Simplified diagram of the experimental setup to test wave-particle complementarity in a quantum-controlled interferometer (image: Roberto Menezes Serra/UFABC)

Brazilian experiment confirms one of the keystones of quantum physics

Researchers used sophisticated quantum control methods to test the validity of the complementarity principle proposed by Niels Bohr in 1927. The results are reported in Communications Physics.

Brazilian experiment confirms one of the keystones of quantum physics

Researchers used sophisticated quantum control methods to test the validity of the complementarity principle proposed by Niels Bohr in 1927. The results are reported in Communications Physics.


Simplified diagram of the experimental setup to test wave-particle complementarity in a quantum-controlled interferometer (image: Roberto Menezes Serra/UFABC)


By José Tadeu Arantes  |  Agência FAPESP – Quantum physics has existed for over a century and has been applied in a wide array of technologies, from the light-emitting diode (LED) to the Global Positioning System (GPS). Initially, it was a huge challenge to the worldview of the scientists involved, giving rise to fierce controversies, especially the battle waged in the 1920s and 1930s between scientific giants Albert Einstein (1879-1955) and Niels Bohr (1885-1962).

The kernel of the debate was the physical reality of the microscopic world: molecular, atomic and sub-atomic. Was it strictly determined, as the macroscopic phenomena of daily life appeared to be, or did the process of scientific observation influence the properties of observed systems?

Einstein argued that the reality of microscopic states did not depend on the experimental context. Acquiring knowledge of this reality was the difficulty. To do so, it was necessary to complete quantum theory by investigating a number of hitherto unknown “hidden variables”. Bohr, on the other hand, claimed that quantum systems had “mutually exclusive and complementary aspects” which could never be accessed at the same time in any experiment.  The observation process determined which aspect was made manifest.

Historians of science disagree as to whether there was a winning side to this debate, but Bohr’s opinion eventually prevailed, either owing to its intrinsic value or for circumstantial reasons. His famous “complementarity principle”, alongside the “uncertainty principle” posited by Werner Heisenberg (1901-1976), is a cornerstone of what is known as the Copenhagen interpretation of quantum mechanics and has become widely accepted in the scientific community.

Simply put, the complementarity principle holds that microscopic reality cannot be accessed completely in a single configuration. All science can say is how it behaves in the context of a particular observation. Moreover, its behavior is dual, in the sense that it displays one aspect or another depending on how the experiment is performed. Although these features are contradictory and mutually exclusive in the classical worldview, they must both be considered in order for an exhaustive description of a quantum phenomenon to be achieved.

Since 2011, sophisticated experiments have been performed by various groups of researchers around the world with the aim of testing the complementarity principle in a different way from that followed previously. In these experiments, a photon (light quantum) appears to behave as a wave and a particle at the same time in the same setup, apparently violating Bohr’s theory. This has led to a radical revision of the complementarity principles in quantum-controlled experiments. 

A new study along these lines has been conducted at the Federal University of ABC’s Center for Natural and Human Sciences (CCNH-UFABC) in São Paulo state, Brazil. An article reporting the findings is published in Communications Physics.

“Our study had two main aims. The first was to verify the validity of Bohr’s complementarity principle in quantum control scenarios. The second was to investigate physical realism in greater depth in order to find out whether the statistical phenomena observed in quantum-controlled experiments are sufficient to provide an accurate narrative of the particle-wave duality,” said physicist Pedro Ruas Dieguez, first author of the article. Dieguez is a postdoctoral research fellow affiliated with the University of Gdansk’s International Center for Theory of Quantum Technologies (ICTQT) in Poland and the Austrian Academy of Sciences.

“With a different experimental setup from that used in the studies conducted in the past decade, we found experimentally and also via theoretical equations that simultaneous determination of the two properties, wave and particle, is not possible,” Dieguez explained. “Furthermore, the impossibility of violating Bohr’s principle is associated with entanglement, an important quantum property and a non-classical type of correlation. We concluded that the quantum correlations between spins produced in our experiment were sufficient to show that the realism of the wave and particle interpretations can never be observed simultaneously, even using a quantum control that permits interpolation between the two behaviors.”

Wave-particle duality

To understand this result, we have to go back almost 100 years to 1924, when French physicist Louis de Broglie (1892-1987) proposed in his doctoral thesis an equation showing that all material bodies exhibit wave-like behavior. If the body’s mass is very large, as it is in the case of macroscopic entities, the wavelength is too small to be detected by the usual instruments, but molecules, atoms and sub-atomic particles have so little mass that their wave-like properties become significant.

A well-known demonstration of de Broglie’s thesis is the double-slit experiment, in which an electron source emits one particle per period. The particles can only pass through two parallel slits. The result is recorded on a photographic plate. When only one of the slits is opened, the plate displays impressions typical of the impact of corpuscles, but when both slits are opened simultaneously, the shape formed by the impressions on the plate displays the interference pattern that typically appears when two or more waves are superposed.

