Sebastian Will

Metallic and Insulating Phases of Repulsively Interacting Fermions in a 3D Optical Lattice

The fermionic Hubbard model plays a fundamental role in the description of strongly correlated materials. We have realized this Hamiltonian in a repulsively interacting spin mixture of ultracold 40K atoms in a three-dimensional (3D) optical lattice. Using in situ imaging and independent control of external confinement and lattice depth, we were able to directly measure the compressibility of the quantum gas in the trap. Together with a comparison to ab initio dynamical mean field theory calculations, we show how the system evolves for increasing confinement from a compressible dilute metal over a strongly interacting Fermi liquid into a band-insulating state. For strong interactions, we find evidence for an emergent incompressible Mott insulating phase. This demonstrates the potential to model interacting condensed-matter systems using ultracold fermionic atoms.

Fermionic transport and out-of-equilibrium dynamics in a homogeneous Hubbard model with ultracold atoms

Ulrich Schneider, 2, ∗ Lucia Hackermüller, 3 Jens Philipp Ronzheimer, 2 Sebastian Will, 2 Simon Braun, 2 Thorsten Best, Immanuel Bloch, 2, 4 Eugene Demler, Stephan Mandt, David Rasch, and Achim Rosch Institut für Physik, Johannes Gutenberg-Universität, 55099 Mainz, Germany Fakultät für Physik, Ludwig-Maximilians-Universität, 80799 Munich, Germany School of Physics and Astronomy, University of Nottingham, NG7 2RD Nottingham, UK Max-Planck-Institut für Quantenoptik, 85748 Garching, Germany Department of Physics, Harvard University, Cambridge, MA 02138, USA Institut für Theoretische Physik, Universität zu Köln, 50937 Cologne, Germany

Time-resolved observation of coherent multi-body interactions in quantum phase revivals

Interactions lie at the heart of correlated many-body quantum phases. Typically, the interactions between microscopic particles are described as two-body interactions. However, it has been shown that higher-order multi-body interactions could give rise to novel quantum phases with intriguing properties. So far, multi-body interactions have been observed as inelastic loss resonances in three- and four-body recombinations of atom–atom and atom–molecule collisions. Here we demonstrate the presence of effective multi-body interactions in a system of ultracold bosonic atoms in a three-dimensional optical lattice, emerging through virtual transitions of particles from the lowest energy band to higher energy bands. We observe such interactions up to the six-body case in time-resolved traces of quantum phase revivals, using an atom interferometric technique that allows us to precisely measure the absolute energies of atom number states at a lattice site. In addition, we show that the spectral content of these time traces can reveal the atom number statistics at a lattice site, similar to foundational experiments in cavity quantum electrodynamics that yield the statistics of a cavity photon field. Our precision measurement of multi-body interaction energies provides crucial input for the comparison of optical-lattice quantum simulators with many-body quantum theory.

Role of interactions in 87Rb-40K Bose-Fermi mixtures in a 3D optical lattice.

We investigate the effect of interspecies interaction on a degenerate mixture of bosonic 87Rb and fermionic 40K atoms in a three-dimensional optical lattice potential. Using a Feshbach resonance, the 87Rb-40K interaction is tuned over a wide range. Through an analysis of the 87Rb momentum distribution, we find a pronounced asymmetry between strong repulsion and strong attraction. In the latter case, we observe a marked shift in the superfluid to Mott insulator transition, which we attribute to a renormalization of the Bose-Hubbard parameters due to self-trapping.

Anomalous Expansion of Attractively Interacting Fermionic Atoms in an Optical Lattice

Fermion Behavior in an Optical Lattice Due to their extreme tunability, optical lattices loaded with fermions and bosons are expected to act as quantum simulators, answering complicated many-body physics questions beyond the reach of theory and computation. Some of these many-body states, such as the Mott insulator and the superfluid, have been achieved in bosonic optical lattices by simply changing the characteristic depth of the lattice potential wells. Now, Hackermüller et al. (p. 1621) describe an unusual effect in an optical lattice loaded with fermions: When the strength of the attraction between the fermions is increased adiabatically, instead of contracting, the gas expands in order to preserve entropy. Thermodynamic effects cause an ultracold potassium gas to expand unexpectedly when the attraction between atoms is increased. The interplay of thermodynamics and quantum correlations can give rise to counterintuitive phenomena in many-body systems. We report on an isentropic effect in a spin mixture of attractively interacting fermionic atoms in an optical lattice. As we adiabatically increase the attraction between the atoms, we observe that the gas expands instead of contracting. This unexpected behavior demonstrates the crucial role of the lattice potential in the thermodynamics of the fermionic Hubbard model.

