In our lab, we focus on studying strongly correlated quantum many-body systems realized with ultracold atomic gases. In particular, we are interested in two broad areas of many-body physics: quantum magnetism and topological order. Quantum magnetism explores spin systems where the interplay between competing interactions, geometric frustration and quantum fluctuations leads to novel magnetic phases. On the other hand, topological order describes quantum states such as fractional quantum Hall states that do not fit in Landau’s symmetry breaking scheme and cannot be characterized using local order parameters. These topics are at the heart of an emerging area of overlap between condensed matter physics and cold atoms (related experimental work at Princeton in the Yazdani, Hasan and Ong condensed matter groups).
The immediate research goal of our group is to investigate topological ultracold atom systems in the regime of strong correlations. One focus will be studying the rich phenomenology of fractional topological insulators. The recently discovered topological band insulators exhibit behavior similar to quantum Hall materials at room temperature and without the need for large magnetic fields, opening the door for technological applications. On the other hand, fractional topological insulators, analogous to fractional quantum Hall materials, have been predicted but not yet discovered. We will explore this physics by combing spin-orbit coupling and strong interactions of fermions in optical lattices. A second focus will be the preparation of spin systems that exhibit non-Abelian anyonic excitations and using single-atom manipulation techniques to demonstrate braiding sequences necessary for topological quantum computation.
Sampling of previous research
1. Quantum gas microscopy: the development of this new technique enabled the first studies of quantum gases in a strongly correlated regime on the single atom level. A two-dimensional quantum gas is prepared in an optical lattice close to a surface and probed with solid-immersion fluorescence-based imaging. The information gleaned from the resulting images is fundamentally different from that obtained with analogous tools in condensed matter (e.g. STM). Quantum gas microscopy provides a projected snapshot of a quantum fluid, which allows direct extraction of quantities such as quantum fluctuations and correlations in the sample. For more details on quantum gas microscopy, see this Physics Today article or visit the Greiner lab website.
2. Atom-resolved studies of quantum phase transitions: Quantum phase transitions involve a a dramatic change in the many-body wavefunction of a system driven by quantum fluctuations rather than thermal fluctuations. Quantum gas microscopy allowed single-site studies of various quantum phase transitions for the first time, including the superfluid to Mott insulator transition and quantum phase transitions occurring in antiferromagnetic spin chains.
3. Strongly correlated fermionic gases: Using Feshbach resonances, the interactions in a degenerate Fermi gas can be tuned at will. In particular, an attractively interacting degenerate Fermi gas can be studied throughout the crossover regime from Bose-Einstein condensation of tightly bound molecules to Bardeen-Cooper-Schrieffer superfluidity of long-range Cooper pairs. At the resonance, the unitary Fermi gas is a strongly-correlated system that can be used to study “universal” physics. To read more about this topic, visit the Zwierlein lab website. Research in this area includes layered systems of interacting fermions and quantum fluctuations in fermionic superfluids probed with solitons.
4. Spin-orbit coupling in fermionic gases: The coupling of the spin of electrons to their motional state lies at the heart of recently discovered topological phases of matter. Raman fields provide a route to introduce spin-orbit coupling into an atomic Fermi gas. The new eigenstates of the system in the presence of the Raman fields are two helicity bands that are split by a spin-orbit gap. This gap is probed via spin-injection spectroscopy, which characterizes the energy-momentum dispersion and spin composition of the quantum states. Combining spin-orbit coupling with a Feshbach resonance in lower dimensions is a possible avenue towards engineering a p-wave superfluid. Such topological superfluids possess zero-energy fermionic excitations called Majorana modes that are, in a sense, their own antiparticles.