Billions of quantum entangled electrons found in 'strange metal'

Partial view of periodic table of the elements (stock image).

In a new study, U.S. and Austrian physicists have observed quantum entanglement among "billions of billions" of flowing electrons in a quantum critical material.

The research, which appears this week in Science, examined the electronic and magnetic behavior of a "strange metal" compound of ytterbium, rhodium and silicon as it both neared and passed through a critical transition at the boundary between two well-studied quantum phases.

The study at Rice University and Vienna University of Technology (TU Wien) provides the strongest direct evidence to date of entanglement's role in bringing about quantum criticality, said study co-author Qimiao Si of Rice.

"When we think about quantum entanglement, we think about small things," Si said. "We don't associate it with macroscopic objects. But at a quantum critical point, things are so collective that we have this chance to see the effects of entanglement, even in a metallic film that contains billions of billions of quantum mechanical objects."

Si, a theoretical physicist and director of the Rice Center for Quantum Materials (RCQM), has spent more than two decades studying what happens when materials like strange metals and high-temperature superconductors change quantum phases. Better understanding such materials could open the door to new technologies in computing, communications and more.

The international team overcame several challenges to get the result. TU Wien researchers developed a highly complex materials synthesis technique to produce ultrapure films containing one part ytterbium for every two parts rhodium and silicon (YbRh2Si2). At absolute zero temperature, the material undergoes a transition from one quantum phase that forms a magnetic order to another that does not.

At Rice, study co-lead author Xinwei Li, then a graduate student in the lab of co-author and RCQM member Junichiro Kono, performed terahertz spectroscopy experiments on the films at temperatures as low as 1.4 Kelvin. The terahertz measurements revealed the optical conductivity of the YbRh2Si2 films as they were cooled to a quantum critical point that marked the transition from one quantum phase to another.

"With strange metals, there is an unusual connection between electrical resistance and temperature," said corresponding author Silke Bühler-Paschen of TU Wien's Institute for Solid State Physics. "In contrast to simple metals such as copper or gold, this does not seem to be due to the thermal movement of the atoms, but to quantum fluctuations at the absolute zero temperature."

To measure optical conductivity, Li shined coherent electromagnetic radiation in the terahertz frequency range on top of the films and analyzed the amount of terahertz rays that passed through as a function of frequency and temperature. The experiments revealed "frequency over temperature scaling," a telltale sign of quantum criticality, the authors said.

Kono, an engineer and physicist in Rice's Brown School of Engineering, said the measurements were painstaking for Li, who's now a postdoctoral researcher at the California Institute of Technology. For example, only a fraction of the terahertz radiation shined onto the sample passed through to the detector, and the important measurement was how much that fraction rose or fell at different temperatures.

"Less than 0.1% of the total terahertz radiation was transmitted, and the signal, which was the variation of conductivity as a function of frequency, was a further few percent of that," Kono said. "It took many hours to take reliable data at each temperature to average over many, many measurements, and it was necessary to take data at many, many temperatures to prove the existence of scaling.

"Xinwei was very, very patient and persistent," Kono said. "In addition, he carefully processed the huge amounts of data he collected to unfold the scaling law, which was really fascinating to me."

Making the films was even more challenging. To grow them thin enough to pass terahertz rays, the TU Wien team developed a unique molecular beam epitaxy system and an elaborate growth procedure. Ytterbium, rhodium and silicon were simultaneously evaporated from separate sources in the exact 1-2-2 ratio. Because of the high energy needed to evaporate rhodium and silicon, the system required a custom-made ultrahigh vacuum chamber with two electron-beam evaporators.

"Our wild card was finding the perfect substrate: germanium," said TU Wien graduate student Lukas Prochaska, a study co-lead author. The germanium was transparent to terahertz, and had "certain atomic distances (that were) practically identical to those between the ytterbium atoms in YbRh2Si2, which explains the excellent quality of the films," he said.