Coherent Interaction of a Single Fermion with a Small Bosonic Field

We have experimentally studied few-body impurity systems consisting of a single fermionic atom and a small bosonic field on the sites of an optical lattice. Quantum phase revival spectroscopy has allowed us to accurately measure the absolute strength of Bose-Fermi interactions as a function of the interspecies scattering length. Furthermore, we observe the modification of Bose-Bose interactions that is induced by the interacting fermion. Because of an interference between Bose-Bose and Bose-Fermi phase dynamics, we can infer the mean fermionic filling of the mixture and quantify its increase (decrease) when the lattice is loaded with attractive (repulsive) interspecies interactions.

Trapping of ultracold atoms in a hollow-core photonic crystal fiber

Ultracold sodium atoms have been trapped inside a hollow-core optical fiber. The atoms are transferred from a free-space optical dipole trap into a trap formed by a red-detuned Gaussian light mode confined to the core of the fiber. We show that at least 5% of the atoms held initially in the free-space trap can be loaded into the core of the fiber and retrieved outside.

Observation of coherent quench dynamics in a metallic many-body state of fermionic atoms

Quantum simulation with ultracold atoms has become a powerful technique to gain insight into interacting many-body systems. In particular, the possibility to study nonequilibrium dynamics offers a unique pathway to understand correlations and excitations in strongly interacting quantum matter. So far, coherent nonequilibrium dynamics has exclusively been observed in ultracold many-body systems of bosonic atoms. Here we report on the observation of coherent quench dynamics of fermionic atoms. A metallic state of ultracold spin-polarized fermions is prepared along with a Bose-Einstein condensate in a shallow three-dimensional optical lattice. After a quench that suppresses tunnelling between lattice sites for both the fermions and the bosons, we observe long-lived coherent oscillations in the fermionic momentum distribution, with a period that is determined solely by the Fermi-Bose interaction energy. Our results show that coherent quench dynamics can serve as a sensitive probe for correlations in delocalized fermionic quantum states and for quantum metrology.

Two-photon pathway to ultracold ground state molecules of 23Na40K

We report on high-resolution spectroscopy of ultracold fermionic 23Na40K Feshbach molecules, and identify a two-photon pathway to the rovibrational singlet ground state via a resonantly mixed B1Π ~ c3Σ+intermediate state. Photoassociation in a 23Na–40K atomic mixture and one-photon spectroscopy on 23Na40K Feshbach molecules reveal about 20 vibrational levels of the electronically excited c3Σ+state. Two of these levels are found to be strongly perturbed by nearby B1Π levels via spin–orbit coupling, resulting in additional lines of dominant singlet character in the perturbed complex , or of resonantly mixed character in . The dominantly singlet level is used to locate the absolute rovibrational singlet ground state via Autler–Townes spectroscopy. We demonstrate coherent two-photon coupling via dark state spectroscopy between the predominantly triplet Feshbach molecular state and the singlet ground state. Its binding energy is measured to be 5212.0447(1) cm−1, a thousand-fold improvement in accuracy compared to previous determinations. In their absolute singlet ground state, 23Na40K molecules are chemically stable under binary collisions and possess a large electric dipole moment of 2.72 Debye. Our work thus paves the way towards the creation of strongly dipolar Fermi gases of NaK molecules.

Coherent quench dynamics in the one-dimensional Fermi-Hubbard model

Recently, it has been shown that the momentum distribution of a metallic state of fermionic atoms in a lattice Fermi-Bose mixture exhibits coherent oscillations after a global quench that suppresses tunneling. The oscillation period is determined by the Fermi-Bose interaction strength. Here we show that similar dynamics occurs in the fermionic Hubbard model when we quench a noninteracting metallic state by introducing a Hubbard interaction and suppressing tunneling. The period is determined primarily by the interaction strength. Conversely, we show that one can accurately determine the Hubbard interaction strength from the oscillation period, taking into account corrections from any small residual tunneling present in the final Hamiltonian. Such residual tunneling shortens the period and damps the oscillations, the latter being visible in the Fermi-Bose experiment.