Detecting Planck-scale dark matter by leveraging quantum interference

While various studies have hinted at the existence of dark matter, its nature, composition and underlying physics remain poorly understood.

In recent years, physicists have been theorizing about and searching for various possible dark matter candidates, including particles with masses in the Planck scale (around 1.22×10¹⁹ GeV or 2.18×10⁻⁸ kg) that could be tied to quantum gravity effects.

Researchers at Aix-Marseille University and the Institute for Quantum Optics and Quantum Information recently hypothesized that Planck-scale dark matter could be detected using highly sensitive gravity-mediated quantum phase shifts. Their paper, published in Physical Review Letters, introduces a protocol designed to enable the detection of these hypothetical dark matter particles using Josephson junctions.

“This study originated from an idea raised by Alejandro Perez,” Carlo Rovelli, co-author of the paper, told Phys.org.

“The three of us were all teaching at a Quantum Gravity and Quantum Information school organized in the French countryside by the QISS research consortium and, since we know each other but we usually live in different cities, we decided to share an apartment while there.

“Alejandro had the idea that a special kind of quantum interference generated by a gravitational force that is discussed as a possible way of revealing a quantum gravity effect in a laboratory, could also be used to detect Planck-scale dark matter.”

Christodoulou and his colleagues at the Institute for Quantum Optics and Quantum Information had been exploring the possibility of detecting dark matter particles with masses in the Planck-scale for a few years. Originally, they focused on the possibility of detecting these particles using a quantum sensor, an idea that Christodoulou also discussed with Rovelli at a workshop in Greece in 2022.

“I had a student trying a calculation which was about the classical motion of the particle due to its gravitational attraction and was seen at the time as a preliminary step to think of quantum sensing using technologies developed at Vienna. Yet this was a wrong idea,” said Marios Christodoulou, co-author of the study.

“While I was giving a course on the theory behind the gravity, mediated entanglement experiments in France, a main point I was driving was precisely that while the effect of gravity is typically thought to be ‘things falling into each other,’ the reason interferometry can amplify the miniscule effect of gravity is that it has nothing to do with that, but only to do with the value of the action which can take different values in a quantum setting even neglecting the ‘things falling into each other.'”

When he was at the University of Toulon in France, Christodoulou started discussing the ideas he was exploring in his research with Alejandro Perez, a Senior Professor at the University. This initiated the collaboration that ultimately led to this study.

“I then told him that I have a student trying to calculate the ‘things falling into each other’ effect for a classical sensor, which would allows us subsequently think of a quantum sensor. Alejandro mentioned that I had just argued that this is the wrong thing to do, which it was and I had not realized it,” said Christodoulou. “That is when the idea clicked and then Alejandro spent a few days on his laptop doing the calculation that is the backbone of the paper.”

The study by this group of researchers builds on previous studies by Rovelli, which described Planckian black holes (black holes with Planck-level masses) from the theoretical standpoint of loop quantum gravity theory. His theory suggested that these particles only interact gravitationally, which made them promising dark matter candidates.

“I became obsessed with this idea in 2021, when I realized that a sufficiently hot big bang would produce exactly the right amount of such black holes needed to explain the observed dark matter abundance today,” said Perez.

“The big bang needs to be at an initial temperature close to the Planck temperature, which is also a natural possibility from the perspective of quantum gravity. I call this ‘the gravitational miracle’ by analogy of the so-called WIMP miracle that motivated the search for WIMPS when people believed strongly in supersymmetry). Since then, I was trying hard to find some observational handle of this idea or, in other words, if dark matter is made of such tiny black holes, how could we prove it?”

Rovelli, Christodoulou and Perez subsequently started exploring this idea more in-depth and trying to identify potential ways to test it. They first focused on potential methods of testing quantum mechanics in instances where gravity is relevant.

“I attended a lecture by Markus Aspelmeyer at the QISS conference where incredible experiments in this realm, that seemed impossible some time ago, are being performed,” said Perez. “That afternoon the three of us engaged in discussions and the idea of the paper naturally emerged.”

