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

Controlled deflection of cold atomic clouds and of Bose-Einstein condensates

We present a detailed, realistic proposal and analysis of the implementation of a cold atom deflector using time-dependent far off-resonance optical guides. An analytical model and numerical simulations are used to illustrate its characteristics when applied to both non-degenerate atomic ensembles and to Bose-Einstein condensates. Using for all relevant parameters values that are achieved with present technology, we show that it is possible to deflect almost entirely an ensemble of $^{87}$Rb atoms falling in the gravity field. We discuss the limits of this proposal, and illustrate its robustness against non-adiabatic transitions

Phase information revealed by interferences in the ionization of rotational wavepackets

Time-resolved photoelectron spectra are proposed for the measurement of classical information recorded in the quantum phases of a molecular rotational wavepacket. Taking Li2 as a prototypical system, we show that an interference arises from the electron-nuclei entanglement induced by the molecular anisotropy. This phenomenon is used to transfer the information which has been stored initially in the nuclear rotational degree of freedom into the electronic degree of freedom

Coherent Control of Isotope Separation in HD+ Photodissociation by Strong Fields

The photodissociation of the HD+ molecular ion in intense short- pulsed linearly polarized laser fields is studied using a time- dependent wave-packet approach where molecular rotation is fully included. We show that applying a coherent superposition of the fundamental radiation with its second harmonic can lead to asymmetries in the fragment angular distributions, with significant differences between the hydrogen and deuterium distributions in the long wavelength domain where the permanent dipole is most efficient. This effect is used to induce an appreciable isotope separation.Comment: Physical Review Letters, 1995 (in press). 4 pages in revtex format, 3 uuencoded figures. Full postcript version available at: http://chemphys.weizmann.ac.il/~charron/prl.ps or ftp://scipion.ppm.u-psud.fr/coherent.control/prl.p

Effect of picosecond strain pulses on thin layers of the ferromagnetic semiconductor (Ga,Mn)(As,P)

The effect of picosecond acoustic strain pulses (ps-ASP) on a thin layer of (Ga,Mn)As co-doped with phosphorus was probed using magneto-optical Kerr effect (MOKE). A transient MOKE signal followed by low amplitude oscillations was evidenced, with a strong dependence on applied magnetic field, temperature and ps-ASP amplitude. Careful interferometric measurement of the layer's thickness variation induced by the ps-ASP allowed us to model very accurately the resulting signal, and interpret it as the strain modulated reflectivity (differing for $\sigma_{\pm}$ probe polarizations), independently from dynamic magnetization effects.Comment: 6 pages, 5 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

Conceptually driven and visually rich tasks in texts and teaching practice: the case of infinite series

The study we report here examines parts of what Chevallard calls the institutional dimension of the students’ learning experience of a relatively under-researched, yet crucial, concept in Analysis, the concept of infinite series. In particular, we examine how the concept is introduced to students in texts and in teaching practice. To this purpose, we employ Duval's Theory of Registers of Semiotic Representation towards the analysis of 22 texts used in Canada and UK post-compulsory courses. We also draw on interviews with in-service teachers and university lecturers in order to discuss briefly teaching practice and some of their teaching suggestions. Our analysis of the texts highlights that the presentation of the concept is largely a-historical, with few graphical representations, few opportunities to work across different registers (algebraic, graphical, verbal), few applications or intra-mathematical references to the concept's significance and few conceptually driven tasks that go beyond practising with the application of convergence tests and prepare students for the complex topics in which the concept of series is implicated. Our preliminary analysis of the teacher interviews suggests that pedagogical practice often reflects the tendencies in the texts. Furthermore, the interviews with the university lecturers point at the pedagogical potential of: illustrative examples and evocative visual representations in teaching; and, student engagement with systematic guesswork and writing explanatory accounts of their choices and applications of convergence tests