The spectral function of a spin-balanced two-dimensional Fermi gas with short-range interactions is calculated by means of a quantum cluster expansion. Good qualitative agreement is found with a recent experiment by Feld et al. [Nature (London) 480, 75 (2011)]. The effects of pairing are clearly visible in the density of states, which displays a suppression of spectral weight due to the formation of a two-body bound state. In addition, the momentum distribution and the radio-frequency spectrum are derived, which are in excellent agreement with exact universal results. It is demonstrated that in the limit of high temperature, the quasiparticle excitations are well defined, allowing for a kinetic description of the gas.
The spectral function of a spin-balanced two-dimensional Fermi gas with short-range interactions is calculated by means of a quantum cluster expansion. Good qualitative agreement is found with a recent experiment by Feld et al. [Nature (London) 480, 75 (2011)]. The effects of pairing are clearly visible in the density of states, which displays a suppression of spectral weight due to the formation of a two-body bound state. In addition, the momentum distribution and the radio-frequency spectrum are derived, which are in excellent agreement with exact universal results. It is demonstrated that in the limit of high temperature, the quasiparticle excitations are well defined, allowing for a kinetic description of the gas.
We consider the two-dimensional Fermi gas at finite temperature with attractive short-range interactions. Using the virial expansion, which provides a controlled approach at high temperatures, we determine the spectral function and contact for the normal state. Our calculated spectra are in qualitative agreement with recent photoemission measurements [M. Feld et al., Nature (London) 480, 75 (2011).], thus suggesting that the observed pairing gap is a feature of the high-temperature gas rather than being evidence of a pseudogap regime just above the superfluid transition temperature. We further argue that the strong pair correlations result from the fact that the crossover to bosonic dimers occurs at weaker interactions than previously assumed.
In this thesis, cold gases as well as the electron gas are analyzed with two expansion techniques that have, in essence, the same aim: To describe parameter regimes where the few-body aspect dominates over the collective many-body behavior.The Operator Product Expansion (OPE) of quantum field theory is used to extract high-frequency properties of the correlation function that determines the radio-frequency (RF) response of a two-dimensional Fermi gas with zero-range interactions.Exact sum rules that relate the zeroth and first moment of the radio-frequency spectrum to the particle number and the contact of the gas, are derived from these properties.A quantum cluster (virial-) expansion is employed to study the properties of the spectral function of the two-dimensional Fermi gas at small to moderate degeneracy.From the spectral function, observables like the density of states and the momentum distribution are calculated and are found to be in excellent agreement with Tan's universal relations.In the second part of the thesis, the cluster expansion is applied to both bosonic and fermionic three-dimensional quantum gases.Virial coefficients, contacts and momentum distribution are calculated up to third order in the fugacity.This includes three-particle correlations exactly.The results are are in excellent agreement with known universal relations.In the third part of this thesis, an OPE is applied to the problem of the interacting electron gas in both two and three dimensions.A power-law decay of the momentum distribution and the static structure factor at high momenta is found, compatible with earlier findings by J. Kimball.
We study a trapped two-dimensional (2D) spin-imbalanced Fermi gas over a range of temperatures. In the moderate-temperature regime, associated with current experiments, we find reasonable semiquantitative agreement with the measured density profiles as functions of varying spin imbalance and interaction strength. Our calculations show that, in contrast to the three-dimensional case, the phase separation which appears as a spin-balanced core can be associated with noncondensed fermion pairs. To shed light on the nature of 2D quasicondensation we compute the momentum, q, distribution of pairs, called nB(q); a pronounced low momentum peak is found, but importantly there is no macroscopic condensate. Following the protocols of Jochim and collaborators, we compute the characteristic temperature at which this peak disappears, thus providing a phase diagram for a quasicondensation onset temperature in the polarized case. Additional information about nB(q) is reflected in the behavior of the density profiles when the trap is removed. We show how quasicondensed bosons have a distinctive signature; they evolve relatively slowly under time of flight.
The physics of the pseudogap state is intimately linked with the pairing mechanism that gives rise to superfluidity in quantum gases and to superconductivity in high- T c cuprates, and therefore, both in quantum gases and in superconductors, the pseudogap state and preformed pairs have been under intensive experimental scrutiny. Here, we develop a path integral treatment that provides a divergence-free description of the paired state in two-dimensional Fermi gases. Within this formalism, we derive the pseudogap temperature and the pair fluctuation spectral function, and compare these results with a recent experimental measurement of the pairing in the two-dimensional Fermi gas. The removal of the infrared divergence in the number equations is shown both numerically and analytically, through a study of the long-wavelength and low-energy limit of the pair fluctuation density. Besides the pseudogap temperature, the pair formation temperature and the critical temperature for superfluidity are also derived. The latter corresponds to the Berezinski–Kosterlitz–Thouless (BKT) temperature. The pseudogap temperature, which coincides with the pair formation temperature in the mean field, is found to be suppressed with respect to the pair formation temperature by fluctuations. This suppression is strongest for large binding energies of the pairs. Finally, we investigate how the pair formation temperature, the pseudogap temperature and the BKT temperature behave as a function of both binding energy and imbalance between the pairing partners in the Fermi gas. This allows us to set up phase diagrams for the two-dimensional Fermi gas, in which the superfluid phase, the phase-fluctuating quasicondensate and the normal state can be identified.
In a recent experiment [M. Feld et al., Nature (London) 480, 75 (2011); B. Fr\"ohlich et al., Phys. Rev. Lett. 109, 130403 (2012)], a pairing gap was detected in a two-dimensional (2D) Fermi gas with attractive interaction at temperatures where superfluidity does not occur. The question remains open as to whether this gap is a pseudogap phenomenon or is due to a molecular state. In this paper, by using a $t\ensuremath{-}\text{matrix}$ approach, we reproduce quite well the experimental data for a 2D Fermi gas, and set the boundary between the pseudogap and molecular regimes. We also show that pseudogap phenomena occurring in 2D and 3D can be related through a variable spanning the BCS-BEC crossover in a universal way.
This thesis reports on experiments conducted in a single layer, quasi two-dimensional, two-component ultracold Fermi gas in the strongly interacting regime. Ultracold gases can be used to simulate key aspects of more complicated systems like for example cuprates which show high-Tc superconductivity. \nThe momentum distribution of a sample of bosonic dimers in a quasi-2D square lattice geometry was measured to obtain the coherence properties. For shallow lattices, sharp peaks in the momentum distribution, indicating coherence, were observed at zero momentum as well as at positive and negative lattice momenta along each axis. For deeper \nlattices, heating impeded the ability to prepare a Mott-insulator. \nA spatially resolved radio-frequency spectroscopy was employed for a quasi-2D Fermi gas in the normal phase throughout the BEC-BCS crossover. The interaction induced \nenergy shifts were measured in the strongly interacting region where they can be on the order of the Fermi energy and thus the local resolution is crucial. Furthermore, the onset of pairing in the strongly interacting region was measured as a function of temperature and it was shown that the fraction of free atoms decreases faster than expected from thermal non-interacting theory. At last, the pairing gap was measured using an imbalanced sample. On the BEC side it was found to be in very good agreement with two-body physics as expected. In the strongly interacting regime, however, a deviation from two-body physics indicates that here many-body effects play a role and thus further studies are required.