Impact of Early Coherences on the Control of Ultrafast Photodissociation Reactions

By coherent control, the yield of photodissociation reactions can be maximized, starting in a suitable superposition of vibrational states. In ultrafast processes, the interfering pathways are born from the early vibrational coherences in the ground electronic potential. We interpret their effect from a purely classical picture, in which the correlation between the initial position and momentum helps to synchronize the vibrational dynamics at the Franck-Condon window when the pulse is at its maximum intensity. In the quantum domain, we show that this localization in time and space is mediated by dynamic squeezing of the wave packet.

Control of concerted back-to-back double ionization dynamics in helium

Double ionization (DI) is a fundamental process that despite its apparent simplicity provides rich opportunities for probing and controlling the electronic motion. Even for the simplest multielectron atom, helium, new DI mechanisms are still being found. To first order in the field strength, a strong external field doubly ionizes the electrons in helium such that they are ejected into the same direction (front-to-back motion). The ejection into opposite directions (back-to-back motion) cannot be described to first order, making it a challenging target for control. Here, we address this challenge and optimize the field with the objective of back-to-back double ionization using a (1 + 1)-dimensional model. The optimization is performed using four different control procedures: (1) short-time control, (2) derivative-free optimization of basis expansions of the field, (3) the Krotov method, and (4) control of the classical equations of motion. All four procedures lead to fields with dominant back-to-back motion. All the fields obtained exploit essentially the same two-step mechanism leading to back-to-back motion: first, the electrons are displaced by the field into the same direction. Second, after the field turns off, the nuclear attraction and the electron-electron repulsion combine to generate the final motion into opposite directions for each electron. By performing quasi-classical calculations, we confirm that this mechanism is essentially classical.

Exploring the complexity of quantum control optimization trajectories

The control of quantum system dynamics is generally performed by seeking a suitable applied field. The physical objective as a functional of the field forms the quantum control landscape, whose topology, under certain conditions, has been shown to contain no critical point suboptimal traps, thereby enabling effective searches for fields that give the global maximum of the objective. This paper addresses the structure of the landscape as a complement to topological critical point features. Recent work showed that landscape structure is highly favorable for optimization of state-to-state transition probabilities, in that gradient-based control trajectories to the global maximum value are nearly straight paths. The landscape structure is codified in the metric R ≥ 1.0, defined as the ratio of the length of the control trajectory to the Euclidean distance between the initial and optimal controls. A value of R = 1 would indicate an exactly straight trajectory to the optimal observable value. This paper extends the state-to-state transition probability results to the quantum ensemble and unitary transformation control landscapes. Again, nearly straight trajectories predominate, and we demonstrate that R can take values approaching 1.0 with high precision. However, the interplay of optimization trajectories with critical saddle submanifolds is found to influence landscape structure. A fundamental relationship necessary for perfectly straight gradient-based control trajectories is derived, wherein the gradient on the quantum control landscape must be an eigenfunction of the Hessian. This relation is an indicator of landscape structure and may provide a means to identify physical conditions when control trajectories can achieve perfect linearity. The collective favorable landscape topology and structure provide a foundation to understand why optimal quantum control can be readily achieved.

Optimal control of charge transfer for slow H+ + D collisions with shaped laser pulses

We show that optimally shaped laser pulses can beneficially influence charge transfer in slow H(+)+D collisions. Time-dependent wave packet optimal control simulations are performed based on a two-state adiabatic Hamiltonian. Optimal control is performed using either an adaptive or a fixed target to obtain the desired laser control field. In the adaptive target scheme, the target state is updated according to the renormalized fragmentary yield in the exit channel throughout the optimization process. In the fixed target scheme, the target state in the exit channel is a normalized outgoing Gaussian wave packet located at a large internuclear separation. Both approaches produced excellent optimal outcomes, far exceeding that achieved in the field-free collisional charge transfer. The adaptive target scheme proves to be more efficient, and often with complex final wave packet. In contrast, the fixed target scheme, although more slowly convergent, is found to produce high fidelity for the desired target wave packet. The control mechanism in both cases utilizes bound vibrational states of the transient HD(+) complex.

