Ultra-cold atomic Fermi gases at nano-Kelvin temperatures provide a new paradigm for the foundations of quantum many-body theory. Here, we summarize our recent theoretical efforts to understand the intriguing properties of these strongly correlated Fermi gases. A number of powerful theoretical techniques have been developed, including (i) a quantitative diagrammatic theory taken to infinite order; (ii) a virial expansion at high temperature; (iii) exact solutions for one-dimensional many-body systems; and (iv) new quantum simulations using the Gaussian Fermi representation. We have employed these techniques to predict universal thermodynamics in the strongly interacting limit and exotic quantum superfluid phases with imbalanced spin populations. More insights into strongly interacting Fermi gases are anticipated, by extending the Gaussian Fermi simulations to new regimes.
Ultra-cold atomic Fermi gases at nano-Kelvin temperatures provide a new paradigm for the foundations of quantum many-body theory. Here, we summarize our recent theoretical efforts to understand the intriguing properties of these strongly correlated Fermi gases. A number of powerful theoretical techniques have been developed, including (i) a quantitative diagrammatic theory taken to infinite order; (ii) a virial expansion at high temperature; (iii) exact solutions for one-dimensional many-body systems; and (iv) new quantum simulations using the Gaussian Fermi representation. We have employed these techniques to predict universal thermodynamics in the strongly interacting limit and exotic quantum superfluid phases with imbalanced spin populations. More insights into strongly interacting Fermi gases are anticipated, by extending the Gaussian Fermi simulations to new regimes.
Experiments on ultra-cold atomic gases at nano-Kelvin temperatures are revolutionizing many areas of physics. Their exceptional adaptability and simplicity allows tests of many-body theory in areas long thought to be inaccessible, due to strong interactions. Ultra-cold Fermi gases are now providing new insight into the foundations of quantum theory. They are expected to exhibit a universal thermodynamic behaviour in the strongly interacting limit, independent of any microscopic details of the underlying interactions. Here, we present a systematic theoretical study of strong interacting fermions, using different field-theoretic methods and comparisons with quantum Monte Carlo simulations. Pioneering measurements have dramatically confirmed our theoretical predictions, giving the first known evidence for universal fermion thermodynamics.
Recent breakthroughs in the creation of ultracold atomic gases in the laboratory have ushered in major changes in physical science. Many novel experiments are now possible, with an unprecedented control of interaction, geometry and purity. Quantum many-body theory is facing severe challenges in quantitatively understanding new experimental results. Here, we review some recently developed theoretical techniques that provide successful predictions for density response of a strongly correlated atomic Fermi gas. These include the strong-coupling random-phase approximation theory, hightemperature quantum virial expansion, and asymptotically exact Tan relations applicable at large momentum.
We briefly review current research progress in the field of strongly correlated atomic Fermi gases. A deep understanding of strongly correlated quantum gases is plagued by the lack of either exact solutions or a controllable small interaction parameter. In this work, we present a systematic virial expansion method to study the high-temperature thermodynamics of a strongly correlated Fermi gas,where the controllable parameter is given by the fugacity,exp (μkBT),with μ being the chemical potential. A practical way is proposed to obtain the expansion coefficients for both homogeneous and harmonically trapped Fermi gases. We calculate, for the first time accurately, the third-order virial coefficient. The resulting equation of states at high temperatures is compared with a recent thermodynamic measurement and with Monte Carlo simulations.
Interacting Fermi gases are one of the chief paradigms of condensed matter physics. They have been studied since the beginning of the development of quantum mechanics, but continue to produce surprises today. Recent experimental developments in the field of ultracold atomic gases, as well as conventional solid state materials, have produced new and exotic forms of Fermi gases, the theoretical understanding of which is still in its infancy. This Thesis aims to provide updated tools and additional insights into some of these systems, through the application of both numerical and analytical techniques. The first Part of this Thesis is concerned with the development of improved numerical tools for the study of interacting Fermi gases. These tools take the form of accurate model potentials for the dipolar and contact interactions, as found in various ultracold atomic gas experiments, and a new form of Jastrow correlation factor that interpolates between the radial symmetry of the inter-electron Coulomb potential at short inter-particle distances, and the symmetry of the numerical simulation cell at large separation. These methods are designed primarily for use in quantum Monte Carlo numerical calculations, and provide high accuracy along with considerable acceleration of simulations. The second Part shifts focus to an analytical analysis of spin-imbalanced Fermi gases with an attractive contact interaction. The spin-imbalanced Fermi gas is shown to be unstable to the formation of multi-particle instabilities, generalisations of a Cooper pair containing more than two fermions, and then a theory of superconductivity is built from these instabilities. This multi-particle superconductivity is shown to be energetically favourable over conventional superconducting phases in spin-imbalanced Fermi gases, and its unusual experimental consequences are discussed.
Strongly interacting, dilute Fermi gases exhibit a scale-invariant, universal thermodynamic behavior. This is notoriously difficult to understand theoretically because of the absence of a small interaction parameter. Here, we present a systematic comparison of theoretical predictions from different quantum many-body theories with recent experimental data of Nascimbne et al (2010 Nature 463 1057). Our comparisons have no adjustable parameters, either theoretically or experimentally. All the model approximations seem to fluctuate rather than converge on the experimental data. It turns out that a simple Gaussian pair fluctuation theory gives the best quantitative agreement, except at the critical superfluid transition region. In the normal state, we also calculate the equation of state by using a quantum cluster expansion theory and explore in detail its applicability to low temperatures. Using the accurate experimental result for the thermodynamic function S ( T ), we determine the temperature T of a trapped Fermi gas at unitarity as a function of a non-interacting temperature T i , which can be obtained by an adiabatic sweep to the free gas limit. By analyzing the recent experimental data, we find a characteristic temperature ( T / T F ) 0 =0.19±0.02 or ( T i / T F ) 0 =0.16±0.02 in a harmonic trap, below which there are deviations from normal Fermi-liquid-like behavior that may be attributed to pairing effects. Here, T F is the Fermi temperature for a trapped ideal, non-interacting Fermi gas. Our thorough comparison may shed light on the further theoretical development of strongly interacting fermions.
The study of strongly correlated quantum gases in two dimensions has important ramifications for understanding many intriguing phenomena in solid materials, such as high-Tc superconductivity and the fractional quantum-Hall effect. However, theoretical methods are plagued by the existence of significant quantum fluctuations. Here, we present two- and three-body exact solutions for both fermions and bosons trapped in a two-dimensional harmonic potential with an arbitrary s-wave scattering length. These few-particle solutions link in a natural way to the high-temperature properties of many-particle systems via a quantum virial expansion. As a concrete example, using the energy spectrum of few fermions, we calculate the second and third virial coefficients of a strongly interacting Fermi gas in two dimensions, and consequently investigate its high-temperature thermodynamics. Our thermodynamic results may be useful for ongoing experiments on two-dimensional Fermi gases. These exact results also provide an unbiased benchmark for quantum Monte Carlo simulations of two-dimensional Fermi gases at high temperatures.