Si recalled discussing the experiment with Bühler-Paschen more than 15 years ago when they were exploring the means to test a new class of quantum critical point. The hallmark of the quantum critical point that they were advancing with co-workers is that the quantum entanglement between spins and charges is critical.

"At a magnetic quantum critical point, conventional wisdom dictates that only the spin sector will be critical," he said. "But if the charge and spin sectors are quantum-entangled, the charge sector will end up being critical as well."

At the time, the technology was not available to test the hypothesis, but by 2016, the situation had changed. TU Wien could grow the films, Rice had recently installed a powerful microscope that could scan them for defects, and Kono had the terahertz spectrometer to measure optical conductivity. During Bühler-Paschen's sabbatical visit to Rice that year, she, Si, Kono and Rice microscopy expert Emilie Ringe received support to pursue the project via an Interdisciplinary Excellence Award from Rice's newly established Creative Ventures program.

"Conceptually, it was really a dream experiment," Si said. "Probe the charge sector at the magnetic quantum critical point to see whether it's critical, whether it has dynamical scaling. If you don't see anything that's collective, that's scaling, the critical point has to belong to some textbook type of description. But, if you see something singular, which in fact we did, then it is very direct and new evidence for the quantum entanglement nature of quantum criticality."

Si said all the efforts that went into the study were well worth it, because the findings have far-reaching implications.

"Quantum entanglement is the basis for storage and processing of quantum information," Si said. "At the same time, quantum criticality is believed to drive high-temperature superconductivity. So our findings suggest that the same underlying physics -- quantum criticality -- can lead to a platform for both quantum information and high-temperature superconductivity. When one contemplates that possibility, one cannot help but marvel at the wonder of nature."

Si is the Harry C. and Olga K. Wiess Professor in Rice's Department of Physics and Astronomy. Kono is a professor in Rice's departments of Electrical and Computer Engineering, Physics and Astronomy, and Materials Science and NanoEngineering and the director of Rice's Applied Physics Graduate Program. Ringe is now at the University of Cambridge.

Additional co-authors include Maxwell Andrews, Maximilian Bonta, Werner Schrenk, Andreas Limbeck and Gottfried Strasser, all of the TU Wien; Hermann Detz, formerly of TU Wien and currently at Brno University; Elisabeth Bianco, formerly of Rice and currently at Cornell University; Sadegh Yazdi, formerly of Rice and currently at the University of Colorado Boulder; and co-lead author Donald MacFarland, formerly of TU Wien and currently at the University at Buffalo.

The research was supported by the European Research Council (ERC-227378), the Army Research Office (W911NF-14-1-0496, W911NF-17-1-0259, W911NF-14-1-0525), the Austrian Science Fund (FWF-W1243, P29279-N27, P29296-N27), the European Union's Horizon 2020 program (824109-EMP), the National Science Foundation (DMR-1720595, DMR-1920740, PHY-1607611), the Robert A. Welch Foundation (C-1411), Los Alamos National Laboratory and Rice University.

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Materials provided by Rice University. Original written by Jade Boyd. Note: Content may be edited for style and length.

Fractal Pattern in a Quantum Material Confirmed for the First Time!

Image by: Arkadiusz Jadczyk

The word fractal has become increasingly popular, although the concept started more than two centuries ago in the 17th century with prominent and prolific mathematician and philosopher Gottfried Wilhelm Leibnitz. Leibnitz is believed to have addressed for the first time the notion of recursive self-similarity, and it wasn’t until 1960 that the concept was formally stabilized both theoretically and practically, through the mathematical development and computerized visualizations by Benoit Mandelbrot, who settled on the name “fractal”.

Fractals are defined mainly by three characteristics:

1. Self-similarity: identical or very similar shapes and forms at all scales.
2. Iteration: a recursive relationship limited only by computer capacity. With sufficiently high performance, the iterations could be infinite. This allows for very detailed shapes at every scale, that modify with respect to the first iteration, manifesting the original shape at some levels of iteration. Because of this, fractals may have emergent properties, which make them a suitable tool for complex systems.
3. Fractal dimension, or fractional dimensions: describes the counter-intuitive notion that a measured length changes with the length of the measuring stick used; it quantifies how the number of scaled measuring sticks required to measure, for example, a coastline, changes with the scale applied to the stick.