Photophysics of fulvene under the non-resonant stark effect. Shaping the conical intersection seam

We introduce a mechanistic strategy to control the excited state lifetime of fulvene based on shaping the topography of an extended seam of intersection with the non-resonant dynamic Stark effect. Fulvene has a very short excited state lifetime due to an energetically accessible seam of intersection which lies along the methylene torsion coordinate, and the initial decay occurs at the seam segment around the planar conical intersection structure. We have followed a three-step approach to simulate the control. First, we have calculated the effect of a non-resonant electric field on the potential energy surface at the ab initio level, including the field in a self-consistent way. The relative energy of the planar segment of the seam is increased by the non-resonant field. In the second step we simulate the control carrying out MCTDH quantum dynamics propagations under a static non-resonant field to derive the main control mechanisms. At moderately intense fields (epsilon < or = 0.03 a.u.) the decay is faster as compared to the field free case because the vibrational overlap between the excited and ground state vibrational functions is increased. However, at more intense fields (epsilon = 0.04 a.u.) the planar conical intersection is energetically inaccessible and the decay occurs at a slower time scale, at the segment of the seam with more twisted geometries. In the third step, the control over the dynamics is exerted with a non-resonant dynamic field. The acceleration of the decay due to the improved vibrational overlap does not occur, but the decay can be made slower with a dynamic field of 0.08 a.u. The results show the viability of our approach to control the photophysics shaping the topology of the conical intersection seam, and they prove that the extended nature of the seam is crucial for simulating and understanding the control.

Controlling the dynamics of many-electron systems from first principles: a combination of optimal control and time-dependent density-functional theory

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 many electron systems (atoms, molecules, quantum dots, etc.) irradiated with laser pulses. The full solution of the many-electron Schrödinger equation is not feasible in general, and therefore, if we aim for an ab initio description, a suitable choice is the time-dependent density-functional theory (TDDFT). In this Letter, we establish the equations that combine TDDFT with QOCT and demonstrate their numerical feasibility.

Design of an infrared laser pulse to control the multiphoton dissociation of the Fe-CO bond in CO-heme compounds

Optimal control theory is used to design a laser pulse for the multiphoton dissociation of the Fe-CO bond in the CO-heme compounds. The study uses a hexacoordinated iron-porphyrin-imidazole-CO complex in its ground electronic state as a model for CO liganded to the heme group. The potential energy and dipole moment surfaces for the interaction of the CO ligand with the heme group are calculated using density functional theory. Optimal control theory, combined with a time-dependent quantum dynamical treatment of the laser-molecule interaction, is then used to design a laser pulse capable of efficiently dissociating the CO-heme complex model. The genetic algorithm method is used within the mathematical framework of optimal control theory to perform the optimization process. This method provides good control over the parameters of the laser pulse, allowing optimized pulses with simple time and frequency structures to be designed. The dependence of photodissociation yield on the choice of initial vibrational state and of initial laser field parameters is also investigated. The current work uses a reduced dimensionality model in which only the Fe-C and C-O stretching coordinates are explicitly taken into account in the time-dependent quantum dynamical calculations. The limitations arising from this are discussed in Sec. IV.

Quantum gate operations using midinfrared binary shaped pulses on the rovibrational states of carbon monoxide

Frequency domain shaped binary laser pulses were optimized to perform 2 qubit quantum gate operations in (12)C(16)O. The qubit rovibrational state representation was chosen so that all gate operations consisted of one-photon transitions. The amplitude and phase varied binary pulses were determined using a genetic algorithm optimization routine. Binary pulses have two possible amplitudes, 0 or 1, and two phases, 0 or pi, for each frequency component of the pulse. Binary pulses are the simplest to shape experimentally and provide a minimum fidelity limit for amplitude and phase shaped pulses. With the current choice of qubit representation and using optimized binary pulses, fidelities of 0.80 and as high as 0.97 were achieved for the controlled-NOT and alternative controlled-NOT quantum gates. This indicates that with a judicious choice of qubits, most of the required control can be obtained with a binary pulse. Limited control was observed for 2 qubit NOT and Hadamard gates due to the need to control multiple excitations. The current choice of qubit representation produces pulses with decreased energies and superior fidelities when compared with rovibrational qubit representations consisting of two-photon transitions. The choice of input pulse energy is important and applying pulses of increased energy does not necessarily lead to a better fidelity.