Claude M. Dion

TWO-FREQUENCY IR LASER ORIENTATION OF POLAR MOLECULES. NUMERICAL SIMULATIONS FOR HCN

Abstract Using ab initio nuclear-coordinate-dependent dipole moments and polarizabilities, we study the orientation dynamics of HCN, by numerically solving the time-dependent Schrodinger equation, in the presence of a superposition of intense, linearly-polarized infrared laser pulses of frequency ω and 2ω. We show that polarizability acts in concert with permanent dipole moments to orient polar molecules, as opposed to alignment which occurs alone with a single laser frequency or one moment only (permanent or induced). Optimal orientation occurs for the field configuration E (t)= E 0 (t) cos ωt+0.5 cos 2ωt , where 2ω is resonant with a 0 → 1 vibrational transition and E 0 (t) is a picosecond pulse.

Optimal molecular alignment and orientation through rotational ladder climbing

We study the control by electromagnetic fields of molecular alignment and orientation in a linear, rigid-rotor model. With the help of a monotonically convergent algorithm, we find that the optimal field is in the microwave part of the spectrum and acts by resonantly exciting the rotation of the molecule progressively from the ground state, i.e., by rotational ladder climbing. This mechanism is present not only when maximizing orientation or alignment, but also when using prescribed target states that simultaneously optimize the efficiency of orientation/alignment and its duration. The extension of the optimization method to consider a finite rotational temperature is also presented.

Reaching optimally oriented molecular states by laser kicks

We present a strategy for postpulse molecular orientation aiming both at efficiency and maximal duration within a rotational period. We first identify the optimally oriented states which fulfill both requirements. We show that a sequence of half-cycle pulses of moderate intensity can be devised for reaching these target states.

NUMERICAL SIMULATION OF THE ISOMERIZATION OF HCN BY TWO PERPENDICULAR INTENSE IR LASER PULSES

Isomerization of HCN is studied numerically for a laser excitation configuration of two perpendicular intense IR pulses. This scheme confines the molecule to a plane and promotes proton transfer along the curved reaction path. It is shown that internal rotation of the CN group enhances isomerization when compared to a fixed C≡N orientation model. Isomerization rates with rotation exceed those without rotation of the CN by about a factor of 3. Internal rotation also enhances dissociation and destroys phase control of the isomerization. It is found that at intensities I∼1013 W/cm2, maximum isomerization occurs with negligible dissociation for a 2 ps pulse excitation. Maximum isomerization is also found for one field frequency resonant with the CH bend frequency ωbend and the other perpendicular frequency at 2ωbend.

Spectral method for the time-dependent Gross-Pitaevskii equation with a harmonic trap

We study the numerical resolution of the time-dependent Gross-Pitaevskii equation, a nonlinear Schrödinger equation used to simulate the dynamics of Bose-Einstein condensates. Considering condensates trapped in harmonic potentials, we present an efficient algorithm by making use of a spectral-Galerkin method, using a basis set of harmonic-oscillator functions, and the Gauss-Hermite quadrature. We apply this algorithm to the simulation of condensate breathing and scissor modes.

Evolutionary algorithms for the optimal laser control of molecular orientation

In terms of optimal control, laser-induced molecular orientation is an optimization problem involving a global minimum search on a multi-dimensional surface function of varying parameters characterizing the laser pulse (frequency, peak intensity, temporal shape). Genetic algorithms, aiming at the optimization of different possible targets, may temporarily be trapped in a local minimum, before reaching the global one. A careful study of such local (robust) minima provides a key for the thorough interpretation of the orientation dynamics, in terms of basic mechanisms. Two targets are retained: the first, simple, one searching for an angle between molecular and laser polarization axes as close as possible to zero (orientation) at a given time; the second, hybrid, one combining the efficiency of orientation with its duration. Their respective roles are illustrated referring to two molecular systems, HCN and LiF, taken at a rigid rotor approximation level. A sudden and asymmetric laser pulse (provided by a frequency ω superposed on its second harmonic 2ω) leads to the kick mechanism. The result is a very fast (as compared to the rotational period) angular momentum transfer to the molecule, that turns out to be responsible for an efficient orientation after the laser pulse is turned off.

Ground state of the time-independent Gross-Pitaevskii equation

We present a suite of programs to determine the ground state of the time-independent Gross-Pitaevskii equation, used in the simulation of Bose-Einstein condensates. The calculation is based on the Optimal Damping Algorithm, ensuring a fast convergence to the true ground state. Versions are given for the one-, two-, and three-dimensional equation, using either a spectral method, well suited for harmonic trapping potentials, or a spatial grid.

Control of mixed-state quantum systems by a train of short pulses

A density matrix approach is developed for the control of a mixed-state quantum system using a time-dependent external field such as a train of pulses. This leads to the definition of a target density matrix constructed in a reduced Hilbert space as a specific combination of the eigenvectors of a given observable through weighting factors related to the initial statistics of the system. A train of pulses is considered as a possible strategy to reach this target. An illustration is given by considering the laser control of molecular alignment and orientation in thermal equilibrium.

Optimally Controlled Field-Free Orientation of the Kicked Molecule

Efficient and long-lived field-free molecular orientation is achieved using only two kicks appropriately delayed in time. The understanding of the mechanism rests upon a molecular target state providing the best efficiency versus persistence compromise. An optimal control scheme is referred to for fixing the free parameters (amplitudes and the time delay between them). The limited number of kicks, the robustness and the transposability to different molecular systems advocate in favor of the process, when considering its experimental feasibility.

OPTIMAL LASER CONTROL OF MOLECULAR SYSTEMS: METHODOLOGY AND RESULTS

We report on some mathematical and numerical work related to the control of the evolution of molecular systems using laser fields. More precisely, the control of the orientation of molecules is our goal. We treat this as an optimal control problem and optimize the laser field to be used experimentally by using both deterministic and stochastic algorithms. Comparisons between the different strategies are drawn. In particular, when gradients of the cost functional are used, the different ways for their computation are compared and analyzed.