Saving the most beautiful experiment in physics

Described as the “most beautiful experiment in physics”,  Richard Feynman spoke of the double-slit experiment as the heart of quantum physics. He was underscoring that the diffraction of individual particles at a grating is an unambiguous demonstration of wave-particle duality, contrary to classical physics and only explicable in quantum terms. Now, a new experimental set-up has shown perhaps the clearest example yet of Feynman’s thought experiment  

Feynman outlined his thought experiment in 1964 in the third volume of his famous series The Feynman Lectures on Physics to illustrate wave-particle duality in quantum mechanics. Feynman invited readers to imagine being able to fire individual electrons towards two slits and marking the position where each electron strikes a screen behind the slits. As shown experimentally, after the passage through the slits of many electrons, the marks on the screen would comprise a diffraction pattern – illustrating the wave-like behaviour of each electron. But, Feynman then went on to ask readers to imagine covering up one of the slits so that each electron could only pass through the other slit. In this case, the diffraction pattern would not appear – showing that each electron does indeed travel through both slits.

[caption id="attachment_36278" align="alignright" width="200"] Figure 1: The experimental set-up, which comprises three sections: beam preparation, coherent manipulation and detection.[/caption]

It should be remembered that, at the time, matter–wave interference had been observed for over 200 hundred years, first with photons and then with electrons. But, while these experiments clearly showed that beams of light or electrons can behave as a wave when confronted with the double-slit, experimental proof that a single electron would behave like a wave had not been shown. This was first demonstrated in 1974 by Giulio Pozzi and colleagues at the University of Bologna in Italy, who passed single electrons through a biprism – an electron optical device – and observed the build-up of a diffraction pattern. This work was repeated in 1989 by Akira Tonomura and colleagues at Hitachi's research lab in Japan.

Although the biprism serves the same function as a double slit, the first single-electron experiment to use a physical double-slit was reported just over five years ago by Pozzi and colleagues. The Italian team showed the build-up of the diffraction pattern when both slits were open but when one slit was closed, as expected the diffraction pattern was not created.

Feynman’s thought experiment, and the very recent work on single electron diffraction, emphasise that the quantum wavefunction associated with a massive object is widely delocalised while the object itself is always observed as a localised particle.

Now, the clearest physical demonstration yet of Feynman’s experiment has been provided by Professor Markus Arndt of the Quantum Nanophysics & Molecular Quantum Optics group at the University of Vienna, Austria. Arndt’s group demonstrated the diffraction of single, massive molecules at two slits but, unlike the interference patterns created by photons and electrons that are irretrievably lost in the detection process, used fluorescent molecules and nanometric detection accuracy to provide clear and tangible evidence of the quantum behaviour of large molecules in real time.

The team used a laser-controlled micro-evaporation source to produce an intense and coherent beam of phthalocyanine and phthalocyanine-derivative molecules with masses of 514 AMU and 1,298 AMU respectively. This beam of slow and neutral molecules was directed at a double-slit nanofabricated in 10 nm thick silicon nitride membranes and wide-field microscopy used to detect the position of each molecule to an accuracy of 10 nm. The key to the set-up was the use of an Andor iXon 885 EMCCD camera as the detector, offering nanometric spatial accuracy and a molecule-specific detection efficiency of almost 100%.

[caption id="attachment_36279" align="alignleft" width="200"] Figure 2: Typical fluorescence image of surface-deposited phthalocyanine molecules
Thomas Juffmann, Adriana Milic, Michael Muellneritsch, Peter Asenbaum, Alexander Tsukernik, Jens Tuexen, Marcel Mayor, Ori Cheshnovsky and Markus Arndt. “Real-time single-molecule imaging of quantum interference” Nature Nanotechnology 7, 297–300 (2012) http://www.quantumnano.at/far-field-more.3953.html[/caption]

According to Professor Arndt, the key to the experiment is the high detection efficiency of the Andor iXon 885 EMCCD camera, which exceeds that of electron-impact quadrupole mass spectrometry by more than a factor of 10⁴. This huge gain allowed the team to optically visualise the real-time build-up of a two-dimensional quantum interference pattern caused by individual molecules arriving at the detector for the first time. The result is a particularly clear and permanent demonstration of wave-particle duality.

