Interacting Fermi systems in two dimensions display intriguing phenomena such as high temperature superfluidity and pseudogap physics. These features emerge from the collective behavior of the constituent particles but are extremely hard to predict from microscopic theory. I will report on experiments that realize microscopic two-dimensional systems with ultracold fermionic lithium atoms. With the ability to deterministically prepare few-body ground states and to observe individual particles in momentum space, they enable a microscopic view of strongly interacting two-dimensional Fermi systems. Surprisingly, we find that characteristic features of many-body Fermi gases can already be found in systems of no more than a dozen particles: In spectroscopy, we observe collective excitations that are the few-body precursor of the Higgs amplitude mode of a superfluid. Moreover, in spin-resolved momentum space probes, we can directly image individual ‘Cooper pairs’ and show the presence of fermionic pairing even in a microscopic setting. These findings may broaden our understanding of finite-size Fermi systems, such as atomic nuclei and superconducting grains.
Interacting Fermi systems in two dimensions display intriguing phenomena such as high temperature superfluidity and pseudogap physics. These features emerge from the collective behavior of the constituent particles but are extremely hard to predict from microscopic theory. I will report on experiments that realize microscopic two-dimensional systems with ultracold fermionic lithium atoms. With the ability to deterministically prepare few-body ground states and to observe individual particles in momentum space, they enable a microscopic view of strongly interacting two-dimensional Fermi systems. Surprisingly, we find that characteristic features of many-body Fermi gases can already be found in systems of no more than a dozen particles: In spectroscopy, we observe collective excitations that are the few-body precursor of the Higgs amplitude mode of a superfluid. Moreover, in spin-resolved momentum space probes, we can directly image individual ‘Cooper pairs’ and show the presence of fermionic pairing even in a microscopic setting. These findings may broaden our understanding of finite-size Fermi systems, such as atomic nuclei and superconducting grains.
This thesis reports on experiments investigating the emergence of many-body physics in mesoscopic two-dimensional (2D) few-fermion systems. \nThe starting point are low-entropy samples of ultracold 6Li atoms in a quasi-2D geometry. When scanning the depth of the trapping potential, we observe an enhanced stability of closed-shell configurations of the 2D harmonic oscillator. This enables us to deterministically initialize closed-shell configurations of 2, 6 and 12 atoms in the ground state. \nBy modulating the interaction strength we probe the excitation spectrum arising from the interplay of the finite single-particle gap in closed-shell configurations with the tunable attractive interactions. The full atom-counting statistics reveal pair excitations with a non-monotonous interaction dependence. These modes can be identified as the few-body precursors of a Higgs mode associated with a normal to superfluid phase transition in the thermodynamic limit. \nAdditionally, we can access the momentum distribution with single-particle resolution. This is demonstrated by measuring the momentum distribution of up to six non-interacting fermions in the ground state of the 2D trap. We observe strong density correlations that arise from fermionic quantum statistics. In the future, extending the imaging scheme to interacting systems will allow us to observe the emergence of fermionic many-body paring directly in momentum space.
Strongly interacting gases of ultracold fermions have become an amazingly rich test-bed for many-body theories of fermionic matter. Here we present our recent experiments on these systems. Firstly, we discuss high-precision measurements on the thermodynamics of a strongly interacting Fermi gas across the superfluid transition. The onset of superfluidity is directly observed in the compressibility, the chemical potential, the entropy, and the heat capacity. Our measurements provide benchmarks for current many-body theories on strongly interacting fermions. Secondly, we have studied the evolution of fermion pairing from three to two dimensions in these gases, relating to the physics of layered superconductors. In the presence of p-wave interactions, Fermi gases are predicted to display toplogical superfluidity carrying Majorana edge states. Two possible avenues in this direction are discussed, our creation and direct observation of spin-orbit coupling in Fermi gases and the creation of fermionic molecules of 23Na 40K that will feature strong dipolar interactions in their absolute ground state.
