Experimental setup

The particles are evaporated in a thermal source. Their velocity is selected using the gravitational free-fall through a sequence of three slits. The interferometer itself consists of three gratings G 1 , G 2 and G 3 in a vacuum chamber at a pressure of p<10−8 mbar. The first grating is a SiN x membrane with 90-nm wide slits arranged with a periodicity of d=266 nm. Each slit of G 1 imposes a constraint onto the transverse molecular position that, following Heisenberg's uncertainty relation, leads to a momentum uncertainty. The latter turns into a growing delocalization and transverse coherence of the matter wave with increasing distance from G 1 . The second grating, G 2 , is a standing laser light wave with a wavelength of λ=532 nm. The interaction between the electric laser light field and the molecular optical polarizability creates a sinusoidal potential, which phase-modulates the incident matter waves. The distance between the first two gratings is chosen such that quantum interference leads to the formation of a periodic molecular density pattern 105 mm behind G 2 . This molecular nanostructure is sampled by scanning a second SiN x grating (G 3 , identical to G 1 ) across the molecular beam while counting the number of the transmitted particles in a quadrupole mass spectrometer (QMS).

In extension to earlier experiments, we have added various technological refinements: the oven was adapted to liquid samples, a liquid-nitrogen-cooled chamber became essential to maintain the source pressure low, a new mass analyser allowed us to increase the detected molecular flux by a factor of four and many optimization cycles in the interferometer alignment were needed to meet all requirements for high-contrast experiments with very massive particles.

Observed interferograms

We recorded quantum interferograms for all molecules of Figure 1, as shown in Figure 3. In all cases the measured fringe visibility V, that is, the amplitude of the sinusoidal modulation normalized to the mean of the signal, exceeds the maximally expected classical moiré fringe contrast by a significant multiple of the experimental uncertainty. This is best shown for TPPF84 and PFNS8, which reached the highest observed interference contrast in our high-mass experiments so far, with individual scans up to V obs =33% for TPPF84 (m=2,814 AMU) and V obs =49% for PFNS8 at a mass of m=5,672 AMU. In addition, we have observed a maximum contrast of V obs =17±4% for PFNS10 and V obs =16±2% for TPPF152 (see Figure 3), in which our classical model predicts V class =1%. This supports our claim of true quantum interference for all these complex molecules.

Figure 3: Quantum interferograms of tailor-made large organic molecules. Quantum interference well beyond the classical expectations has been observed for all molecules in the set. In all panels, the black circles represent the experimental result, the blue line is a sinusoidal fit to the data and the shaded area indicates the detector dark rate. (a) The beam of perfluoroalkylated nanospheres, PFNS8, is characterized by a mean velocity of v=63 m s−1 with a full width Δv FWHM =13 m s−1. The observed contrast of V obs =49±6% is in good agreement with the expected quantum contrast of V quant =51% and is clearly discernible from the classically expected visibility of V class <1%. The stated uncertainty is the standard deviation of the fit to the data. (b) For PFNS10, the signal was too weak to allow a precise velocity measurement and quantum calculation. The oven position for these particles, however, limits the molecular velocity to v<80 m s−1 and therefore allows us to define an upper bound to the classical visibility. (c) For TPPF84, we measure v=95 m s−1 with Δv FWHM =34 m s−1. This results in V obs =33±3% with V quant =30% and V class <1%. (d) The signal for TPPF152 is equally low compared with that of PFNS10. For this compound we find V obs =16±2%, V quant =45% and V class =1%. Full size image

The most massive molecules are also the slowest and therefore the most sensitive ones to external perturbations. In our particle set, these are PFNS10 and TPPF152, which, in addition, exhibited the smallest count rates and therefore the highest statistical fluctuations. To record the interferograms, we had to open the vertical beam delimiter S 2 and accept various imperfections: an increased velocity spread, a higher sensitivity to grating misalignments and also an averaging over intensity variations in the Gaussian-shaped diffraction laser beam G 2 . In addition, we had to enhance the QMS transmission efficiency at the expense of transmitting a broader mass range. The recorded signals associated with PFNS10 and TPPF152 covered a mass window of Δm FWHM =500 AMU around their nominal masses. Although all samples were well characterized before the evaporation process, we can therefore not exclude some contamination with adducts or fragments in this high mass range. But even if there were a relative mass spread of 10%, this would only influence the wavelength distribution Δλ dB /λ dB the same way as does the velocity spread. Owing to the inherent design of the Kapitza-Dirac-Talbot-Lau interferometer22, these experimental settings are still compatible with sizeable quantum interference, even under such adverse conditions.

Comparison of theory and experiment

The experimental values have to be compared with the theoretical predictions based on a classical and a quantum model23. The measured interference visibility is plotted as a function of the diffracting laser power P in Figure 4 for TPPF84 (4a) and PFNS8 (4b). Our data are in very good agreement with the full quantum calculation and in clear discrepancy with the classical prediction. The abscissa scaling of the V(P) curve is a good indicator for that. The quantum prediction mimics the classical curve qualitatively, but it is stretched in the laser power by a factor of about six (see Methods).

Figure 4: Quantum interference visibility as a function of the diffracting laser power. The best distinction between quantum and classical behaviour is made by tracing the interference fringe visibility as a function of the laser power, which determines the phase imprinted by the second grating. Each of the two experimental runs per molecule is represented by full circles and the error bar provides the 68% confidence bound of the sinusoidal fit to the interference fringe. The thick solid line is the quantum fit in which the shaded region covers a variation of the mean molecular velocity by Δv=±2 m s−1. (a) The TPPF84 data are well reproduced by the quantum model (see text) and completely missed by the classical curve (thin line on the left). (b) The same holds for PFNS8. The following parameters were used for the models: TPPF84: v=95 m s−1±16%, α=200 Å3×4πɛ 0 (fit), σ opt =10−21 m−2, w x =34±3 μm and w y =500±50 μm. PFNS8: v=75 m s−1±10%, α=190 Å3×4πɛ 0 (fit), σ opt =10−21m−2, w x =27±3 μm and w y =620±50 μm. Full size image

The laser power can be calibrated with an accuracy of ±1% but the abscissa also scales in proportion to the optical molecular polarizability and inversely with the vertical laser waist. The theoretical curves of Figure 4 are plotted assuming α opt =200 Å3×4πɛ 0 for TPPF84 and α opt =190 Å3×4πɛ 0 for PFNS8. These numbers have to be compared with the static polarizabilities computed using Gaussian09 (ref. 24). These are α stat =155 Å3×4πɛ 0 for TPPF84 and α stat =200 Å3×4πɛ 0 for PFNS8. A variation in the polarizability changes the horizontal scale of the plot as does a different laser waist. Both are bound by a relative uncertainty of less than 30%. A classical explanation is therefore safely excluded as an explanation for the experiments.

The quantitative agreement of the experimental and expected contrast is surprisingly good, given the high complexity of the particles. Various factors contribute to the remaining small discrepancies. The interference visibility is highly sensitive to apparatus vibrations, variations in the grating period on the level of 0.5 Å and a misalignment below 100 μrad in the grating roll angle.