Title:
"Realizing a Pfaffian quantum Hall state with ultracold atoms in an optical lattice"
Abstract:
One of the major frontiers of modern physics is the study of topological states, where global entanglement leads to strange and exciting behaviors. Perhaps the most famous examples are the fractional quantum Hall (FQH) states, which appear when charged particles confined to two dimensions interact in the presence of a magnetic field. FQH states are exciting for many reasons, including the possibility that they naturally host non-abelian anyons, which have potential applications in quantum computing. As interesting as these states are, it is difficult to study microscopic properties (like anyonic excitations) in condensed matter systems, where one can’t easily measure the individual electrons and must rely on indirect evidence to study the structure of the wavefunction that underlies the interesting effects.
This is the type of problem we address with quantum simulation. In the Greiner lab at Harvard University, instead of studying FQH states in materials, we use cold atoms in an optical lattice, where we can control almost every aspect of the system, to build a small quantum model that captures key properties of the target phase. This also requires us to use an artificial gauge field to make our neutral atoms behave like charged particles in an effective magnetic field. Using a quantum gas microscope, we can take images that resolve the positions of the individual atoms. This lets us measure density correlations and directly probe an important aspect of the structure of the many-body wavefunction. Starting from our early work on a two-particle Laughlin state on a 4x4 grid, one of the simplest types of FQH states, we have now built up to engineering a Pfaffian state, one of the most complex and theoretically interesting. Even in the small system of three particles on a 5x5 grid, we observe the suppression of three-particle correlations relative to two-particle correlations, indicating that any two particles can approach each other to form a pair, but a third particle avoids them. This is a defining feature of the Moore-Read wavefunction that describes p-wave pairing, and represents the first direct measurement of Pfaffian state correlations in a cold atom system. We also recreate an analogous experiment to the more traditional type of Hall drift measurements made in condensed matter systems by turning off our confinement and measuring the center-of-mass drift in response to a weak applied force. This drift velocity agrees with theory, establishing a proof-of-concept for linking these small systems to their larger counterparts. Together, these measurements pave the way towards engineering larger states and measuring more complicated topological observables.
