Can't Get No Diffraction?

thesis Can’t get no diffraction?

In the year 1900, no one would have guessed example — demonstrates diffraction. This that light — to all appearances an ethereal It would be the first technique was demonstrated over a decade wave-like phenomenon — might take the ago in experiments. form of localized particles. Nor would definitive failure of the But everything can be taken a step anyone have expected that the billiard- mathematical paradigm further by replacing the physical grating ball atoms of physical matter would turn with a grating made entirely of light. As it out to act as waves, showing diffraction of quantum mechanics. turns out, the physical grating introduces and interference much like light. In that limitations traced to van-der-Waals-type pre-quantum age, light and matter sat on weak interactions between the particles two sides of a conceptual divide. Experiments of this kind over the past and the walls of the grating. These can That divide was soon annihilated, of two decades have demonstrated diffraction be eliminated by replacing the grating course, when Einstein, in 1905, showed phenomena for a host of atoms including with a standing-wave laser field of the light to be absorbed as discrete photons, hydrogen, helium, sodium and even complex same periodicity. Using this technique, and Davisson and Germer, in 1927, fullerene molecules such as C60. In 1999, for Hornberger and colleagues have recently demonstrated that slow-moving electrons example, physicists in Vienna sent a beam demonstrated clear quantum diffraction create a diffraction pattern when reflected of C60 molecules with a velocity of about for a variety of organic molecules, from a crystal surface. This effect had 100 ms−1 onto a grating with a slit separation some containing more than 400 atoms been foreseen by Louis de Broglie, whose of 100 nm and detected interference maxima and weighing as much as 7,000 amu PhD thesis of 1924 was the first attempt to and minima at a distance of about 1 m (S. Gerlich et al. Nature Commun. obliterate the wave–particle divide: “When (M. Arndt et al. Nature 401, 680–682; 1999). 2, 263; 2011). I conceived the first basic ideas of wave Seeing similar effects for even larger The pay-off of this experimental advance mechanics,” he later wrote, “I was guided by particles seems to require a shift in strategy. is the chance to test various theories the aim to perform a real physical synthesis, Most diffraction experiments have explored proposed to reconcile fundamental puzzles valid for all particles, of the coexistence of so-called far-field diffraction — that is, the in quantum physics. Why, for example, do the wave and of the corpuscular aspects.” effects apparent when viewed sufficiently small quantum particles such as electrons Present-day quantum theory is the long far from the source, where the wave fronts routinely exist in superpositions — and outgrowth of de Broglie’s idea, but of course are effectively plane waves. Achieving therefore show interference effects — also still subject to revision. Ironically, some observable diffraction in this setting whereas we never see such effects for large of the strongest tests of quantum theory at requires molecular beams collimated more objects on the macroscopic scale? One present originate in diffraction experiments precisely than the diffraction angle. In the proposal, embodied in so-called continuous directly analogous to those of Davisson experiments with C60, for example, the beam spontaneous localization theories, is that and Germer, yet also different in a way that had to be collimated to less than 10 μm, the linear Schrödinger equation is actually de Broglie may not have imagined — with which also strongly reduced the detected incomplete, and needs to be generalized to light itself forming the physical structure particle flux. This technique runs into include real nonlinear processes by which that plays the role of the crystal, and several practical limitations if applied to the wavefunction occasionally collapses material particles, even large complex even larger particles for which the de Broglie from superposed states into states with molecules, the things being diffracted. wavelengths tend to be smaller still. precise spatial positions. A coherent beam of particles of any kind A promising alternative is to turn The parameters of these hypothetical can show wave-like diffraction effects when away from the far field, and instead theories can be chosen so that tiny particles made to pass through a grating of slits. detect diffraction effects in the near field, such as electrons act just as standard Far away from the grating, the density of closer to the grating (K. Hornberger et al. quantum theory says they should, while detected particles should show an oscillatory Rev. Mod. Phys.; in the press). The physics superpositions in large ensembles (of pattern with well-defined maxima and is more difficult to analyse, but the near order 1024 particles) collapse very rapidly. minima along different directions. However, field offers advantages — in particular, the This would explain the quantum–classical the ease of seeing such phenomena decreases required spacing of the grating scales divide quite naturally. But it implies that with increasing particle mass and velocity. inversely to the square root of the particle experiments aiming to see diffraction in That’s because the de Broglie wavelength, mass, rather than simply in inverse sufficiently large particles should begin

λDB, associated with a particle is inversely proportion to the mass. Moreover, the to fail. proportional to its momentum, and technique does not require molecular beams As Hornberger et al. point out, the pronounced diffraction effects only occur if of very narrow width. experiments are getting close to the point the spacing of the grating is small enough to Mathematically, when a plane wave where they will begin to constrain the be comparable to the incident wavelength. illuminates a grating of spacing d, the parameters in these theories — if they For low-energy electrons, the periodic intensity pattern across the grating will be continue to see diffraction. If they do not, arrangement of atoms in a crystal provides reproduced exactly at the so-called Talbot it would be the first definitive failure of a convenient grating of the right size. length LT in the forward direction, where the standard mathematical paradigm of 2 Observing the same kind of thing for larger LT = d /λDB. This intensity distribution is an quantum mechanics, and could help chart particles — a basic test of the validity of inherent reflection of wave physics, and it’s the way to a better theory beyond. ❐ quantum principles — requires gratings with detection — by observing the distribution finer resolution. of particles on some clean surface, for MARK BUCHANAN

NATURE PHYSICS | VOL 8 | FEBRUARY 2012 | www.nature.com/naturephysics 103