The development of wave optics for light brought many new insights into our understanding of physics, driven by fundamental experiments like the ones by Young, Fizeau, Michelson-Morley and others. Quantum mechanics, and especially the de Broglie’s postulate relating the momentum p of a particle to the wave vector k of an matter wave: k = 2 λ = p/ℏ, suggested that wave optical experiments should be also possible with massive particles (see table 1), and over the last 40 years electron and neutron interferometers have demonstrated many fundamental aspects of quantum mechanics [1].

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Optics and interferometry with atoms and molecules

In 1935, Schrodinger attempted to demonstrate the limitations of quantum mechanics using a thought experiment in which a cat is put in a quantum superposition of alive and dead states. The idea remained an academic curiosity until the 1980s when it was proposed that, under suitable conditions, a macroscopic object with many microscopic degrees of freedom could behave quantum mechanically, provided that it was sufficiently decoupled from its environment. Although much progress has been made in demonstrating the macroscopic quantum behaviour of various systems such as superconductors, nanoscale magnets, laser-cooled trapped ions, photons in a microwave cavity and C60 molecules, there has been no experimental demonstration of a quantum superposition of truly macroscopically distinct states. Here we present experimental evidence that a superconducting quantum interference device (SQUID) can be put into a superposition of two magnetic-flux states: one corresponding to a few microamperes of current flowing clockwise, the other corresponding to the same amount of current flowing anticlockwise.

Quantum superposition of distinct macroscopic states

Quantum superposition lies at the heart of quantum mechanics and gives rise to many of its paradoxes. Superposition of de Broglie matter waves1 has been observed for massive particles such as electrons2, atoms and dimers3, small van der Waals clusters4, and neutrons5. But matter wave interferometry with larger objects has remained experimentally challenging, despite the development of powerful atom interferometric techniques for experiments in fundamental quantum mechanics, metrology and lithography6. Here we report the observation of de Broglie wave interference of C60 molecules by diffraction at a material absorption grating. This molecule is the most massive and complex object in which wave behaviour has been observed. Of particular interest is the fact that C60 is almost a classical body, because of its many excited internal degrees of freedom and their possible couplings to the environment. Such couplings are essential for the appearance of decoherence7,8, suggesting that interference experiments with large molecules should facilitate detailed studies of this process.

Wave–particle duality of C 60 molecules

Quantum mechanics is an extremely successful theory that agrees with every experimental test. However, the principle of linear superposition, a central tenet of the theory, apparently contradicts a commonplace observation: macroscopic objects are never found in a linear superposition of position states. Moreover, the theory does not explain why during a quantum measurement, deterministic evolution is replaced by probabilistic evolution, whose random outcomes obey the Born probability rule. In this article a review is given of an experimentally falsifiable phenomenological proposal, known as continuous spontaneous collapse: a stochastic nonlinear modification of the Schr\"odinger equation, which resolves these problems, while giving the same experimental results as quantum theory in the microscopic regime. Two underlying theories for this phenomenology are reviewed: trace dynamics and gravity-induced collapse. As the macroscopic scale is approached, predictions of this proposal begin to differ appreciably from those of quantum theory and are being confronted by ongoing laboratory experiments that include molecular interferometry and optomechanics. These experiments, which test the validity of linear superposition for large systems, are reviewed here, and their technical challenges, current results, and future prospects summarized. It is likely that over the next two decades or so, these experiments can verify or rule out the proposed stochastic modification of quantum theory.

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Models of Wave-function Collapse, Underlying Theories, and Experimental Tests

Microwave spectroscopy experiments have been performed on two quantum levels of a macroscopic superconducting loop with three Josephson junctions. Level repulsion of the ground state and first excited state is found where two classical persistent-current states with opposite polarity are degenerate, indicating symmetric and antisymmetric quantum superpositions of macroscopic states. The two classical states have persistent currents of 0.5 microampere and correspond to the center-of-mass motion of millions of Cooper pairs.

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Quantum Superposition of Macroscopic Persistent-Current States

While in the last decade atom interferometry[1] has become a rapidly expanding field, coherent de Broglie optics with large molecules has still remained completely unexplored. We propose that interesting new physics is to be expected in such experiments. In particular the mechanisms of decoherence in mesoscopic systems may be studied far beyond existing experiments[2]. New insights may also be expected for the possibilities of entanglement of large objects. New boundary effects should be observable in the scattering of large particles at small apertures. Finally, new experimental technologies like molecular nano-lithography and quantum physics of small biomolecules would be opened up. In order to successfully perform such experiments it is essential to find suitable beam sources, efficient detectors, and coherent optical elements for macromolecules. Some prospects shall be outlined below. Large molecules pose several experimental challenges since most of them cannot simply be thermally vaporized without fragmentation or structural changes nor can their de Broglie wavelengths be easily modified. We have chosen C60 for our first experiments because of its ready availability, its exceptionally high stability against thermal decomposition and its particularly high symmetry.

Towards Coherent Matter Wave Optics with Macromolecules

In their 1959 seminal paper Aharonov and Bohm showed, as Ehrenberg and Si-day earlier [1], that in quantum mechanics potentials have a significance that goes beyond that of a mere convenient mathematical tool, as is the case in classical mechanics. This essentially arises from the fact that in quantum mechanics the potentials themselves enter the Schrodinger equation, while in classical mechanics they affect the motion of particles only through their derivatives. To illustrate their conclusions Aharonov and Bohm (AB) proposed two effects in electron interference experiments: the electric or scalar AB effect, resulting from a non-zero electrostatic potential, and the magnetic or vector AB effect, resulting from a non-zero magnetic vector potential.

Gerbrand van der Zouw

Papers

Wave–particle duality of C 60 molecules

Towards Coherent Matter Wave Optics with Macromolecules

Observation of the Nondispersivity of Scalar Aharonov-Bohm Phase Shifts by Neutron Interferometry