Diffractive mirrors for neutral-atom matter-wave optics.

Mirrors for atoms and molecules are essential tools for matter-wave optics with neutral particles. Their realization has required either a clean and atomically smooth crystal surface, sophisticated tailored electromagnetic fields, nanofabrication, or particle cooling because of the inherently short de Broglie wavelengths and strong interactions of atoms with surfaces. Here, we demonstrate reflection of He atoms from inexpensive, readily available, and robust gratings designed for light waves. Using different types of blazed gratings with different periods, we study how microscopic and macroscopic grating properties affect the mirror performance. A holographic grating with 417 nm period shows reflectivity up to 47% for He atoms, demonstrating that commercial gratings can serve as mirrors for thermal energy atoms and molecules. We also observe reflection of He2 and He3 which implies that the grating might also function as a mirror for other breakable particles that, under typical conditions, do not scatter nondestructively from a solid surface such as, e.g., metastable atoms or antihydrogen atoms.

Enhanced elastic scattering of He2 and He3 from solids by multiple-edge diffraction.

We report on a method of enhanced elastic and coherent reflection of 4He2 and 4He3 from a micro-structured solid surface under grazing incidence conditions. The van der Waals bound ground-state helium clusters exhibit fundamental quantum effects: 4He2, characterized by a single ro-vibrational bound state of 10-7 eV dissociation energy, is known to be a quantum halo state; and 4He3 is the only electronic ground-state triatomic system possessing an Efimov state in addition to the ro-vibrational ground state. Classical methods to select and manipulate these clusters by interaction with a solid surface fail due to their exceedingly fragile bonds. Quantum reflection under grazing incidence conditions was demonstrated as a viable tool for elastic scattering from a solid surface but suffers from small reflection probabilities for typical conditions. Here we demonstrate that multiple-edge diffraction enables enhanced elastic scattering of the clusters from a solid. A dual-period reflection grating, where the strips consist of micro-structured edge arrays, shows an up to ten fold increased reflection probability as compared to its conventional counterpart where the strips are plane patches enabling quantum reflection of the clusters. The observed diffraction patterns of the clusters provide evidence of the coherent and elastic nature of scattering by multiple-edge diffraction.

Experimental test of Babinet's principle in matter-wave diffraction.

We report on an experimental test of Babinet's principle in quantum reflection of an atom beam from diffraction gratings. The He beam is reflected and diffracted from a square-wave grating at near grazing-incidence conditions. According to Babinet's principle the diffraction peak intensities (except for the specular-reflected beam) are expected to be identical for any pair of gratings of complementary geometry. We observe conditions where Babinet's principle holds and also where it fails. Our data indicate breakdown conditions when either the incident or a diffracted beam propagates close to the grating surface. At these conditions, the incident or the diffracted He beam is strongly affected by the dispersive interaction between the atoms and the grating surface. Babinet's principle is also found to break down, when the complementary grating pair shows a large asymmetry in the strip widths. For very small strip widths, edge diffraction from half planes becomes dominant, whereas for the complementary wide strips the atom-surface interactions leads to a strong reduction of all non-specular diffraction peak intensities.

Scattering of adiabatically aligned molecules by nonresonant optical standing waves.

We study the effect of rotational state-dependent alignment in the scattering of molecules by optical fields. CS2 molecules in their lowest few rotational states are adiabatically aligned and transversely accelerated by a nonresonant optical standing wave. The width of the measured transverse velocity distribution increases to 160 m/s with the field intensity, while its central peak position moves from 10 to -10 m/s. These changes are well reproduced by numerical simulations based on the rotational state-dependent alignment but cannot be modeled when ignoring these effects. Moreover, the molecular scattering by an off-resonant optical field amounts to manipulating the translational motion of molecules in a rotational state-specific way. Conversely, our results demonstrate that scattering from a nonresonant optical standing wave is a viable method for rotational state selection of nonpolar molecules.

Matter-Wave Diffraction from a Periodic Array of Half Planes.

We report on reflection and diffraction of beams of He and D_{2} from square-wave gratings of a 400-µm period and strip widths ranging from 10 to 200 µm at grazing-incidence conditions. In each case we observe fully resolved matter-wave diffraction patterns including the specular reflection and diffracted beams up to the second diffraction order. With decreasing strip width, the observed diffraction efficiencies exhibit a transformation from the known regime of quantum reflection from the grating strips to the regime of edge diffraction from a half-plane array. The latter is described by a single-parameter model developed previously to describe phenomena as diverse as quantum billiards, scattering of radio waves in urban areas, and reflection of matter waves from microstructures. Our data provide experimental confirmation of the widespread model. Moreover, our results demonstrate that neither classical reflection nor quantum reflection are essential for reflective diffraction of matter waves from a structured solid, but it can result exclusively from half-plane edge diffraction.

Universal Diffraction of Atomic and Molecular Matter-Waves: A Comparison of He and D2 Quantum Reflected from a Grating.

Molecular beams of He and D2 are scattered from a ruled diffraction grating in conical-mount geometry under grazing-incidence conditions. Fully resolved diffraction patterns as a function of detection angle are recorded for different grating azimuth angles and for two different kinetic energies of the particle beams. Variations in diffraction peak widths are traced back to different velocity spreads of He and D2 determined by time-of-flight measurements. A comprehensive analysis of diffraction intensities confirms universal diffraction, that is, for identical de Broglie wavelengths, the relative diffraction intensities for He and D2 are the same. Universal diffraction results from peculiarities of quantum reflection of the atoms and molecules from the diffraction grating. In quantum reflection particles scatter many nanometers in front of the surface from the long-range attractive branch of the particle-surface interaction potential without probing the potential well and the short-range repulsive branch of the potential.

Strong Optical Dipole Force Exerted on Molecules Having Low Rotational Temperature.

The optical dipole force acting on molecules is enhanced by decreasing the rotational temperature of the molecule and aligning the molecular axis with a linearly polarized nonresonant laser beam. The rotational temperature is decreased by increasing the source pressure from 2 to 81 bar. By using the effective polarizability directly pertaining to the optical dipole force, the force and the resulting change in the velocity of the molecules can be evaluated. Theoretical calculations are compared with measurements based on velocity map imaging techniques. If the rotational temperature is reduced from 295 to 1 K, the maximum alignment is increased from =0.33 to 0.92, and the average optical force is enhanced by 74 %.

Rotational-State-Dependent Dispersion of Molecules by Pulsed Optical Standing Waves.

We report on the rotational-state-dependent, transverse acceleration of CS_{2} molecules affected by pulsed optical standing waves. The steep gradient of the standing wave potential imparts far stronger dipole forces on the molecules than propagating pulses do. Moreover, large changes in the transverse velocities (i.e., up to 80 m/s) obtained with the standing waves are well reproduced in numerical simulations using the effective polarizability that depends on the molecular rotational states. Our analysis based on the rotational-state-dependent effective polarizability can therefore serve as a basis for developing a new technique of state selection for both polar and nonpolar molecules.