![]() ![]() In this respect, our experiments resemble small-angle X-ray scattering, aimed to reveal long range order in bio-systems. This is a magnification by more than 10 6. Even though it is smaller than each molecule by about three orders of magnitude, we can see diffraction and a high-contrast interference pattern: Grating diffraction, thus, translates a relative path length difference of a few picometers into peak separations on the order of dozens of micrometers. In the experiments presented here, the de Broglie wavelength ranges between 2 and 6 pm. However, we also observe pronounced differences, associated with the molecular mass and complex internal dynamics: Molecules fall visibly in the gravitational field and they are attracted by nearby walls. Within the framework of the de Broglie hypothesis, the patterns agree astonishingly well with predictions from general wave optics, as used for light. We have demonstrated molecular diffraction at a single-, double-, and triple slit as well as a rotated nanomechanical grating. At this angle, the diffraction envelope is about five times wider than under normal incidence. At 60°, the effective period d eff is half of the geometrical one, and the slit width is reduced by a factor of 5. In consequence, diffraction up to the ± 6 t h orders can be observed. This confinement of the matter wave in the effective slit widens the single-slit envelope and leads to a stronger population of higher diffraction orders. Due to the grating thickness, the slit width is reduced from s geo = 61 nm to s eff = 32 nm. For θ grat = 40 °, the effective grating period d eff = d geo cos ( θ grat ) is reduced to 77 nm, resulting in larger diffraction angles. Rotating the grating broadens the envelope function and shifts the position of the diffraction orders. For θ grat = 0 °, the pattern is dominated by the zeroth and both first diffraction orders. They span molecular velocities v from 500 to 110 m/s, corresponding to de Broglie wavelengths λ dB between 1.6 and 7.1 pm. The diffraction patterns recorded at θ grat = 0 °, 40 °, and 60° are shown in Fig. This leads to a position-dependent phase ϕ, which is imprinted onto the molecular matter wave in each slit The factor C 3 includes the frequency-dependent polarizability of the particle and the dielectric function of the material grating, i.e., the response of both interaction partners to oscillating electric fields. 37,38 Approximating the grating thickness T as infinite, the potential V pot between the molecules and the grating can be written in the form V pot ( x ) = − C 3 / x 3. While the attractive potential scales with 1 / x 6 between two isolated particles, we have to integrate over the half-sphere of the grating, resulting in a potential, which scales with 1 / x 3. Here, the induced dipole moments interact with their mirror images in the material. 36 As the maximum distance between molecule and the nearest grating bar is 40 nm during transmission, we are in the short range limit, known as the van der Waals interactions. For PcH 2 moving at v = 250 m/s, the transverse coherence width amounts to X T ≃ 5.7 μm, i.e., 57 times the grating periods of 100 nm.Ĭasimir–Polder interactions result from fluctuations in the electron density of nearby objects. Heisenberg's principle, thus, helps us to prepare the transverse coherence required to illuminate several slits by the same molecular wave function. When the molecules reach the grating after L 1 = 1.55 m, this has evolved into a position uncertainty. (2) to estimate the associated transverse momentum uncertainty of Δ p ≃ 3.5 × 10 − 28 kg m/s. Approximating the evaporation spot as a rectangle, we can use Eq. This localized evaporation can be seen as a position measurement. This is where the first quantum effect comes into play: The position of the emitted molecules is defined by the spot size s 1 of the focused laser beam, which is twice the laser waist s 1 = 2 w 0 = ( 1.7 ± 0.5 ) μm. ![]() To launch the matter wave, we focus a laser at λ = 420 nm with a 50× objective onto the film. ![]() 34 A thin film of the molecule phthalocyanine (PcH 2, mass m = 514.5 u) is coated onto a window, which is mounted onto a vacuum chamber at a base pressure of P < 1 × 10 − 7 mbar. To record molecular diffraction patterns, we use the experimental setup sketched in Fig. ![]()
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