Matter-wave Diffraction Research Articles

Optics of anisotropic nanostructures

The analytical formalism of Rokushima and Yamakita [J. Opt. Soc. Am. 73, 901–908 (1983)] treating the Fraunhofer diffraction in planar multilayered anisotropic gratings proved to be a useful introduction to new fundamental and practical situations encountered in laterally structured periodic (both isotropic and anisotropic) multilayer media. These are employed in the spectroscopic ellipsometry for modeling surface roughness and in-depth profiles, as well as in the design of various frequency-selective elements including photonic crystals. The subject forms the basis for the solution of inverse problems in scatterometry of periodic nanostructures including magnetic and magneto-optic recording media. It has no principal limitations as for the frequencies and period to radiation wavelength ratios and may include matter wave diffraction. The aim of the paper is to make this formalism easily accessible to a broader community of students and non-specialists. Many aspects of traditional electromagnetic optics are covered as special cases from a modern and more general point of view, e.g., plane wave propagation in isotropic media, reflection and refraction at interfaces, Fabry-Perot resonator, optics of thin films and multilayers, slab dielectric waveguides, crystal optics, acousto-, electro-, and magneto-optics, diffraction gratings, etc. The formalism is illustrated on a model simulating the diffraction on a ferromagnetic wire grating.

Subdiffractive band-edge solitons in Bose-Einstein condensates in periodic potentials

A type of matter wave diffraction management is presented that leads to subdiffractive solitonlike structures. The proposed management technique uses two counter-moving, identical periodic potentials (e.g., optical lattices). For suitable lattice parameters, a different type of atomic bandgap structure appears in which the effective atomic mass becomes infinite at the lowest edge of an energy band. This way, normal matter-wave diffraction (proportional to the square of the atomic momentum) is replaced by fourth-order diffraction, and hence the evolution of the system becomes subdiffractive.

Matter-wave diffraction in time with a linear potential

Diffraction in time of matter waves incident on a shutter which is removed at time $t=0$ is studied in the presence of a linear potential. The solution is also discussed in phase space in terms of the Wigner function. An alternative configuration relevant to current experiments where particles are released from a hard wall trap is also analyzed for single-particle states and for a Tonks-Girardeau gas.

Magic numbers, excitation levels, and other properties of small neutral He4 clusters (N⩽50)

The ground-state energies and the radial and pair distribution functions of neutral 4He clusters are systematically calculated by the diffusion Monte Carlo method in steps of one 4He atom from 3 to 50 atoms. In addition the chemical potential and the low-lying excitation levels of each cluster are determined with high precision. These calculations reveal that the "magic numbers" observed in experimental 4He cluster size distributions, measured for free jet gas expansions by nondestructive matter-wave diffraction, are not caused by enhanced stabilities. Instead they are explained in terms of an enhanced growth due to sharp peaks in the equilibrium concentrations in the early part of the expansion. These peaks appear at cluster sizes which can just accommodate one more additional stable excitation. The good agreement with experiment provides not only experimental confirmation of the energy level and the chemical potential calculations, but also evidence for a new mechanism which can lead to magic numbers in cluster size distributions. By accounting for the falloff of the radial density distributions at the surface and a size-dependent surface tension, the energy levels are demonstrated to be consistent with a modified Rayleigh model of surface excitations. The compressibility coefficient of these small clusters is found to be one order of magnitude smaller than the bulk compressibility.

Using atomic diffraction of Na from material gratings to measure atom-surface interactions

In atom optics a material structure is commonly regarded as an amplitude mask for atom waves. However, atomic diffraction patterns formed using material gratings indicate that material structures also operate as phase masks. In this study a well collimated beam of sodium atoms is used to illuminate a silicon nitride grating with a period of 100 nm. During passage through the grating slots atoms acquire a phase shift due to the van der Waals (vdW) interaction with the grating walls. As a result the relative intensities of the matter-wave diffraction peaks deviate from those expected for a purely absorbing grating. Thus a complex transmission function is required to explain the observed diffraction envelopes. An optics perspective to the theory of atomic diffraction from material gratings is put forth in the hopes of providing a more intuitive picture concerning the influence of the vdW potential. The van der Waals coefficient ${C}_{3}=2.7\ifmmode\pm\else\textpm\fi{}0.8\phantom{\rule{0.3em}{0ex}}\mathrm{meV}\phantom{\rule{0.3em}{0ex}}{\mathrm{nm}}^{3}$ is determined by fitting a modified Fresnel optical theory to the experimental data. This value of ${C}_{3}$ is consistent with a van der Waals interaction between atomic sodium and a silicon nitride surface.

Talbot-Lau effect for atomic de Broglie waves manipulated with light

We have demonstrated the Talbot-Lau effect for atomic de Broglie waves in the time domain. This effect is based on Fresnel diffraction of matter waves from an incoherent source. In the experiment, de Broglie waves of atoms in a particular internal state have been manipulated and the resulting density directly imaged by resonant optical fields. These experiments allow us to probe the quantum dynamics of the atomic center of mass. We have also used this effect to create patterns in the density of the atoms with period as small as $1∕10$ of the optical wavelength, demonstrating the potential application of this technique for atom nanofabrication.

Diffraction-limited focusing of Bose–Einstein condensates

Adjustable magnetic reflection and focusing of an87Rb Bose–Einstein condensate was achieved using a particularly smooth mirror and a verystraightforward apparatus. In this paper, we discuss a simple Thomas–Fermi model and aMonte Carlo method for analysing the bouncing. Both models are in close agreement withthe observed condensate evolution. Additionally, the theory predicts very tightcondensate focusing, and atomic matter-wave diffraction should be observable.The effect of mirror anharmonicities on the condensate focusing is investigated.

