An international team, co-led by UC Santa Cruz physicist Jairo Velasco, Jr., has answered the question of where patterns emerge from chaos. The team described an experiment that validates a theory proposed 40 years ago, which suggests that electrons confined in quantum space follow common paths instead of producing a chaotic array of trajectories. The study was published in the journal Nature.
The pattern of quantum scars captured in the lab of physics Professor Jairo Velasco, Jr. Image Credit: Velasco Lab
Electrons do not just roll like a ball but have particle and wave-like characteristics. In addition to their frequently counterintuitive behavior, electrons can concentrate their movement into specific patterns due to the interference of their waves under specific circumstances. Physicists refer to these common routes as “unique closed orbits.”
This was made possible in Velasco's lab by a complex fusion of cutting-edge imaging methods and exact control over electron behavior in graphene. Graphene is a material frequently used in research due to its special qualities and two-dimensional structure, which make it perfect for observing quantum effects.
To detect electron movements without physically disturbing the graphene surface, Velasco's team first created a trap for electrons using the finely tipped probe of a scanning tunneling microscope. They then hovered close to the graphene surface.
According to Velasco, the advantage of electrons traveling in closed orbits in a small area is that the properties of the subatomic particle would be better maintained as it traveled from one location to another. He explained how information encoded in an electron's properties could be transferred without loss, potentially leading to lower-power, highly efficient transistors. He said this has enormous implications for everyday electronics.
One of the most promising aspects of this discovery is its potential use in information processing. By slightly disturbing, or ‘nudging’ these orbits, electrons could travel predictably across a device, carrying information from one end to the other.
Jairo Velasco Jr., Department of Physics, University of California
Quantum Scars Make Their Mark
These distinct electron orbits are called “quantum scars” in physics. Eric Heller, a Physicist at Harvard University, first explained this in a theoretical study in 1984. He used computer simulations to show that confined electrons would travel along high-density orbits if their wave motions interfered with one another.
Quantum scarring is not a curiosity. But rather, it is a window onto the strange quantum world. Scarring is a localization around orbits that come back on themselves. These returns have no long-term consequence in our normal classical world they are soon forgotten. But they are remembered forever in the quantum world.
Eric Heller, Physicist, Harvard University
Now that Heller's theory has been validated, scientists have the empirical groundwork necessary to investigate possible uses. By using quantum scar-based designs, today's transistors which are already at the nanoelectronic scale could become even more efficient, improving gadgets like computers, smartphones, and tablets that depend on densely packed transistors to increase processing power.
Velasco said, “For future studies, we plan to build on our visualization of quantum scars to develop methods to harness and manipulate scar states. The harnessing of chaotic quantum phenomena could enable novel methods for selective and flexible delivery of electrons at the nanoscale thus, innovating new modes of quantum control.”
Classical Chaos vs. Quantum Chaos
Velasco's team uses a visual model known as a “billiard” to demonstrate the classical mechanics of linear versus chaotic systems. A “stadium” is a common shape used in physics, with straight edges and curved ends. A billiard is a bounded area that shows how particles move inside. In classical chaos, a particle would randomly and unpredictably bounce around, eventually covering the entire surface.
In this experiment, the team used atom-thin graphene, about 400 nm long, to create a stadium billiard. Thanks to the scanning tunneling microscope, they finally saw the pattern of electron orbits inside the stadium billiard they made in Velasco's lab, allowing them to witness quantum chaos in action.
I am very excited we successfully imaged quantum scars in a real quantum system. Hopefully, these studies will help us gain a deeper understanding of chaotic quantum systems.
Zhehao Ge, Study First, Co-Corresponding Author and Graduate Student, University of California
The study's co-authors are Peter Polizogopoulos, Ryan Van Haren, and David Lederman at UC Santa Cruz; Anton Graf and Joonas Keski-Rahkonen at Harvard; Sergey Slizovskiy and Vladimir Fal’ko at the University of Manchester; and Takashi Taniguchi and Kenji Watanabe at Japan's National Institute for Materials Science.
Journal Reference:
Ge, Z., et al. (2024) Direct visualization of relativistic quantum scars in graphene quantum dots. Nature. doi.org/10.1038/s41586-024-08190-6.