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The fractal dimension of a curve can be explained intuitively thinking of a fractal line as an object too detailed to be one-dimensional, but too simple to be two-dimensional.7

Although fractals now-a-days are commonly used for the macroscopic regime such as the branches of a tree, a broccoli, blood vessels and many others, for the first time physicists at MIT have discovered fractal-like patterns in a quantum material. The material is neodymium nickel oxide or NdNiO3, a rare earth nickelate that conduces electricity or acts as an insulator, depending on its temperature. It also presents inhomogeneous magnetism: domains or regions with a specific magnetic orientation that vary in size and shape throughout the material. The material exhibits this peculiar electronic and magnetic behavior as a result of quantum, atomic-scale effects, and for this reason it is called a quantum material.

The researchers had to design a very special X-ray-focusing lens in order to map the size, shape, and orientation of magnetic domains point by point at different temperatures, confirming that the material formed magnetic domains below a certain critical temperature. Above this temperature, the domains disappeared erasing the magnetic order. Nevertheless, if they cooled the sample back to below the critical temperature, the magnetic domains reappeared almost in the same place as before! This means that the system has memory, which was very unexpected. One could have a system robust against external perturbations, even if subjected to heat, such that the information is not lost.

Secondly, after mapping the material’s magnetic domains and measuring the size of each domain, the researchers counted the number of domains of a given size and plotted their number as a function of size. The resulting distribution showed the same pattern again and again, no matter what range of domain size they focused on. They found that these magnetic patterns have a fractal nature!
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“It was completely unexpected — it was serendipity.”
-Riccardo Comin, assistant professor of physics at MIT.

Because the material acts as an insulator or conductor depending on the temperature, scientists are exploring neodymium nickel oxide for neuromorphic devices — devices that mimic biological neurons. Here, temperature would play the role of voltage in the biological system, which is active or inactive depending on the voltage that it receives. Another potential application is resilient, magnetic data storage devices.

Artificial Intelligence Meets Quantum Physics!

As many theoretical and computational chemists and physicists know, quantum chemical calculations involving more than an electron and nuclei are very difficult to solve. They belong to a field called many body problems and require an extensive amount of computational infrastructure and hours of calculations depending on the size (the number of particles) of the system.

Here is where artificial intelligence – a combination of artificial neural networks and machine learning – comes into play. Neural networks have been around for more than 50 years, and they are more actualized than ever before. This is because they can learn through something called backward propagation, reaching a high level of predictability and increasing accuracy by training the network.

Quantum theoretical models, together with their computational packages, have been outstandingly successful in describing the quantum regime. While these models and packages supply fast and accurate predictions of atomic chemical properties, they do not capture all the electronic degrees of freedom of a molecule, limiting their applicability in chemical reactions and chemical analysis. Molecules and nanoparticles also require much more time to reach convergence, as compared to atoms. Calculations may even take weeks or months!

Initially used to predict pattern recognition such as market behavior and facial recognition, AI is now used to predict physical-chemical molecular properties in order to design drugs or new materials, among others. In order to perform accurately, AI must incorporate the fundamental laws of quantum physics. Deep machine learning has met this challenge with the proper algorithm capable of predicting the quantum states of molecules – also known as wave functions – where all properties emerge. Such an algorithm allowing AI to solve the fundamental equations of quantum mechanics has been published in Nature Communications under the title, “Unifying machine learning and quantum chemistry with a deep neural network for molecular wavefunctions.” The work was done by researchers at the University of Warwick, the Technological University of Berlin and the University of Luxembourg. Their newly developed AI algorithm can supply accurate predictions within seconds on a laptop or mobile phone.

