This CAREER award aims to identify and explore the universality of quantum systems with a specific number of ultracold atoms. "Universal" behavior occurs at low temperatures when the physical properties of a system depend only on a single parameter, called the two-body scattering length. The implications of universality are understood in the two-body and many-body limits where they describe, for example energy shifts and cross sections in two-atom collisions and the mean-field energy of a Bose-Einstein condensate. The goal of this project is answering the question of how universality persists in few-body systems and link the physics of two- and many-body systems. The experiments will be performed with Bosons (Cs) and Fermions (Li) loaded into two-dimensional optical lattices from quantum degenerate gases. The optical lattice will be a thin layer of two-dimensional lattice sites formed by intersecting five laser beams. The project will use a novel interferometric detection of two- and three-body interactions by probing the evolution of quantum superpositions of atoms in the optical lattice sites.
Because of universality these experiments will provide an unprecedented testing ground to investigate fundamental issues in nuclear, condensed matter physics and in physical chemistry. The project also includes a strong education component to train research personnel, and provide research projects for undergraduate and high school students. The project will also support interaction of the PI with the recently created Woodlawn High School in Chicago through the PIs Science Mathematics and Research Training (SMART) program to strengthen the curriculum and motivate interest in science and mathematics.
Summary We report the observation of quantum criticality of ultracold atoms in optical lattices across the superfluid to vacuum quantum phase transition. The observation is based on the critical scaling behavior of the equation of state that emerges at low temperatures. From our measurements, critical points, exponents and universal scaling laws are determined. Furthermore, we investigate quench dynamic of 2D Bose gas and identify acoustic Sakharov oscillations as a generic feature, independent of the interactions both in the weak and strong interaction regime. In particular, we observe oscillations in the time and the momentum domains. The spatial and temporal scales of the oscillations allow us to determine the dispersion in the weak coupling regime and to determine the general sonic horizon. Last but not least, we successfully prepare 2D Bose gases with tunable and strong interaction. From the equation of state measurement, we identify the mean-field corrections when the interaction parameter approaches and exceeds unity. Logarithmic corrections to both the many-body coupling constants and the critical parameters are evident. This work opens the door to new research to investigate fluctuations and correlations in strongly interaction 2D gases. Personnel In 2012, our group consists of 3 graduate students (Harry Ha, Jacob Johansen and Logan Clark), Three undergraduate students (Francisco Fonta, Kate Schreiber and Dylan Banahene-Sabulsky) and three postdocs (Shih-Kuang Tung, Colin Parker and Eric Hazlett). Exploring quantum criticality based on ultracold atoms in optical lattices Critical behavior developed near a quantum phase transition offers exciting opportunities to explore the universality of strongly correlated systems near the ground state. Cold atoms in optical lattices represent a paradigmatic system, for which the microscopic physics is simple and well characterized and the quantum phase transition between the superfluid and Mott insulator states can be externally induced by tuning the microscopic parameters. We study quantum criticality of cesium atoms in a two-dimensional (2D) lattice based on in situ density measurements. Our research agenda involves testing critical scaling of thermodynamic observables and extracting transport properties in the quantum critical regime. In particular, the thermodynamic measurement suggests that the equation of state near the critical point follows the predicted scaling law at sufficiently low temperatures. The result is published in Science 335 1070 (2012). Observation of Sakharov Oscillations in Quenched Atomic Superfluids Dynamics of many-body systems far from equilibrium is both a challenging theoretical topic and a subject open to new experimental discoveries. While a general theoretical framework for many-body dynamics is unavailable, many generic features have been hypothesized. One intriguing example is the Sakharov oscillations in hydrodynamic systems, which manifests in the anisotropy of the cosmic microwave background (CMB) and the large-scale correlations of galaxies. Here we report the observation of Sakharov oscillations in the density fluctuations of quenched atomic supefluids. A systematic study of the superuid fluctuations in both space and time domains and with tunable interaction strengths suggests that Sakharov oscillation is a generic behavior in the quenched dynamics of superuids. Our work suggests new perspectives to formulate nonequilibrium dynamics of quantum many-body systems and to explore its analogues in cosmology and astrophysics. Preparation of strongly interacting two-dimensional Bose gases We prepare and study strongly interacting two-dimensional Bose gases in the superfluid, the classical Berezinskii-Kosterlitz-Thouless (BKT) transition, and the vacuum-to-superfluid quantum critical regimes. A wide range of the two-body interaction strength 0.05 < g < 3 is covered by tuning the scattering length and by loading the sample into an optical lattice. Based on the equations of state measurements, we extract the coupling constants as well as critical thermodynamic quantities in different regimes. In the superfluid and the BKT transition regimes, the extracted coupling constants show significant downshifts from the mean-field and perturbation calculations when g approaches or exceeds 1. In the BKT and the quantum critical regimes, all measured thermodynamic quantities show logarithmic dependence on the interaction strength, a tendency confirmed by the extended classical-field and renormalization calculations.
