Uncovering universal physics in the dynamics of a quantum system

New experiments using one-dimensional gases of ultra-cold atoms reveal a universality in how quantum systems composed of many particles change over time following a large influx of energy that throws the system out of equilibrium. A team of physicists at Penn State showed that these gases immediately respond, “evolving” with features that are common to all “many-body” quantum systems thrown out of equilibrium in this way. A paper describing the experiments appears May 17, 2023 in the journal Nature.

“Many major advances in physics over the last century have concerned the behavior of quantum systems with many particles,” said David Weiss, Distinguished Professor of Physics at Penn State and one of the leaders of the research team. “Despite the staggering array of diverse ‘many-body’ phenomena, like superconductivity, superfluidity, and magnetism, it was found that their behavior near equilibrium is often similar enough that they can be sorted into a small set of universal classes. In contrast, the behavior of systems that are far from equilibrium has yielded to few such unifying descriptions.”

These quantum many-body systems are ensembles of particles, like atoms, that are free to move around relative to each other, Weiss explained. When they are some combination of dense and cold enough, which can vary depending on the context, quantum mechanics—the fundamental theory that describes the properties of nature at the atomic or subatomic scale—is required to describe their dynamics.

Dramatically out-of-equilibrium systems are routinely created in particle accelerators when pairs of heavy ions are collided at speeds near the speed-of-light. The collisions produce a plasma—composed of the subatomic particles “quarks” and “gluons”—that emerges very early in the collision and can be described by a hydrodynamic theory—similar to the classical theory used to describe air flow or other moving fluids—well before the plasma reaches local thermal equilibrium. But what happens in the astonishingly short time before hydrodynamic theory can be used?

“The physical process that occurs before hydrodynamics can be used has been called ‘hydrodynamization,” said Marcos Rigol, professor of physics at Penn State and another leader of the research team. “Many theories have been developed to try to understand hydrodynamization in these collisions, but the situation is quite complicated and it is not possible to actually observe it as it happens in the particle accelerator experiments. Using cold atoms, we can observe what is happening during hydrodynamization.”

The Penn State researchers took advantage of two special features of one-dimensional gases, which are trapped and cooled to near absolute zero by lasers, in order to understand the evolution of the system after it is thrown of out of equilibrium, but before hydrodynamics can be applied. The first feature is experimental. Interactions in the experiment can be suddenly turned off at any point following the influx of energy, so the evolution of the system can be directly observed and measured. Specifically, they observed the time-evolution of one-dimensional momentum distributions after the sudden quench in energy.

“Ultra-cold atoms in traps made from lasers allow for such exquisite control and measurement that they can really shed light on many-body physics,” said Weiss. “It is amazing that the same basic physics that characterize relativistic heavy ion collisions, some of the most energetic collisions ever made in a lab, also show up in the much less energetic collisions we make in our lab.”

The second feature is theoretical. A collection of particles that interact with each other in a complicated way can be described as a collection of “quasiparticles” whose mutual interactions are much simpler. Unlike in most systems, the quasiparticle description of one-dimensional gases is mathematically exact. It allows for a very clear description of why energy is rapidly redistributed across the system after it is thrown out of equilibrium.

“Known laws of physics, including conservation laws, in these one-dimensional gases imply that a hydrodynamic description will be accurate once this initial evolution plays out,” said Rigol. “The experiment shows that this occurs before local equilibrium is reached. The experiment and theory together therefore provide a model example of hydrodynamization. Since hydrodynamization happens so fast, the underlying understanding in terms of quasi-particles can be applied to any many-body quantum system to which a very large amount of energy is added.”

In addition to Weiss and Rigol, the research team at Penn State includes Yuan Le, Yicheng Zhang, and Sarang Gopalakrishnan. The research was funded by the U.S. National Science Foundation. Computations were carried out at the Penn State Institute for Computational and Data Sciences.