This thesis investigates the dynamics of a degenerate Fermi gas in the unitary limit of strong interactions, in particular, the dynamics of a transversely magnetized unitary Fermi gas in an inhomogeneous magnetic field. Short-range interactions between ultracold fermionic potassium atoms are tuned to their quantum mechanical limit by employing a Feshbach resonance. Spin-echo measurements of magnetization dynamics show that demagnetization is caused by diffusive spin transport with a diffusion constant that saturates at low temperatures to the conjectured quantum-mechanical lower bound ~/m, where m is the particle mass. A prediction for the increase in temperature due to demagnetization based on universal thermodynamics is compared to measured momentum distributions. The development of pair correlations is observed by time-resolved radiofrequency spectroscopy of Tan's contact parameter.
This thesis investigates the dynamics of a degenerate Fermi gas in the unitary limit of strong interactions, in particular, the dynamics of a transversely magnetized unitary Fermi gas in an inhomogeneous magnetic field. Short-range interactions between ultracold fermionic potassium atoms are tuned to their quantum mechanical limit by employing a Feshbach resonance. Spin-echo measurements of magnetization dynamics show that demagnetization is caused by diffusive spin transport with a diffusion constant that saturates at low temperatures to the conjectured quantum-mechanical lower bound ~/m, where m is the particle mass. A prediction for the increase in temperature due to demagnetization based on universal thermodynamics is compared to measured momentum distributions. The development of pair correlations is observed by time-resolved radiofrequency spectroscopy of Tan's contact parameter.
Understanding the quantum dynamics of strongly interacting fermions is a problem relevant to diverse forms of matter, including high-temperature superconductors, neutron stars, and quark-gluon plasma. An appealing benchmark is offered by cold atomic gases in the unitary limit of strong interactions. Here, we study the dynamics of a transversely magnetized unitary Fermi gas in an inhomogeneous magnetic field. We observe the demagnetization of the gas, caused by diffusive spin transport. At low temperatures, the diffusion constant saturates to the conjectured quantum-mechanical lower bound ≃ ħ/m, where m is the particle mass. The development of pair correlations, indicating the transformation of the initially noninteracting gas toward a unitary spin mixture, is observed by measuring Tan's contact parameter.
This thesis summarizes experimental work investigating strongly interacting Fermi gases in two and three dimensions. Radio-frequency spin manipulation is used to initialize and probe strongly interacting Fermi gases dynamically to measure relaxation to a steady-state. Time-resolved spectroscopy is used to discover the p-wave contacts by observing how correlations in the system develop after quenching the atoms into an interacting state. By combining quasi-steady state measurements with new contact relations, an attractive p-wave interaction energy as large as half the Fermi energy is inferred. Spin echo measurements of the magnetization dynamics are used to observe spin transport in two and three dimensions in the presence of strong interactions. The bare spin diffusivity is distinguished from the Leggett-Rice effect, in which demagnetization is slowed by precession of a spin current around the local magnetization. Observations of the demagnetization dynamics support the conjecture that a general quantum bound on spin transport is obeyed where the diffusivity D greater than or similar to ħ/m, where m is the particle mass.
We measure the transport properties of two-dimensional ultracold Fermi gases during transverse demagnetization in a magnetic field gradient. Using a phase-coherent spin-echo sequence, we are able to distinguish bare spin diffusion from the Leggett-Rice effect, in which demagnetization is slowed by the precession of a spin current around the local magnetization. When the two-dimensional scattering length is tuned to be comparable to the inverse Fermi wave vector k_{F}^{-1}, we find that the bare transverse spin diffusivity reaches a minimum of 1.7(6)ℏ/m, where m is the bare particle mass. The rate of demagnetization is also reflected in the growth rate of the s-wave contact, observed using time-resolved spectroscopy. The contact rises to 0.28(3)k_{F}^{2} per particle, which quantifies how scaling symmetry is broken by near-resonant interactions, unlike in unitary three-dimensional systems. Our observations support the conjecture that, in systems with strong scattering, the local relaxation rate is bounded from above by k_{B}T/ℏ.