Heat energy leaps through empty space, thanks to quantum weirdness

Heat energy leaps through empty space, thanks to quantum weirdness

\If you use a vacuum-insulated thermos to help keep your coffee hot, you may know it's a good insulator because heat energy has a hard time moving through empty space. Vibrations of atoms or molecules, which carry thermal energy, simply can't travel if there are no atoms or molecules around.

But a new study by researchers at the University of California, Berkeley, shows how the weirdness of quantum mechanics can turn even this basic tenet of classical physics on its head.

The study, appearing this week in the journal Nature, shows that heat energy can leap across a few hundred nanometers of a complete vacuum, thanks to a quantum mechanical phenomenon called the Casimir interaction.

Though this interaction is only significant on very short length scales, it could have profound implications for the design of computer chips and other nanoscale electronic components where heat dissipation is key. It also upends what many of us learned about heat transfer in high school physics.

"Heat is usually conducted in a solid through the vibrations of atoms or molecules, or so-called phonons -- but in a vacuum, there is no physical medium. So, for many years, textbooks told us that phonons cannot travel through a vacuum," said Xiang Zhang, the professor of mechanical engineering at UC Berkeley who guided the study. "What we discovered, surprisingly, is that phonons can indeed be transferred across a vacuum by invisible quantum fluctuations."

In the experiment, Zhang's team placed two gold-coated silicon nitride membranes a few hundred nanometers apart inside a vacuum chamber. When they heated up one of the membranes, the other warmed up, too -- even though there was nothing connecting the two membranes and negligible light energy passing between them.

"This discovery of a new mechanism of heat transfer opens up unprecedented opportunities for thermal management at the nanoscale, which is important for high-speed computation and data storage," said Hao-Kun Li, a former Ph.D. student in Zhang's group and co-first author of the study. "Now, we can engineer the quantum vacuum to extract heat in integrated circuits."

No such thing as empty space

The seemingly impossible feat of moving molecular vibrations across a vacuum can be accomplished because, according to quantum mechanics, there is no such thing as truly empty space, said King Yan Fong, a former postdoctoral scholar at UC Berkeley and the study's other first author.

"Even if you have empty space -- no matter, no light -- quantum mechanics says it cannot be truly empty. There are still some quantum field fluctuations in a vacuum," Fong said. "These fluctuations give rise to a force that connects two objects, which is called the Casimir interaction. So, when one object heats up and starts shaking and oscillating, that motion can actually be transmitted to the other object across the vacuum because of these quantum fluctuations."

Though theorists have long speculated that the Casimir interaction could help molecular vibrations travel through empty space, proving it experimentally has been a major challenge. To do so, the team engineered extremely thin silicon nitride membranes, which they fabricated in a dust-free clean room, and then devised a way to precisely control and monitor their temperature.

They found that, by carefully selecting the size and design of the membranes, they could transfer the heat energy over a few hundred nanometers of vacuum. This distance was far enough that other possible modes of heat transfer were negligible -- such as energy carried by electromagnetic radiation, which is how energy from the sun heats up Earth.

Because molecular vibrations are also the basis of the sounds that we hear, this discovery hints that sounds can also travel through a vacuum, Zhang said.

"Twenty-five years ago, during my Ph.D. qualifying exam at Berkeley, one professor asked me 'Why can you hear my voice across this table?' I answered that, 'It is because your sound travels by vibrating molecules in the air.' He further asked, 'What if we suck all air molecules out of this room? Can you still hear me?' I said, 'No, because there is no medium to vibrate,'" Zhang said. "Today, what we discovered is a surprising new mode of heat conduction across a vacuum without a medium, which is achieved by the intriguing quantum vacuum fluctuations. So, I was wrong in my 1994 exam. Now, you can shout through a vacuum."

Co-authors of the paper include Rongkuo Zhao, Sui Yang and Yuan Wang of UC Berkeley.

