Atom Clouds Resist Being Agitated
A single spoke, or rotor, can be set spinning on its axis ever faster by repeatedly kicking it. If the kick strength exceeds a threshold, the motion becomes chaotic. The quantum version of the kicked rotor behaves differently and counterintuitively. Above a threshold, quantum interference prevents the rotor from absorbing any more energy. Rather than growing indefinitely, the momentum settles—or becomes “localized”—into a finite set of states. Both the kicked rotor and its quantum cousin have become foundational models in nonlinear dynamics, yet, possessing just one particle, they are also highly idealized. Can a many-body system also undergo localization in momentum space? The answer is yes, but there remains uncertainty over the effect of interactions between particles. Now Hanns-Christoph Nägerl of the University of Innsbruck in Austria and his collaborators have shown localization in a many-body kicked rotor consisting of cesium atoms trapped in a 1D optical lattice [1]. By tuning the interaction strength, they found that this so-called many-body dynamical localization (MBDL) persists even when particles interact strongly.
In conceiving their experiment, Nägerl and his collaborators started with a model devised by Elliott Lieb and Werner Liniger. In 1963, the two theorists set out to calculate the ground-state energy of a gas of interacting bosons confined in one dimension at absolute zero. In the model, pairs of particles interact with each other when they find themselves in the same position. The model’s variables are the density of particles and the interaction strength, which ranges from zero to infinity. In 2020, Colin Rylands of Coventry University in the UK and his collaborators further developed this model, exploring the emergence of localization under certain conditions [2].
To realize the Lieb-Liniger model in their lab, Nägerl and his collaborators loaded cesium atoms into a 2D optical lattice consisting of an array of narrow, vertically oriented traps. Each of the 5000 tube-shaped traps contained about 18 atoms cooled to 2 nanokelvin. The researchers kicked the atoms by firing periodic laser pulses at the traps, with the number of pulses varied between 0 and 1051. They also controlled the atom–atom interactions through the application of an external magnetic field. The strengths of these interactions were set to three different values, where the lowest value was near zero and the highest value corresponded to a strongly interacting regime.
After the firing of laser pulses, the team measured the resulting momenta of the atoms by releasing all of them at once and using absorption imaging to see how far they traveled after a fixed flight time of 20 ms. Combining and averaging images from all the traps yielded crisp images, from which the researchers inferred the atoms’ momentum distribution. The data revealed a series of peaks at integer multiples of the momentum imparted by each kick. For the lowest interaction strength, the peaks shifted to higher and higher momentum as the number of pulses increased. But after about 50 pulses, this trend stopped with the peaks settling down in one place: evidence that MBDL had set in. For the highest interaction strength, the atoms gained more momentum from a longer sequence of pulses. Nevertheless, after 400 pulses or so, MBDL also set in. No amount of additional kicking could shake the atoms out of their frozen, localized state.
Nägerl and colleagues are not the first to observe MBDL. Several previous experiments with trapped atoms have recorded evidence of momentum localization in systems with little or no atom–atom interactions. In 2022, David Weld of the University of California, Santa Barbara, and his collaborators subjected a 3D Bose-Einstein condensate to periodic kicks and found that MBDL broke down when interactions became too strong [3]. This new work by Nägerl and his collaborators demonstrates that MBDL can survive into the strongly interacting regime, at least in 1D.
MBDL is the momentum-space counterpart of Anderson localization, in which particles diffusing in a disordered medium become frozen in place by the destructive interference of their wave functions. To show the role of interference in their experiment, Nägerl and his collaborators subjected their trapped atoms to pulses whose random timing forestalled interference. In this case, the atoms’ energy and entropy rose precipitously without limit—in other words, no localization. The implication is that MBDL requires that the laser kicks occur in a coherent fashion, so that the higher momentum states can destructively interfere with each other.
Theorist Victor Galitski of the University of Maryland, College Park, coined the term MBDL. He points out that researchers have long been looking for ways to evade runaway chaos. On paper, MBDL offers an escape route. However, exploiting it usually requires imposing disorder, which introduces fluctuations that complicate both rigorous theoretical analyses and unambiguous experiments. “The MBDL reported by Nägerl and colleagues is a cleaner phenomenon,” he says. “Here, disorder is emergent and rare events are irrelevant, which potentially opens a path to proving lack of chaos in a class of interacting quantum systems.”
–Charles Day
Charles Day is a Senior Editor for Physics Magazine.
References
- Y. Guo et al., “Observation of many-body dynamical localization,” Science 389, 716 (2025).
- C. Rylands et al., “Many-body dynamical localization in a kicked Lieb-Liniger gas,” Phys. Rev. Lett. 124, 155302 (2020).
- A. Cao et al., “Interaction-driven breakdown of dynamical localization in a kicked quantum gas,” Nat. Phys. 18, 1302 (2022).