Real-Time Single-Molecule Imaging of Quantum Interference
The observation of interference patterns in double-slit experiments with massive particles is generally regarded as the ultimate demonstration of the quantum nature of these objects. Such matter-wave interference has been observed for electrons1, neutrons2, atoms3, 4 and molecules5, 6, 7 and, in contrast to classical physics, quantum interference can be observed when single particles arrive at the detector one by one.
The build-up of such patterns in experiments with electrons has been described as the “most beautiful experiment in physics”8, 9, 10, 11.
Here, we show how a combination of nanofabrication and nano-imaging allows us to record the full two-dimensional build-up of quantum interference patterns in real time for phthalocyanine molecules and for derivatives of phthalocyanine molecules, which have masses of 514 AMU and 1,298 AMU respectively.
A laser-controlled micro-evaporation source was used to produce a beam of molecules with the required intensity and coherence, and the gratings were machined in 10-nm-thick silicon nitride membranes to reduce the effect of van der Waals forces. Wide-field fluorescence microscopy detected the position of each molecule with an accuracy of 10 nm and revealed the build-up of a deterministic ensemble interference pattern from single molecules that arrived stochastically at the detector.
In addition to providing this particularly clear demonstration of wave-particle duality, our approach could also be used to study larger molecules and explore the boundary between quantum and classical physics.
When Richard Feynman described the double-slit experiment with electrons as being ‘at the heart of quantum physics’12 he was emphasizing how the fundamentally non-classical nature of the superposition principle allows the quantum wavefunction associated with a massive object to be widely delocalized, while the object itself is always observed as a well-localized particle.
Recent experiments have focused this discussion by demonstrating the stochastic build-up of interference patterns11, 13, by implementing double-slit diffraction in the time domain14, 15 (including down to the attosecond level16), and by identifying a single molecule as the smallest double-slit for electron interference17, 18 that enables fundamental studies of decoherence19.
The extension of this work20 to large molecules requires a sufficiently intense and coherent beam of slow and neutral molecules, a nanoscale diffraction grating, and a detector that offers a spatial accuracy of a few nanometres and a molecule-specific detection efficiency of close to 100%. We achieve that in this work with a combination of micro-evaporation, nanofabrication and nano-imaging.
Our experimental set-up comprises three sections: beam preparation, coherent manipulation and detection (Fig. 1). The molecules need to be prepared such that each one interferes with itself, and all lead to similar interference patterns on the screen. Because the transverse and longitudinal coherence functions are determined by the Fourier transforms of the source spatial extension and velocity distribution21, we require a good collimation and velocity selection.
Under ‘far-field’ conditions we can approximate the molecular wavefunctions as plane waves, and the angle θn of the nth order diffraction peak is given by the equation sin θn = nΛ/d, where Λ = h/mv is the de Broglie wavelength, h is Planck’s constant, m is the particle mass, v is the velocity, and d is the period of the diffraction grating. Massive particles therefore need to be slow to achieve sizable diffraction angles.
Although deceleration techniques have been advanced for molecules even as complex as benzonitrile22, effusive beams (Fig. 1b) are still well suited for preparing slow beams of particles a hundred times more massive than that23, 24.