This research was funded in part by the National Science Foundation (NSF) under grant 1725335, the King Abdullah University of Science and Technology Office of Sponsored Research (OSR) (award OSR-2016-CRG5-2950-03; OSR-2016-CRG5-2996) and the Ernest S. Kuh Endowed Chair in Engineering.

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Materials provided by University of California - Berkeley. Original written by Kara Manke. Note: Content may be edited for style and length.

Ultrafast quantum simulations: A new twist to an old approach

Ultrafast quantum simulations

Billions of tiny interactions occur between thousands of particles in every piece of matter in the blink of an eye. Simulating these interactions in their full dynamics was said to be elusive but has now been made possible by new work of researchers from Oxford and Warwick.

In doing so, they have paved the way for new insights into the complex mutual interactions between the particles in extreme environments such as at the heart of large planets or laser nuclear fusion.

Researchers at the University of Warwick and University of Oxford have developed a new way to simulate quantum systems of many particles, that allows for the investigation of the dynamic properties of quantum systems fully coupled to slowly moving ions.

Effectively, they have made the simulation of the quantum electrons so fast that it could run extremely long without restrictions and the effect of their motion on the movement of the slow ions would be visible.

Reported in the journal Science Advances, it is based on a long-known alternative formulation of quantum mechanics (Bohm dynamics) which the scientists have now empowered to allow to study the dynamics of large quantum systems.

Many quantum phenomena have been studied for single or just a few interacting particles as large complex quantum systems overpower scientists' theoretical and computational capabilities to make predictions. This is complicated by the vast difference in timescale the different particle species act on: ions evolve thousands of times more slowly than electrons due to their larger mass. To overcome this problem, most methods involve decoupling electrons and ions and ignoring the dynamics of their interactions -- but this severely limits our knowledge on quantum dynamics.

To develop a method that allows scientists to account for the full electron-ion interactions, the researchers revived an old alternative formulation of quantum mechanics developed by David Bohm. In quantum mechanics, one needs to know the wave function of a particle. It turns out that describing it by the mean trajectory and a phase, as done by Bohm, is very advantageous. However, it took an additional suit of approximations and many tests to speed up the calculations as dramatic as required. Indeed, the new methods demonstrated an increase of speed by more than a factor of 10,000 (four orders of magnitude) yet is still consistent with previous calculations for static properties of quantum systems.

The new approach was then applied to a simulation of warm dense matter, a state between solids and hot plasmas, that is known for its inherent coupling of all particle types and the need for a quantum description. In such systems, both the electrons and the ions can have excitations in the form of waves and both waves will influence each other. Here, the new approach can show its strength and determined the influence of the quantum electrons on the waves of the classical ions while the static properties were proven to agree with previous data.

Many-body quantum systems are the core of many scientific problem ranging from the complex biochemistry in our bodies to the behaviour of matter inside of large planets or even technological challenges like high-temperature superconductivity or fusion energy which demonstrates the possible range of applications of the new approach.

Prof Gianluca Gregori (Oxford), who led the investigation, said: "Bohm quantum mechanics has often been treated with skepticism and controversy. In its original formulation, however, this is just a different reformulation of quantum mechanics. The advantage in employing this formalism is that different approximations become simpler to implement and this can increase the speed and accuracy of simulations involving many-body systems."

Dr Dirk Gericke from the University of Warwick, who assisted the design of the new computer code, said: "With this huge increase of numerical efficiency, it is now possible to follow the full dynamics of fully interacting electron-ion systems. This new approach thus opens new classes of problems for efficient solutions, in particular, where either the system is evolving or where the quantum dynamics of the electrons has a significant effect on the heavier ions or the entire system.

"This new numerical tool will be a great asset when designing and interpreting experiments on warm dense matter. From its results, and especially when combined with designated experiments, we can learn much about matter in large planets and for laser fusion research. However, I believe its true strength lies in its universality and possible applications in quantum chemistry or strongly driven solids."

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Materials provided by University of Warwick. Note: Content may be edited for style and length.