Based on Rovelli’s previous theoretical studies of black holes, the researchers hypothesized that Planck-scale objects do exist. In these past papers, they proposed that at the end of their lives, black holes could become Planck-scale particles with long lifetimes. These particles would be extremely tiny and yet possess considerable masses, around a few fractions of a microgram.

“Our main hypothesis was that Planck mass particles with a cross section of about Planck exist in nature,” said Christodoulou.

“These would have a relatively significant gravitational attraction since Planck mass is about the mass of a human hair. It is small but large enough for its gravitational attraction to be barely detectable. These make very natural dark matter candidates because we know dark matter interacts gravitationally but in no other way significantly, and this is how these particles would be expected to behave.”

Essentially, the researchers proposed that a test particle (i.e., probe) in a superposition (i.e., existing simultaneously in multiple states), which is at two different locations, would feel a gravitational field at both these locations when a particle with a Planck-scale mass passes it by. This would produce a quantum effect that could be detectable if the two states of the probe are experimentally prompted to interfere with one another.

“To actually measure the effect (as the wave function only tells us what the probability of finding where the probe particle is) one has to repeat the observation many times and do statistics,” said Perez.

“The problem is that we do not have such a luxury as the dark matter particles are very rare (their density is very small) and so the experiment cannot be repeated many times at will.

“For practical issues, it is best to assume that the probe particle has spin (as an electron) and then it is easier to produce an ideal experiment where one measures the interference (not in position) but in the spin variable. Yet the difficulty of having to repeat the experiment many times remains in this improved scenario.”

In their paper, the team show that it could be possible to search for Planck-scale particles using a system where many particles are in a coherent collective quantum state. This protocol would eliminate the need to repeat an experiment several times.

“One has about 10²³ electrons/cm³ in a special quantum state where all behave like a single one (they are described by a collective single wave function),” said Perez.

“In a Josephson junction they are (in a way) in a superposition of different locations at each side of the junction (a spatial gap separating two superconductors). The passage of a dark matter particle acts differently (gravitationally) on each side of the junction because they are at different distances, the interference between the wave function at the two sides produces a macroscopic effect: a current across the junctions (electrons tunneling across the gap).”

The protocol proposed by the researchers eliminates the need to repeat an experiment several times. This is due to the large number of electrons involved in a single passage of a Planck-scale dark matter particle, which reduces the need for statistical calculations.

“The current across the gap is the average (in the statistical sense) of the probabilistic response of each of the 10²³ electrons/cm³,” Perez said. “It is as if a macroscopic number of experiments of the first type would have been done at once.”

This recent paper by Rovelli, Christodoulou and Perez could soon open new possibilities for the search of Planck-scale dark matter particles. In the future, the protocol they proposed could contribute to the first detection of these highly elusive particles.

“Our work provides a concrete way to detect such particles,” said Rovelli.

“The interest is that such particles could be a major component of the mysterious dark matter that is revealed by the astronomers. If the detection we propose could be achieved, it would be spectacular: at the same time, it would tell us what dark matter is, it would validate the quantum gravity ideas, leading to the idea that this particle exists, and in particular loop quantum gravity, which is the basis of the prediction, and it would also reveal a new kind of object in nature: these Planck scale particles.”

The protocol developed by this research team could serve as the basis for the development of new detectors to search for dark matter particles with Planck-scale masses. Rovelli, who is a theoretical physicist, is currently conducting new studies aimed at understanding how black holes might evolve into these hypothetical dark matter particles.

“The detection of such particles will be a huge challenge technologically and there may be room to think of other ways of detection, using the same principle but different sensors,” said Christodoulou. “This is something that I keep in the back of my head and think about.”

While Rovelli is now continuing his theoretical work, Christodoulou and Perez have initiated collaborations with other experimental physicists, such as Gerard Higgins and Martin Zemlicka at the OEAW in Vienna. These collaborations could lead to studies exploring the possibility of measuring gravitational fields using superconductors.

“I believe that the hypothesis that dark matter is made of Planckian mass particles must have other observational consequences in astrophysics,” added Perez.

“For example, their extremely weak interaction with other particles (combined with their quantum mechanical nature) might imply that such dark matter behaves differently than expected when forming structure via their gravitational attraction: it is possible that it could explain some puzzles in the structure of the galactic halos.”

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