A more sophisticated way to observe the wave-particle duality is provided by the single-photon Mach-Zehnder interferometer. In this case, the interference pattern appears when the device is closed and disappears when it is open.

“According to Bohr, wave or particle reality is established only when the experimental setup has been determined,” Dieguez said. “What would happen if it were possible to choose whether to open or close the interferometer only after the photon had traveled through it and hence acquired the aspect of a wave or particle? This is the interesting experiment proposed by American physicist John Wheeler [1911-2008] to test the validity of Bohr’s complementarity principle.”

Wheeler presented his proposal as a thought experiment, as it seemed very hard to perform, yet this test, which became known as “the delayed-choice experiment”, was in fact carried out in practice nearly 30 years later. The results were published in 2007 in the journal Science.

“They showed that the complementarity principle wasn’t violated when the choice was delayed,” Dieguez said. “With the interferometer closed, the quantum system behaved as a wave, and with the interferometer open it behaved as a particle. The experimental setup itself – whether the interferometer was closed or open – was associated with the wave-like or particle-like behavior of the system.”

The complementarity principle appeared to have been vindicated. But scientists are rarely satisfied with the results of their experiments, and in 2011 a fully quantum version of Wheeler’s test was designed by theoretical physicists who, instead of delayed choice, used a concept known as quantum superposition to construct an interferometer that could be open and closed at the same time.

This paradoxical situation differs from tossing a coin, which can have one of two mutually exclusive outcomes, heads or tails. In quantum superposition, both possibilities coexist, just as two waves on the surface of a lake can overlap. In this new generation of experiments, an additional quantum system is used to control the interferometer setup.

“This theoretical proposal gave rise to quantum-controlled experiments by scientists around the world, including a Brazilian research group,” Dieguez said. “The results seemed to show something surprising. Based on smooth interpolation of the statistics between a wave-like and particle-like pattern, the researchers concluded that the behavior was hybrid, combining wave and particle, when the same experimental setup was used for detection. This appeared to contradict Bohr’s complementarity principle for the first time in history, and gave rise to a series of debates in the scientific literature.”

New experimental setup

It was against this background that Dieguez and collaborators performed the novel experiment reported in the recently published article. “We used a quantifier of the degree of physical realism of a given quantum state for a certain observable feature,” he explained. “On the basis of this reality criterion, we showed that there was no connection between the statistics observed in previous experiments and the reality elements of wave and particle. This was an important point. From there we were able to argue that instead of revising Bohr’s principle we should first revise the experimental setup used in quantum delayed-choice experiments.”

The group therefore proposed a different experimental setup to establish the link between the visible results supplied by the interferometer, as given by the final statistics, and the wave-particle reality elements inside the device.

“We implemented these ideas in a proof-of-principle experiment using nuclear magnetic resonance [NMR], which is similar to the MRI technique used in medicine. In this experiment, the spins [magnetic properties of elementary particles analogous to the position of a compass needle] of the nuclei of the different atoms in a sodium formate [HCO2Na] molecule were manipulated with radio waves,” Dieguez said.

The carbon nuclear spin was used for quantum control of the interferometer deployed for the hydrogen nuclear spin. The interferometer was associated with possible configurations of hydrogen, analogous to two paths that could be followed. Depending on the state of the carbon nucleus, the interferometer could be open, closed, or with the two possibilities overlapping.

“This carbon control of hydrogen is due to the interaction between them and well-used radio pulses,” Dieguez said, referring to the experimental setup shown in the figure above. “At the end of the experiment, the probability of observing the hydrogen spin in a given direction was associated with a difference between the two interferometer paths and quantum control by the carbon spin. The new experimental setup produced the same final statistics as previous quantum delayed-choice experiments. However, we showed that in the new setup the reality elements for wave or particle in the interferometer were formally associated with the probability measured. Unlike the experiments performed in the past decade, our results validated Bohr’s complementarity principle once again.

“We concluded that the quantum correlation between the nuclear spins of the hydrogen and carbon in the experiment was sufficient to demonstrate that both the wave and particle realist interpretations could never be observed simultaneously, even using a quantum control that enabled us to interpolate between the two behaviors. This result corroborates the idea that physical reality is described by mutually exclusive but complementary aspects.”

The experiment was conducted at UFABC’s Multiuser NMR Laboratory. The team consisted entirely of Brazilian researchers and was led by Roberto Menezes Serra, a professor at UFABC. Renato Moreira Angelo, a professor at the Federal University of Paraná (UFPR), also took part. 

All the work was done during the COVID-19 pandemic, in strict compliance with the public health safety rules established by the university.

The investigation was conducted under the aegis of the National Institute of Science and Technology (INCT) in Quantum Information, one of the INCTs supported by FAPESP and Brazil’s National Council for Scientific and Technological Development (CNPq) in São Paulo state. Its principal investigator is Amir Caldeira. The project was also supported by FAPESP via a postdoctoral fellowship supervised by Serra.

The article “Experimental assessment of physical realism in a quantum-controlled device” is at:




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