Farklı Bir Kaos Türü
California Üniversitesi, Santa Barbara, Maryland Üniversitesi ve Washington Üniversitesi’nden fizikçiler uzun süredir devam eden bir fizik bulmacasını çözdüler: parçacıklar arası etkileşimler dinamik yerelleştirmeyi nasıl etkiler?
UCSB’de ultra-soğuk atom fiziği ve kuantum simülasyonu uzmanlığı olan deneysel fizikçi David Weld, “Bu, yoğun madde fiziğinden miras kalan gerçekten eski bir soru” dedi. Soru, birden çok etkileşimli parça ile bir kuantum sisteminin fiziksel özelliklerini sorgulayan ‘çok vücut’ fiziği kategorisine girer. Çok cisim problemleri onlarca yıldır bir araştırma ve tartışma konusu olsa da, süperpozisyon ve dolaşma gibi kuantum davranışlarıyla bu sistemlerin karmaşıklığı, çok sayıda olasılığa yol açarak tek başına hesaplama yoluyla çözülmesini imkansız hale getiriyor. Weld, “Sorunun birçok yönü modern bilgisayarların erişiminin ötesinde” diye ekledi.
Neyse ki bu sorun, ultra soğuk lityum atomları ve lazerleri kullanan bir deneyin ulaşamayacağı kadar uzak değildi. Peki, etkileşim düzensiz, kaotik bir kuantum sistemine dahil edildiğinde ne olur?
Weld’e göre “tuhaf bir kuantum hali”. “Bu, bir bakıma klasik tahmin ile etkileşimsiz kuantum tahmini arasında yer alan özelliklere sahip, anormal bir durumdur.”
Fizikçilerin bulguları yakın zamanda yayınlandı.
While this state of localization has been studied in the setting of single, noninteracting particles for decades, what happens when a disordered system contains 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.
“What Victor raised was the question of what happens if, instead of this pure non-interacting quantum system which is stabilized by interference, you have a bunch of these rotors and they can all bump into and interact with each other,” Weld recalled. “Does the localization persist, or is it destroyed by the interactions?”
“Indeed, it is a very difficult question that relates to foundations of statistical mechanics and the basic notion of ergodicity, whereby most interacting systems eventually thermalize into a universal state,” said Galitski.
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 nor 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, which was recognized by the Lars Onsager Prize earlier this year, is difficult to rigorously prove theoretically or establish experimentally,” Galitski said.
Weld’s group had the technology and expertise to shed light on the situation, literally. In their lab is a gas of 100,000 ultracold lithium atoms suspended in a standing wave of light. Each atom represents a quantum rotor that can be kicked by laser pulses.
“We can use a tool called a Feshbach resonance to keep the atoms cloaked from each other, or we can make them bounce off each other with arbitrarily strong interactions,” Weld said. 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 expected, when the atoms were invisible to each other they took the laser kicking up to a certain point, after which they stopped moving in their dynamically localized state, despite repeated kicks. But when the researchers dialed up the interaction, not only did the localized state diminish, but the system appeared to absorb energy from the repeated kicks, mimicking classical chaotic behavior.
However, Weld pointed out, while the interacting disordered quantum system was absorbing energy, it was doing so at a much slower rate than would a classical system.
“What we’re seeing is something that absorbs energy, but not as well as a classical system can,” he said. “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.”
Testing for Chaos
Weld’s team used a technique called an “echo” in which the kinetic evolution is run forward and then backward to directly measure the way in which interactions destroy time reversibility. This destruction of time reversibility is a key signature of quantum chaos.
“Another way to think about this is to ask: How much memory of the initial state does the system have after some time?” said co-author Roshan Sajjad, a graduate student researcher on the lithium team. In the absence of any perturbations such as stray light or gas collisions, he explained, 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,” he said. “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.”
“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 is practically impossible to return to its initial state,” said lead author Alec Cao. 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, he explained
“Naively, you’d expect interactions to ruin time reversal, but we saw something more interesting: A little bit of interaction actually helps!” Sajjad added. “This was one of the more surprising results of this work.”
Weld and Galitski weren’t the only ones to witness this fuzzy quantum state. University of Washington physicist Subhadeep Gupta and his team ran a complementary experiment at the same time, producing similar results using heavier atoms in a one-dimensional context. That result is published alongside those of UC Santa Barbara’s and University of Maryland’s in Nature Physics.
“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 been in conflict,” said Gupta, whose group collaborated with theorist Chuanwei Zhang and his team at the University of Texas in Dallas.
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.
“David’s experiment is the first attempt to probe a dynamical version of MBL in a more controlled laboratory setting,” Galitski commented. “While it has not unambiguously resolved the fundamental question one way or another, the data show something strange is going on.”
“How can we understand these results in the context of the very large body of work on many-body localization in condensed matter systems?” Weld asked. “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.”
“Interaction-driven breakdown of dynamical localization in a kicked quantum gas” by Alec Cao, Roshan Sajjad, Hector Mas, Ethan Q. Simmons, Jeremy L. Tanlimco, Eber Nolasco-Martinez, Toshihiko Shimasaki, H. Esat Kondakci, Victor Galitski and David M. Weld, 26 September 2022, Nature Physics.
“Many-body dynamical delocalization in a kicked one-dimensional ultracold gas” by Jun Hui See Toh, Katherine C. McCormick, Xinxin Tang, Ying Su, Xi-Wang Luo, Chuanwei Zhang and Subhadeep Gupta, 26 September 2022, Nature Physics.