Fermion pairing underlies collective quantum phenomena across widely different forms of matter. In extended systems such as ultracold Fermi gases, pairing is commonly understood through the BCS--BEC crossover, where the pair size evolves from large, overlapping Cooper pairs to tightly bound dimers. In finite systems such as atomic nuclei, superconducting grains and quantum dots, however, the same pairing tendency competes with confinement, shell filling and spatial inhomogeneity, making the microscopic structure of pairs much harder to access. Here, we image pair correlations in a finite, tunable system of few fermionic atoms with single-particle resolution and full counting statistics. We observe that confinement and shell structure re-organize pairing in real space: In the weakly interacting, confinement-dominated regime, closed-shell configurations suppress correlations in the high-density trap center. Pairing is mainly observed toward the low-density surface. Open-shell systems, however, support substantially stronger central pairing. Already for surprisingly small systems, increasing either interaction strength or particle number restores a locally bulk-like Cooper-pair profile in the trap center, whereas the edge retains dimer-like correlations. By resolving where pairs form and how their character changes from localized dimers to overlapping Cooper pairs, our measurements provide a microscopic view of pairing in finite fermionic matter and connect the physics of mesoscopic cold atoms to pairing phenomena in nuclei and superconducting nanostructures.
Many-body physics describes phenomena that cannot be understood by looking only at the constituents of a system1. Striking examples are broken symmetry, phase transitions and collective excitations2. To understand how such collective behaviour emerges as a system is gradually assembled from individual particles has been a goal in atomic, nuclear and solid-state physics for decades3–6. Here we observe the few-body precursor of a quantum phase transition from a normal to a superfluid phase. The transition is signalled by the softening of the mode associated with amplitude vibrations of the order parameter, usually referred to as a Higgs mode7. We achieve fine control over ultracold fermions confined to two-dimensional harmonic potentials and prepare closed-shell configurations of 2, 6 and 12 fermionic atoms in the ground state with high fidelity. Spectroscopy is then performed on our mesoscopic system while tuning the pair energy from zero to a value larger than the shell spacing. Using full atom counting statistics, we find the lowest resonance to consist of coherently excited pairs only. The distinct non-monotonic interaction dependence of this many-body excitation, combined with comparison with numerical calculations allows us to identify it as the precursor of the Higgs mode. Our atomic simulator provides a way to study the emergence of collective phenomena and the thermodynamic limit, particle by particle. An atomic simulator formed of a few ultracold fermionic atoms trapped in a two-dimensional harmonic potential exhibits precursors of a quantum phase transition, revealing the onset of collective quantum many-body phenomena in a few-body system.
We review the current understanding of the uniform two-dimensional (2D) Fermi gas with short-range interactions. We first outline the basics of two-body scattering in 2D, including a discussion of how such a 2D system may be realized in practice using an anisotropic confining potential. We then discuss the thermodynamic and dynamical properties of 2D Fermi gases, which cold-atom experiments have only just begun to explore. Of particular interest are the different pairing regimes as the interparticle attraction is varied; the superfluid transition and associated finite-temperature phenomenology; few-body properties and their impact on the many-body system; the Fermi polaron problem; and the symmetries underlying the collective modes. Where possible, we include the contributions from 2D experiment. An underlying theme throughout is the effect of the quasi-2D geometry, which we view as an added richness to the problem rather than an unwanted complication.
The pairing and superfluid phenomena in a two-component ultracold atomic Fermi gas is an analogue of Cooper pairing and superconductivity in an electron system, in particular, the high T c superconductors. Owing to the various tunable parameters that have been made accessible experimentally in recent years, atomic Fermi gases can be explored as a prototype or quantum simulator of superconductors. It is hoped that, utilizing such an analogy, the study of atomic Fermi gases may shed light to the mysteries of high T c superconductivity. One obstacle to the ultimate understanding of high T c superconductivity, from day one of its discovery, is the anomalous yet widespread pseudogap phenomena, for which a consensus is yet to be reached within the physics community, after over 27 years of intensive research efforts. In this article, we shall review the progress in the study of pseudogap phenomena in atomic Fermi gases in terms of both theoretical understanding and experimental observations. We show that there is strong, unambiguous evidence for the existence of a pseudogap in strongly interacting Fermi gases. In this context, we shall present a pairing fluctuation theory of the pseudogap physics and show that it is indeed a strong candidate theory for high T c superconductivity.