Formation of soliton trains in Bose–Einstein condensates as a nonlinear Fresnel diffraction of matter waves

The problem of generation of atomic soliton trains in elongated Bose–Einstein condensates is considered in framework of Whitham theory of modulations of nonlinear waves. Complete analytical solution is presented for the case when the initial density distribution has sharp enough boundaries. In this case the process of soliton train formation can be viewed as a nonlinear Fresnel diffraction of matter waves. Theoretical predictions are compared with results of numerical simulations of one- and three-dimensional Gross–Pitaevskii equation and with experimental data on formation of Bose–Einstein bright solitons in cigar-shaped traps.

Diffraction of diatomic molecules from a lattice with coupling to the internal excited vibrational state

Matter wave diffraction of diatomic molecules from a lattice of grids is considered with the energy exchange with the internal excited vibrational states of the molecules. The energy exchange leads, in general, to a shift in the matter wave fringes, reminiscent of the Aharonov–Bohm shift, with the important difference that it is independent of ℏ, while the AB shift involves ℏ. When the interference is considered strictly to be one-dimensional, then the phase difference describing the shift is the sole nonzero phase difference and describes a macroscopic interference with a mesoscopic wave length which is independent of ℏ.

Adiabatic propagation in potential structures

In this work the adiabatic approximation is applied to the propagation of matter waves in confined geometries like those experimentally realized in recent atom optical experiments. Adiabatic propagation along a channel is assumed not to mix the various transverse modes. Nonadiabatic corrections arise from the potential squeezing and bending. Here we investigate the effect of the former. Detailed calculations of two-dimensional propagation are carried out both exactly and in an adiabatic approximation. This offers the possibility to analyze the validity of adiabaticity criteria. A semiclassical (sc) approach, based on the sc Massey parameter is shown to be inadequate, and the diffraction due to wave effects must be included separately. This brings in the Fresnel parameter well known from optical systems. Using these two parameters, we have an adequate understanding of adiabaticity on the system analyzed. Thus quantum adiabaticity must also take cognizance of the intrinsic diffraction of matter waves.

Atom Optical Elements Based on Near-field Grating Sequences

We develop a Talbot-optical approach to grating-based atom optics. The method is used to describe matter wave diffraction produced by a near-field sequence of gratings. The possibilities for de Broglie wavefront design are demonstrated through a series of examples involving two consecutive gratings.

Observation of Quantum Accelerator Modes

We have realized a quantum accelerator mode using a system consisting of ultracold cesium atoms falling through a pulsed standing wave of off resonant light. We present a picture of this system based on diffraction and show that the effect arises from the application of blazed matter wave diffraction gratings. The implications of our results for quantum chaos and the prospect of constructing a large angular separation matter wave beam splitter are discussed.

Effects of atomic diffraction on the collective atomic recoil laser

We formulate a wave atom optics theory of the Collective Atomic Recoil Laser, where the atomic center-of-mass motion is treated quantum mechanically. By comparing the predictions of this theory with those of the ray atom optics theory, which treats the center-of-mass motion classically, we show that for the case of a far off-resonant pump laser the ray optics model fails to predict the linear response of the CARL when the temperature is of the order of the recoil temperature or less. This is due to the fact that in theis temperature regime one can no longer ignore the effects of matter-wave diffraction on the atomic center-of-mass motion.

Diffraction of matter waves in space and in time

In analogy to the well-known diffraction of waves at spatial structures, one can also define diffraction in time when a wave is temporarily modulated. In the present paper we investigate this phenomenon starting from a Green's-function approach. Diffraction in time appears for Schr\"odinger waves and not for light in vacuum. Specific cases of diffraction in time investigated here are diffraction at an ``edge in time'' and a Fresnel lens in time. We then investigate in detail the simultaneous diffraction both in space and in time representing a general solution. Then we analyze in detail diffraction at an edge, both in space and in time, of a single slit in space and in time, a double slit in space, and a single slit in time, a single slit in space and a double slit in time, and, finally, a double slit both in space and in time. In all cases we analyze the possibilities of various approximations which can be made, and show the limits and validity of the Fraunhofer approximation both in space and in time. We give explicit results for a gedanken experiment with very cold atoms.

X-ray/VUV transmission gratings for astrophysical and laboratory applications

Free-standing and membrane-supported transmission gratings are very useful for applications in VUV, X-ray, and matter-wave diffraction and spectroscopy. We will describe the techniques used to fabricate deep-submicron-period transmission gratings and review some of the applications for these diffractors. Our fabrication process begins with holographic lithography to define a master grating pattern. Spatial periods as small as 0.2 µm (5000 lines mm−1) are routinely achieved, and a new technique, called achromatic holographic lithography, has achieved a period of 0.1 µm (10 000 lines mm−1). Holography is followed by SiO2 shadow-evaporation, reactive-ion etching, and gold liftoff or electroplating to transform this pattern into absorbers for C K (45 Å) or Cu L (13 Å) X-rays. This patterning is performed on the membrane of an X-ray mask, which is then printed using X-ray lithography. The X-ray lithography process transfers the master pattern into a thick-resist coated substrate, which is then gold, silver, or nickel electroplated to form the final grating pattern. These structures can be supported on 0.5-1.0 µm-thick polyimide membranes, or made free standing by the support of a metal mesh. Progress in this area has been fueled primarily by the requirements of the Advanced X-ray Astrophysics Facility (AXAF) X-ray telescope, for which thousands of square centimeters of high-quality transmission gratings are required. However, other applications, including X-ray nanolithography development, solar astronomy, X-ray and matter-wave interferometry, and laboratory VUV/X-ray spectroscopy are also driving this technology.