Cold Atoms Bear a Quantum Scar

Abstract

Theorists attribute the unexpectedly slow thermalization of cold atoms seen in recent experiments to an effect called quantum many-body scarring. R esearchers still have some way to go before they can assemble enough quantum bits (qubits) to make a practical, large-scale quantum computer. But already the best prototypes, made up of several tens of qubits, are opening our eyes to new behavior in the quantum realm. Last year, a team from Harvard University and the Massachusetts Institute of Technology (MIT) unveiled a quantum "simulator" made up of a row of 51 interacting atoms [1]. Exciting the individual atoms in various patterns (Fig. 1), they discovered something unexpected: atoms in certain patterns took at least 10 times longer to relax towards thermal equilibrium than atoms in other patterns. Four groups of theorists have tried to make sense of this observation [2-6], in all cases attributing the slow thermalization to a never-before-seen effect called quantum many-body scar-Figure 1: The Harvard-MIT experimentalists arranged 51 equally spaced cold atoms in a row [1]. Each atom could be prepared in its ground state (red circles) or in a highly excited Rydberg state (yellow circles). The researchers found that excitation patterns with every other atom excited (bottom row) took much longer to thermalize compared with other patterns-a surprising result that several theoretical groups have attributed to an effect called quantum many-body scarring [2-6]. (The circled regions highlight deviations from the ordering in the fourth row.) (APS/Alan Stonebraker) * Institute for Theoretical Physics, University of Amsterdam, Nether-lands ring. Because scarring protects a quantum system from the scrambling of information caused by thermalization, the effect may prove useful for quantum computing. The notion of a quantum scar was introduced in the early 1980s in a theoretical paper by physicist Eric Heller [7]. Researchers had long known that a classical chaotic system can still display periodic behavior. For example, a frictionless billiard ball set to bounce around a stadium-shaped table will typically follow a nonrepeating path, undergoing motion that is called ergodic because it explores all points on the table. But for certain initial angles, the ball retraces its path after a certain number of bounces. Such periodic trajectories are unstable to small shifts that send the ball onto a nonre-peating path. Heller considered what would happen if the classical billiard problem were translated into the "particle in a box" problem of quantum mechanics, where the ball is replaced with a quantum particle whose energy is quantized [7]. He found that certain quantum states bear an imprint, or "scar," from the classical periodic orbits. A particle in one of these scarred states is much more likely to be found near an unstable periodic path. So far, physicists haven't succeeded in generalizing Heller's description of a single quantum particle to the much more complicated case of many interacting particles. However, the Harvard-MIT experiment and the theoretical papers it has inspired suggest that many-body quantum scarring may have been observed [1-6]. In the experiments, the 51 atoms were spaced a few micrometers apart in a linear array, and each atom could be prepared in either its ground state or a highly excited "Rydberg" state (Fig. 1). The researchers then turned on interactions between the atoms, allowing the exchange of energy, and they tracked the evolving distribution of excited atoms by detecting the fluo-rescence of individual atoms. The researchers expected that after some characteristic time, the atom chain would ther-malize, redistributing the initial energy among the atoms as the chain passed through many possible quantum states. For most cases, thermalization proceeded as expected. But when the team initialized the simulator with a pattern in which every other atom was in an excited state, they found that thermalization took at least 10 times longer. This slow-to-thermalize case also exhibited long-lived oscillations -sloshing back and forth between two patterns where every other atom is excited. In the same way that the bouncing ball with a periodic path doesn't visit all points on physics.aps.org