Clusters of Exceptional Points for a Laser Control of Selective Vibrational Transfer

When a molecule is exposed to a laser field, all field-free vibrational states become resonances, with complex quasi energies calculated using Floquet theory. There are many ways to produce the coalescences of pairs of such quasi energies, with appropriate wavelength-intensity choices which define Exceptional Points (EP) in the laser parameter plane. We dress for the molecular ion H$_2^+$ an exhaustive map of these exceptional points which appear in clusters. Such clusters can be used to define several vibrational transfer scenarios implying more than a single exceptional point, exchanging single or multiple vibrational quanta. The ultimate goal is molecular vibrational cooling by transferring an initial (thermal, for instance) population on a final (ground, for instance) single vibrational state. When a molecule is exposed to a laser field, all field-free vibrational states become resonances, with complex quasi energies calculated using Floquet theory. There are many ways to produce the coalescences of pairs of such quasi energies, with appropriate wavelength-intensity choices which define Exceptional Points (EP) in the laser parameter plane. We dress for the molecular ion H$_2^+$ an exhaustive map of these exceptional points which appear in clusters. Such clusters can be used to define several vibrational transfer scenarios implying more than a single exceptional point, exchanging single or multiple vibrational quanta. The ultimate goal is molecular vibrational cooling by transferring an initial (thermal, for instance) population on a final (ground, for instance) single vibrational state.Comment: 16 pages, 7 figures, 1 tabl

Molecular orientation entanglement and temporal Bell-type inequalities

We detail and extend the results of [Milman {\it et al.}, Phys. Rev. Lett. {\bf 99}, 130405 (2007)] on Bell-type inequalities based on correlations between measurements of continuous observables performed on trapped molecular systems. We show that for some observables with a continuous spectrum which is bounded, one is able to construct non-locality tests sharing common properties with those for two-level systems. The specific observable studied here is molecular spatial orientation, and it can be experimentally measured for single molecules, as required in our protocol. We also provide some useful general properties of the derived inequalities and study their robustness to noise. Finally, we detail possible experimental scenarii and analyze the role played by different experimental parameters.Comment: 10 pages and 5 figure

Anisotropy Control in Photoelectron Spectra: A Coherent Two-Pulse Interference Strategy

Coherence among rotational ion channels during photoionization is exploited to control the anisotropy of the resulting photoelectron angular distributions at specific photoelectron energies. The strategy refers to a robust and single parameter control using two ultra-short light pulses delayed in time. The first pulse prepares a superposition of a few ion rotational states, whereas the second pulse serves as a probe that gives access to a control of the molecular asymmetry parameter $\beta$ for individual rotational channels. This is achieved by tuning the time delay between the pulses leading to channel interferences that can be turned from constructive to destructive. The illustrative example is the ionization of the $E(1\Sigma_{g}^{+})$ state of Li$_{2}$. Quantum wave packet evolutions are conducted including both electronic and nuclear degrees of freedom to reach angle-resolved photoelectron spectra. A simple interference model based on coherent phase accumulation during the field-free dynamics between the two pulses is precisely exploited to control the photoelectron angular distributions from almost isotropic, to marked anisotropic

Molecular Alignment and Orientation: From Laser-Induced Mechanisms to Optimal Control

Genetic algorithms, as implemented in optimal control strategies, are currently successfully exploited in a wide range of problems in molecular physics. In this context, laser control of molecular alignment and orientation remains a very promising issue with challenging applications extending from chemical reactivity to nanoscale design. We emphasize the complementarity between basic quantum mechanisms monitoring alignment/orientation processes and optimal control scenarios. More explicitly, if on one hand we can help the optimal control scheme to take advantage of such mechanisms by appropriately building the targets and delineating the parameter sampling space, on the other hand we expect to learn, from optimal control results, some robust and physically sound dynamical mechanisms. We present basic mechanisms for alignment and orientation, such as pendular states accommodated by the molecule-plus-field effective potential and the "kick" mechanism obtained by a sudden excitation. Very interestingly, an optimal control scheme for orientation, based on genetic algorithms, also leads to a sudden pulsed field bearing the characteristic features of the kick mechanism. Optimal pulse shaping for very efficient and long-lasting orientation, together with robustness with respect to temperature effects, are among our future prospects

Towards Laser Control of Open Quantum Systems: Memory Effects

Laser control of Open Quantum Systems (OQS) is a challenging issue as compared to its counterpart in isolated small size molecules, basically due to very large numbers of degrees of freedom to be accounted for. Such a control aims at appropriately optimizing decoherence processes of a central two-level system (a given vibrational mode, for instance) towards its environmental bath (including, for instance, all other normal modes). A variety of applications could potentially be envisioned, either to preserve the central system from decaying (long duration molecular alignment or orientation, qubit decoherence protection) or, to speed up the information flow towards the bath (efficient charge or proton transfers in long chain organic compounds). Achieving such controls require some quantitative measures of decoherence in relation with memory effects in the bath response, actually given by the degree of non-Markovianity. Characteristic decoherence rates of a Spin-Boson model are calculated using a Nakajima-Zwanzig type master equation with converged HEOM expansion for the memory kernel. It is shown that, by adequately tuning the two-level transition frequency through a controlled Stark shift produced by an external laser field, non-Markovianity can be enhanced in a continuous way leading to a first attempt towards the control of OQS

Time-dependent unitary perturbation theory for intense laser driven molecular orientation

We apply a time-dependent perturbation theory based on unitary transformations combined with averaging techniques, on molecular orientation dynamics by ultrashort pulses. We test the validity and the accuracy of this approach on LiCl described within a rigid-rotor model and find that it is more accurate than other approximations. Furthermore, it is shown that a noticeable orientation can be achieved for experimentally standard short laser pulses of zero time average. In this case, we determine the dynamically relevant parameters by using the perturbative propagator, that is derived from this scheme, and we investigate the temperature effects on the molecular orientation dynamics.Comment: 16 pages, 6 figure

Quantum phase gate and controlled entanglement with polar molecules

We propose an alternative scenario for the generation of entanglement between rotational quantum states of two polar molecules. This entanglement arises from dipole-dipole interaction, and is controlled by a sequence of laser pulses simultaneously exciting both molecules. We study the efficiency of the process, and discuss possible experimental implementations with cold molecules trapped in optical lattices or in solid matrices. Finally, various entanglement detection procedures are presented, and their suitability for these two physical situations is analyzed

Ultrafast Molecular Imaging by Laser Induced Electron Diffraction

We address the feasibility of imaging geometric and orbital structure of a polyatomic molecule on an attosecond time-scale using the laser induced electron diffraction (LIED) technique. We present numerical results for the highest molecular orbitals of the CO2 molecule excited by a near infrared few-cycle laser pulse. The molecular geometry (bond-lengths) is determined within 3% of accuracy from a diffraction pattern which also reflects the nodal properties of the initial molecular orbital. Robustness of the structure determination is discussed with respect to vibrational and rotational motions with a complete interpretation of the laser-induced mechanisms