# Ultracold Fermi gases

We employ ultracold atomic Fermi gases to study quantum many-body physics. Often, our work is motivated by unresolved problems from condensed matter physics, which we emulate with trapped atomic gases. Moreover, we strive to realize new quantum phases not encountered in the solid state.

**Local probing of interacting fermions in optical lattices**

** **

Quantum gases of interacting fermionic atoms in optical lattices promise to shed new light on the low-temperature phases of Hubbard-type models, such as spin-ordered phases or possible d-wave superconductivity. We emulate the physics of the Hubbard model by loading a quantum degenerate two-component Fermi gas of 40K atoms into a three-dimensional optical lattice geometry. Using high-resolution absorption imaging combined with radio-frequency spectroscopy we can resolve the in-situ distribution of singly and doubly occupied lattice sites within a single two-dimensional layer. This allows the observation of the fermionic Mott insulator and a measurement of the equation of state for the repulsive Hubbard model in two dimensions.

**Universal spin dynamics in two-dimensional Fermi gases**

**Nature Physics 9, 405 (2013).**

Harnesing spins as information carriers has emerged as an elegant extension to the transport of electrical charges. The coherence of such spin transport in spintronic circuits is determined by the lifetime of spin excitations and by spin diffusion. Fermionic quantum gases allow the study of spin transport from first principles because interactions can be precisely tailored and the dynamics is on directly observable timescales. In particular, at unitarity, spin transport is dictated by diffusion and the spin diffusivity is expected to reach a universal, quantum-limited value on the order of the reduced Planck constant hbar divided by the mass m. Here, we study a two-dimensional Fermi gas after a quench into a metastable, transversely polarized state. Using the spin-echo technique, for strong interactions, we measure the lowest transverse spin diffusion constant so far 0.25(3) hbar/m. For weak interactions, we observe a collective transverse spinwave mode that exhibits mode softening when approaching the strongly interacting regime.

**Attractive and repulsive Fermi polarons in two dimensions**

**Nature 485, 619 (2012)**

The dynamics of a single impurity in an environment is a fundamental problem in many-body physics. In the solid state, a well known case is an impurity coupled to a bosonic bath (such as lattice vibrations); the impurity and its accompanying lattice distortion form a new entity, a polaron. This quasiparticle plays an important role in the spectral function of high-transition temperature superconductors, as well as in colossal magnetoresistance in manganites. For impurities in a fermionic bath, studies have considered heavy or immobile impurities which exhibit Anderson’s orthogonality catastrophe and the Kondo effect.

More recently, mobile impurities have moved into the focus of research, and they have been found to form new quasiparticles known as Fermi polarons4–7. The Fermi polaron problem constitutes the extreme, but conceptually simple, limit of two important quantum many-body problems: the crossover between a molecular Bose–Einstein condensate and a superfluid with BCS (Bardeen–Cooper–Schrieffer) pairing with spin-imbalance for attractive interactions, and Stoner’s itinerant ferromagnetism for repulsive interactions. It has been proposed that such quantum phases (and other elusive exotic states) might become realizable in Fermi gases confined to two dimensions. Their stability and observability are intimately related to the theoretically debated properties of the Fermi polaron in a two-dimensional Fermi gas. Here we create and investigate Fermi polarons in a two-dimensional, spin-imbalanced Fermi gas, measuring their spectral function using momentum-resolved photoemission spectroscopy. For attractive interactions, we find evidence for a disputed pairing transition between polarons and tightly bound dimers, which provides insight into the elementary pairing mechanism of imbalanced, strongly coupled two-dimensional Fermi gases. Additionally, for repulsive interactions, we study novel quasiparticles—repulsive polarons— the lifetime of which determines the possibility of stabilizing repulsively interacting Fermi systems.

**Observation of a pairing pseudogap in a two-dimensional Fermi gas**

**Nature 480, 75 (2011)**

Pairing of fermions is ubiquitous in nature, underlying many phenomena. Examples include superconductivity, superfluidity of 3He, the anomalous rotation of neutron stars, and the crossover between Bose–Einstein condensation of dimers and the BCS (Bardeen, Cooper and Schrieffer) regime in strongly interacting Fermi gases. When confined to two dimensions, interacting manybody systems show even more subtle effects, many of which are not understood at a fundamental level. Most striking is the (as yet unexplained) phenomenon of high-temperature superconductivity in copper oxides, which is intimately related to the two-dimensional geometry of the crystal structure. In particular, it is not understood how the many-body pairing is established at high temperature, and whether it precedes superconductivity. Here we report the observation of a many-body pairing gap above the superfluid transition temperature in a harmonically trapped, two-dimensional atomic Fermi gas in the regime of strong coupling. Our measurements of the spectral function of the gas are performed using momentum-resolved photoemission spectroscopy, analogous to angle-resolved photoemission spectroscopy in the solid state. Our observations mark a significant step in the emulation of layered two-dimensional strongly correlated superconductors using ultracold atomic gases.

**Optical lattices**

The physics of an interacting quantum gas in the optical lattice can often be described by the Hubbard model which plays a key role in the description of many intriguing phenomena in modern condensed matter physics. In the Hubbard model the physics of the particles is determined by two parameters: the hopping rate between lattice sites J and the onsite interaction strength U. The unique versatility of atoms in optical lattices makes researchers optimistic to study a whole range of phenomena linked to solid-state physics. A particular tantalizing prospect is that fermionic atoms in optical lattices may provide solutions to unanswered questions, such as high-temperature superconductivity. The challenge here is twofold. One central requirement is to reach extremely low temperatures inside the optical lattice. The second challenge is how to extract the information on the quantum many-body state from the experiment.

**Team**

Dr. Daniel Pertot, Dr. Ferdinand Brennecke, Luke Miller, Eugenio Cocchi, Jan Drewes, Jeffrey Chan