The experimental set-up comprised three sections: beam preparation, coherent manipulation and detection (Figure 1). The molecules need to be prepared such that each one interferes with itself and all lead to similar interference patterns on the screen. Also, the group were producing massive particles which needed to be moving slowly in order to achieve sizable diffraction angles. Although deceleration techniques have been employed for complex molecules like benzonitrile, Arndt’s team set out to use particles a hundred times more massive and chose to use effusive beams (Figure 1b) to prepare the slow beams of particles. For the thermolabile organic molecules, which may decompose when heated to their evaporation temperature, a blue diode laser was focused onto a thin layer of molecules deposited on the inside of the entrance vacuum window (W_{1 -} Figure 1a). Although high temperatures can be reached locally, this affects only the particles within the focus area and the heat load is reduced to a minimum. The high-mass molecules were specifically synthesised by Jens Tuexen and Professor Marcel Mayor at the University of Basel.

Spectral coherence was achieved by sorting the arriving molecules according to their longitudinal velocity and their respective freefall height in the Earth’s gravitational field. The collimation slit S defines the spatial coherence of the molecular beam. The slit and the grating width further downstream narrow the beam divergence to less than the diffraction angle. The double-slit is defined by gratings machined into thin silicon nitride membrane (Figure 1c) by the team around Professor Ori Cheshnovsky at Tel Aviv University, with the thickness reduced to as little as 10 nm to minimise the dispersive van der Waals interaction between the molecules and the grating wall. This is important for the manipulation of complex molecules, which may exhibit high polarisabilities, permanent, and even thermally-induced electric dipole moments.

The phthalocyanine molecule PcH₂ (Figure 1d) and its derivative F₂₄PcH₂ (Figure 1e) were selected because they are stable molecules and efficient dyes, even in vacuum. Each individually diffracted molecule finally arrives at the 170-mm-thin quartz plate (W₂ – Figure 1) where it was illuminated under a shallow angle so that the excitation laser did not enter the imaging optics. The emerging quantum interference pattern was observed through widefield fluorescence microscopy of the single molecules using a scheme similar to single-molecule high-resolution imaging with photo-bleaching (SHRIMP) and imaged onto the camera. Even if the pointspread function of an optical emitter is bound to Abbe’s diffraction limit, it is still possible to determine its barycentre with nanometre accuracy if the signal-to-noise ratio is high enough and as long as the pointspread functions of neighbouring molecules do not overlap.

Figure 2 shows a typical fluorescence image of surface-deposited phthalocyanine molecules. The team could detect approximately 1 × 10⁵ fluorescence photons per molecule before abrupt bleaching or desorption is observed from one frame to the next, supporting that single molecules were monitored and not aggregates. Then, by fitting a two-dimensional Gaussian to each molecular image, its position was determined with an accuracy of 10 nm. Fig. 3a-e shows selected frames from a false-colour movie recorded with the Andor iXon 885 low-light EMCCD camera and the gradual build-up of the quantum interference pattern for PcH₂ molecules over a period of 90 minutes.

Arndt and his team have shown that it is possible to preserve the diffraction patterns caused by firing massive fluorescent particles at a double-slit, just as suggested by Feynman almost fifty years ago. With detection efficiency to the level of single molecules, fluorescence imaging with nanometre accuracy is orders of magnitude more sensitive than the ionisation methods used in previous work. Although scanning tunnelling microscopy has been used for single-molecule interference imaging, Arndt’s fluorescent imaging technique offers recording speeds up to 1,000 times faster over an imaging area that is a hundred thousand times larger. What’s more, the group suggest that it should be possible to reduce, or even eliminate, the effect of the van der Waals forces by using even thinner gratings made of double-layer graphene or of light.

[caption id="attachment_36280" align="alignright" width="200"] Figure 3: The quantum interference pattern for PcH2 molecules built up over a period of 90 minutes and captured with the Andor iXon 885 low-light camera.[/caption]

The observation of interference patterns with massive particles is generally regarded as the ultimate demonstration of the quantum nature of these objects. The approach taken by the team in Vienna has brought to life Feynman’s thought experiment and could, in the future, be used to study even larger natural and functionalised organic molecules, and quantum dots, to explore the boundary between quantum and classical physics.

To the non-physicist it may still feel like magic. However, the fluorescent patterns achieved by Arndt and his team allow all of us to finally look upon Physics’ most beautiful experiment.