How do interparticle interactions affect dynamical localization?

A different kind of chaos.


Kicked quantum systems can display the emergence of dynamical localization, which restricts energy absorption and causes the breakdown of ergodicity, in contrast to classical driven systems, which display chaotic behavior and diffusive energy accumulation. It has long been unclear how dynamically localized states evolve when many-body interactions exist.

A new study by the physicists at UC Santa Barbara and the University of Maryland, and also at the University of Washington, have found an answer to the longstanding physics question: How do interparticle interactions affect dynamical localization?

The question pertains to “many-body” physics, which explores the physical characteristics of a quantum system with numerous data types. Many-body problems have been the subject of research and discussion for decades.  The complexity of these systems, along with quantum phenomena like superposition and entanglement, leads to a vast range of possibilities, making it difficult to answer through calculation alone.

Fortunately, this problem was not beyond the reach of an experiment that involved ultracold lithium atoms and lasers. So, according to scientists, a weird quantum state emerges when you introduce interaction in a disordered, chaotic quantum system.

David Weld(link is external), an experimental physicist at UCSB with specialties in ultracold atomic physics and quantum simulation said, “It’s a state which is anomalous, with properties which in some sense lie between the classical prediction and the noninteracting quantum prediction.”

“When it comes to strange, counterintuitive behavior, the quantum world does not disappoint. Take, for instance, a regular pendulum, which would behave exactly how we expect it to when subjected to energy pulses.”

“If you kick it and shake it up and down every once in a while, a classical pendulum will continuously absorb energy, start to wiggle all over the place, and explore the whole parameter space chaotically.”

The chaos in quantum systems seems different. The disorder can cause particles to kind of standstill.  Additionally, while a kicked quantum pendulum or “rotor” may initially absorb energy from the kicks, similar to a classical pendulum, with repeated kicks, the system stops absorbing energy, and the momentum distribution freezes in what is known as a dynamically localized state.

This localized state is closely analogous to the behavior of a “dirty” electronic solid, in which disorder results in immobile, localized electrons. It causes a solid to transition from being a metal, or a conductor (moving electrons), to an insulator.

While this state of localization has been explored for decades in the context of single, noninteracting particles, what happens in a disordered system with multiple interacting electrons? Questions like this and related aspects of quantum chaos were on the minds of Weld and his co-author, University of Maryland theorist Victor Galitski, during a discussion several years ago when Galitski was visiting Santa Barbara.

Weld recalled, “Victor raised the question of what happens if, instead of this pure noninteracting quantum system which is stabilized by interference, you have a bunch of these rotors, and they can all bump into and interact with and interact with each other. Does the localization persist, or do the interactions destroy it?”

Galitski said, “Indeed, it is a complicated question that relates to foundations of statistical mechanics and the basic notion of ergodicity, whereby most interacting systems eventually thermalize into a universal state.”

“Imagine for a moment pouring cold milk into hot coffee. The particles in your cup will, over time and through their interactions, arrange themselves into a uniform, equilibrium state that is neither purely hot coffee or cold milk. This type of behavior — thermalization — was expected of all interacting systems. That is, until about 16 years ago when it was argued that disorder in a quantum system was thought to result in many-body localization (MBL).”

“This phenomenon, recognized by the Lars Onsager Prize earlier this year, is difficult to prove theoretically or experimentally rigorously.”

Weld’s team has the tool, technology, and knowledge to effectively shed light on the matter. 100,000 ultra-cold lithium atoms are suspended in a standing wave of light in gas in their lab. Each atom represents a quantum rotor that laser pulses can spark.

Using a Feshbach resonance tool, scientists can keep the atoms cloaked from each other or make them bounce off each other with arbitrarily strong interactions. With a turn of a knob, the researchers could make the lithium atoms go from line dance to mosh pit and capture their behaviors.

As anticipated, when the atoms were unable to see one another, they were able to withstand repeated kicks from the laser until a certain point, at which time they ceased to move in their dynamically localized form. However, as the scientists increased the interaction, not only did the confined state disappear, but it also seemed the system was absorbing the energy from the repeated kicks, simulating classic, chaotic behavior.

Weld said, “However, while the interacting disordered quantum system was absorbing energy, it was doing so at a much slower rate than would a classical system.”

“We’re seeing something that absorbs energy, but not as well as a classical system can. And it seems like the energy is growing roughly with the square root of time instead of linearly with time. So the interactions aren’t making it classical; it’s still a weird quantum state exhibiting anomalous non-localization.”

Scientists used a method called echo. In this method, the kinetic evolution is run forward and then backward to measure how interactions destroy time reversibility directly. One crucial indicator of quantum chaos is the destruction of time reversibility.

Co-author Roshan Sajjad, a graduate student researcher on the lithium team, said, “Another way to think about this is to ask: How much memory of the initial state does the system have after some time?”

“In the absence of any perturbations such as stray light or gas collisions, the system should be able to return to its initial state if the physics is run backward. In our experiment, we reverse time by reversing the phase of the kicks, ‘undoing’ the effects of the first normal set of kicks. Part of our fascination was that different theories had predicted different behaviors on the outcome of this type of interacting setup, but no one had ever done the experiment.”

Lead author Alec Cao said, “The rough idea of chaos is that even though the laws of motion are time-reversible, a many-particle system can be so complicated and sensitive to perturbations that are practically impossible to return to its initial state. The twist was that in an effectively disordered (localized) state, the interactions broke the localization somewhat even as the system lost its capacity to be time-reversed.”

Sajjad said, “Naively, you’d expect interactions to ruin time-reversal, but we saw something more interesting: A little interaction helps! This was one of the more surprising results of this work.”

Scientists ran a complementary experiment that produced similar results using heavier atoms in a one-dimensional context.

Gupta said, “The experiments at UW operated in a very difficult physical regime with 25-times-heavier atoms restricted to move in one dimension only, yet also measured weaker-than-linear energy growth from periodic kicking, shedding light on an area where theoretical results have conflicted.”

Weld said, “these findings, like many important physics results, open up more questions and pave the way for more quantum chaos experiments, where the coveted link between classical and quantum physics may be uncovered.”

Galitski commented, “David’s experiment is the first attempt to probe a dynamical version of MBL in a more controlled laboratory setting. While it has not unambiguously resolved the fundamental question one way or another, the data show something strange is going on.”

Weld said“How can we understand these results in the context of the very large body of work on many-body localization in condensed matter systems? How can we characterize this state of matter? We observe that the system is delocalizing, but not with the expected linear time dependence; what’s going on there? We’re looking forward to future experiments exploring these and other questions.”

Journal Reference:

  1. See Toh, J.H., McCormick, K.C., Tang, X. et al. Many-body dynamical delocalization in a kicked one-dimensional ultracold gas. Nat. Phys. (2022). DOI: 10.1038/s41567-022-01721-w
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