The physics of quantum degenerate atomic Fermi gases in uniform as well as in harmonically trapped configurations is reviewed from a theoretical perspective. Emphasis is given to the effect of interactions that play a crucial role, bringing the gas into a superfluid phase at low temperature. In these dilute systems, interactions are characterized by a single parameter, the s-wave scattering length, whose value can be tuned using an external magnetic field near a broad Feshbach resonance. The BCS limit of ordinary Fermi superfluidity, the Bose-Einstein condensation (BEC) of dimers, and the unitary limit of large scattering length are important regimes exhibited by interacting Fermi gases. In particular, the BEC and the unitary regimes are characterized by a high value of the superfluid critical temperature, on the order of the Fermi temperature. Different physical properties are discussed, including the density profiles and the energy of the ground-state configurations, the momentum distribution, the fraction of condensed pairs, collective oscillations and pair-breaking effects, the expansion of the gas, the main thermodynamic properties, the behavior in the presence of optical lattices, and the signatures of superfluidity, such as the existence of quantized vortices, the quenching of the moment of inertia, and the consequences of spin polarization. Various theoretical approaches are considered, ranging from the mean-field description of the BCS-BEC crossover to nonperturbative methods based on quantum Monte Carlo techniques. A major goal of the review is to compare theoretical predictions with available experimental results.
The experimental realization of stable, ultracold Fermi gases near a Feshbach resonance allows to study gases with attractive interactions of essentially arbitrary strength. They extend the classic paradigm of BCS into a regime which has never been accessible before. We review the theoretical concepts which have been developed in this context, including the Tan relations and the notion of fixed points at zero density, which are at the origin of universality. We discuss in detail the universal thermodynamics of the unitary Fermi gas which allows a fit free comparison between theory and experiment for this strongly interacting system. In addition, we adress the consequences of scale invariance at infinite scattering length and the subtle violation of scale invariance in two dimensions. Finally we discuss the Fermionic excitation spectrum accessible in momentum resolved RF-spectroscopy and the origin of universal lower bounds for the shear viscosity and the spin diffusion constant.
The work described in this thesis can be divided into two parts. The first part is concerned with the production of degenerate Fermi gases and Bose-Fermi mixtures. The second part of the thesis describes studies of strongly interacting spin-mixtures of ultracold fermions. We have cooled a magnetically trapped spin-polarized 6Li Fermi gas into quantum degeneracy by sympathetic cooling with bosonic 23Na. In order to do this, we have converted our previously developed apparatus for Bose-Einstein condensation of 23Na into a two-species cooling facility. We have produced 6Li samples with up to 7 × 107 atoms at temperatures below 0.5TF , and up to 3× 107 atoms at temperatures as low as 0.05TF . Further, we have also produced stable quantum degenerate mixtures of 23Na and 6Li, with several million atoms of each species. In a second set of experiments, we have studied strongly interacting spin-mixtures of 6Li. The strength of interactions was resonantly controlled by applying a magnetic field and tuning to “Feshbach resonances”, which occur when the total energy of the colliding particles coincides with the energy of a bound molecular state. These studies are relevant for the continuing quest for a superfluid transition in a Fermi gas. By studying the inelastic decay of the cloud, we have experimentally identified two Feshbach resonances for the inter-state interactions of the two lowest ground states of 6Li. Most importantly, we found that the lifetime of the strongly interacting system is long enough to observe a superfluid transition in the future. The effects of the coherent collisions in 6Li spin-mixtures were studied using radiofrequency (RF) spectroscopy. We demonstrated the absence of mean field “clock shifts” in a two-state mixture of fermions, and have introduced a three-level method to observe the interaction energy shifts. In the strongly interacting regime, near a Feshbach resonance, we have observed universal behavior of the interaction energy, independent of the value of the scattering length. Finally, we have theoretically studied the effects of Pauli blocking during a free expansion of a degenerate Fermi gas. We have concluded that a strongly interacting normal gas will undergo a hydrodynamic expansion even at zero temperature, due to inefficiency of the Pauli suppression of collisions. Therefore, the already observed hydrodynamic expansion cannot be conclusively interpreted as a signature of superfluidity. Thesis Supervisor: Wolfgang Ketterle Title: John D. MacArthur Professor of Physics