-dimensional treatment of H$_2^+$, where the quantum and semi-classical dynamics can be directly compared, showing remarkably good agreement for a variety of situations. The advantage of the Ehrenfest approach is that it can be easily extended to treat as many nuclear degrees of freedom as needed.

We study electron transfer between two separated nuclei using local control theory. By conditioning the algorithm in a symmetric system formed by two protons, one can favored slow transfer processes, where tunneling is the main mechanism, achieving transfer efficiencies close to unity assuming fixed nuclei. The solution can be parametrized using sequences of pump and dump pi pulses, where the pump pulse is used to excite the electron to a highly excited state where the time for tunneling to the target nuclei is on the order of femtoseconds. The time delay must be chosen to allow for full population transfer via tunneling, and the dump pulse is chosen to remove energy from the state to avoid tunneling back to the original proton. Finally, we study the effect of the nuclear kinetic energy on the transfer efficiency. Even in the absence of relative motion between the protons, the spreading of the nuclear wave function is enough to reduce the yield of electronic transfer to less than one half., Comment: 7 pages, 8 figures

We study laser-driven isomerization reactions through an excited electronic state using the recently developed Geometrical Optimization procedure [J. Phys. Chem. Lett. 6, 1724 (2015)]. The goal is to analyze whether an initial wave packet in the ground state, with optimized amplitudes and phases, can be used to enhance the yield of the reaction at faster rates, exploring how the geometrical restrictions induced by the symmetry of the system impose limitations in the optimization procedure. As an example we model the isomerization in an oriented 2,2'-dimethyl biphenyl molecule with a simple quartic potential. Using long (picosecond) pulses we find that the isomerization can be achieved driven by a single pulse. The phase of the initial superposition state does not affect the yield. However, using short (femtosecond) pulses, one always needs a pair of pulses to force the reaction. High yields can only be obtained by optimizing both the initial state, and the wave packet prepared in the excited state, implying the well known pump-dump mechanism.

We discover a new mechanism of electronic population inversion using strong femtosecond pulses, where the transfer is mediated by vibrational motion on a light-induced potential. The process can be achieved with a single pulse tuning its frequency to the red of the Franck-Condon window. We show the determinant role that the sign of the slope of the transition dipole moment can play on the dynamics, and extend the method to multiphoton processes with odd number of pulses. As an example, we show how the scheme can be applied to population inversion in Na2., Comment: 5 pages, 5 figures

A new perspective on how to manipulate molecules by means of very strong laser pulses is emerging with insights from the so-called light-induced potentials, which are the adiabatic potential energy surfaces of molecules severely distorted by the effect of the strong field. Different effects appear depending on how the laser frequency is tuned, to a certain electronic transition, creating light-induced avoided crossings, or very off-resonant, generating Stark shifts. In the former case it is possible to induce dramatic changes in the geometry and redistribution of charges in the molecule while the lasers are acting and to fully control photodissociation reactions as well as other photochemical processes. Several theoretical proposals taken from the work of the authors are reviewed and analyzed showing the unique features that the strong-laser chemistry opens to control the transient properties and the dynamics of molecules., Comment: 14 pages, 10 figures

Using numerical simulations of two-photon electronic absorption with femtosecond pulses in Na$_2$ we show that: i) it is possible to avoid the characteristic saturation or dumped Rabi oscillations in the yield of absorption by time-delaying the laser pulses; ii) it is possible to accelerate the onset of adiabatic passage by using the vibrational coherence starting in a wave packet; and iii) it is possible to prepare the initial wave packet in order to achieve full state-selective transitions with broadband pulses. The findings can be used, for instance, to achieve ultrafast adiabatic passage by light-induced potentials and understand its intrinsic robustness., Comment: 5 pages, 6 figures

Quantum systems with sublevel structures prevent full population inversion from one manifold of sublevels to the other using strong ultrafast resonant pulses. In this work we explain the mechanism by which this population transfer is blocked. We then develop a novel concept of geometric control, assuming full or partial coherent manipulation within the manifolds and show that by preparing specific coherent superpositions in the initial manifold, full population inversion or full population blockade, {\it i.e} laser-induced transparency, can be achieved. In particular, by parallel population transfer we show how population inversion between the manifolds can be obtained with minimal pulse area. As the number of sublevels increases, population inversion can overcome the pulse area theorem at the expense of full control over the initial manifold of sublevels.

We show that a counter-intuitive pulse sequence leads to adiabatic passage between the vibrational levels of three harmonic potentials through parallel dark states in adiabatic approximation. However, the adiabatic assumptions break down for very intense pulses and non-adiabatic couplings result in the population transfer by light-induced potential shaping., Comment: 5 pages, 2 figures