A team of physicists from Rice University has simulated superconducting materials by substituting ultra-cold atoms in place of electrons, thus solving a challenge, which has intrigued scientists for almost thirty years.
Rice University physicists trapped ultracold atomic gas in grids of intersecting laser beams to mimic the antiferromagnetic order observed in the parent compounds of nearly all high-temperature superconductors. (Credit: P. Duarte/Rice University)
The study, performed by an international theoretical and experimental physicist team will be published online this week in the Nature journal. Led by Randy Hulet, Rice University experimental physicist, the research could help unveil new unexplored avenues of science.
Physicists discovered almost three decades ago that electrons can freely flow through some materials (superconductors) at considerably high temperatures.
The cause for this unconventional or high-temperature superconductivity is still a mystery. The Hubbard model is one of the best theories with regards to unconventional superconductivity.
This model, however, can be expressed mathematically with considerable ease but is impossible to be solved using digital computers.
"The Hubbard model is a set of mathematical equations that could hold the key to explaining high-temperature superconductivity, but they are too complex to solve — even with the fastest supercomputer. That’s where we come in." Hulet, Rice’s Fayez Sarofim Professor of Physics and Astronomy.
The expertise of Hulet’s lab is to cool atoms to very low temperatures so that the principles of quantum mechanics influence their behavior. These principles are the same followed by electrons while flowing through semiconductors.
“Using our cold atoms as stand-ins for electrons and beams of laser light to mimic the crystal lattice in a real material, we were able to simulate the Hubbard model,” Hulet said. “When we did that, we were able to produce antiferromagnetism in exactly the way the Hubbard model predicts. That’s exciting because it’s the first ultracold atomic system that’s able to probe the Hubbard model in this way, and also because antiferromagnetism is known to exist in nearly all of the parent compounds of unconventional superconductors.”
Hulet’s team is one of several research teams, which are in the quest of using ultra-cold atomic systems to mimic the behavior of high-temperature superconductors.
Despite 30 years of effort, people have yet to develop a complete theory for high-temperature superconductivity. Real electronic materials are extraordinarily complex, with impurities and lattice defects that are difficult to fully control. In fact, it has been so difficult to study the phenomenon in these materials that physicists still don’t know the essential ingredients that are required to make an unconventional superconductor or how to make a material that superconducts at even greater temperature.
Hulet, Rice’s Fayez Sarofim Professor of Physics and Astronomy.
Without any lattice disorder or defects, the system designed by Hulet’s team simulates the actual electronic material.
“We believe that magnetism plays a role in this process, and we know that each electron in these materials correlates with every other, in a highly complex way,” he said. “With our latest findings, we’ve confirmed that we can cool our system to the point where we can simulate short-range magnetic correlations between electrons just as they begin to develop.
“That’s significant because our theoretical colleagues — there were five on this paper — were able to use a mathematical technique known as the Quantum Monte Carlo method to verify that our results match the Hubbard model,” Hulet said. “It was a heroic effort, and they pushed their computer simulations as far as they could go. From here on out, as we get colder still, we’ll be extending the boundaries of known physics.”
The Ohio State University professor of Physics, Nandini Trivedi stated that she and her team at the University of California-Davis, who contributed the theoretical part of the research, were given the task of determining how cold the atoms were supposed to be in the experiment.
Some of the big questions we ask are related to the new kinds of ways in which atoms get organized at low temperatures. Because going to such low temperatures is a challenge, theory helped determine the highest temperature at which we might expect the atoms to order themselves like those of an antiferromagnet.
Ohio State University professor of Physics, Nandini Trivedi
Subsequent to the discovery of high-temperature superconductivity in the 1980s, certain theoretical physicists suggested that the Hubbard model could explain the underlying physics. The Hubbard model is a group of equations developed by physicist John Hubbard in the early 1960s to explain the conduction and magnetic characteristics of electrons in transition metal oxides and transition metals.
Each electron has a spin, which acts like a small magnet. Physicists in the 1950s and 1960s observed that the electron spin in transition metal oxides, and transition metals could arrange themselves in ordered patterns.
When Hubbard designed his model, he desired to develop the easiest possible system to describe the response of electrons in these materials towards each other.
The Hubbard model characterizes electrons which can jump between sites in a lattice or an ordered grid. Each lattice site signifies an ion in a material’s crystal lattice and the behavior of the electrons is decided by just a few variables.
Firstly, the Pauli’s exclusion principle prevents electrons from sharing an energy level. Secondly, an energy penalty must be paid by electrons when they occupy the same position since they by rule, repel each other.
“The Hubbard model is remarkably simple to express mathematically,” Hulet said. “But because of the complexity of the solutions, we cannot calculate its properties for anything but a very small number of electrons on the lattice. There is simply too much quantum entanglement among the system’s degrees of freedom.”
Electron behaviors such as superconductivity and anti-ferromagnetism, which are correlated, arise from feedback since the action of each electron causes a reaction influencing all its adjacent electrons. As the number of sites increase, performing these calculations becomes highly time-consuming. Until now, the best computer simulations of 2D and 3D Hubbard models involve systems of just a few 100 electron sites.
These computational challenges have made it impossible for physicists to find out if the Hubbard model comprises the essence of unconventional superconductivity. Study results show that the solutions by the model reveal antiferromagnetism, however it is not clear if superconductivity is also exhibited by them.
Simulating superconducting materials with ultracold atoms
In the latest study, Hulet and team, along with Russell Hart, postdoctoral researcher and Petro Duarte, graduate student, created a new method to cool atoms in the lab to significantly low temperatures to start observing antiferromagnetic order in an optical lattice with around 100,000 sites. This novel technique helps obtain lattice temperatures that are half that obtained in previous experiments.
“The standard technique is to create the cold atomic gas, load it into the lattice and take measurements,” Hart said. “We developed the first method for evaporative cooling of atoms that had already been loaded in a lattice. That technique, which uses what we call a ‘compensated optical lattice,’ also helped control the density of the sample, which becomes critical for forming antiferromagnetic order.”
Hulet stated that the next innovation was the team using the optical method, Bragg scattering for observing the symmetry planes characterizing the antiferromagnetic order.
According to him, for determining the electron pair correlations causing superconductivity, a completely new method was required. And colder samples were also needed, ten times colder than those used in the present study.
“We have some things in mind,” Hulet said. “I am confident we can achieve lower temperatures both by refining what we’ve already done and by developing new techniques. Our immediate goal is to get cold enough to get fully into the antiferromagnetic regime, and from there we’d hope to get into the d-wave pairing regime and confirm whether or not it exists in the Hubbard model.”
Additional co-authors include Tsung-lin Yang and Xinxing Liu, all of Rice; Thereza Paiva of Universidade Federal do Rio de Janeiro; Ehsan Khatami of both the University of California-Davis (UC-Davis) and San Jose State University; David Huse of Princeton University and Richard Scalettar of UC-Davis. The Defense Advanced Research Projects Agency, the National Science Foundation, the Robert Welch Foundation and the Office of Naval Research supported the research at Rice University.
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