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A Two-Dimensional Fermi Gas in the BEC-BCS Crossover

M. G. Ries

Published Jan 1, 2015• 1 citation
Publisher

Abstract

This thesis reports on the preparation of a 2D Fermi gas in the BEC-BCS crossover and \nthe observation of the BKT transition into a quasi long-range ordered superfluid phase. \nThe pair momentum distribution of the gas is probed by means of a matter-wave \nfocusing technique which relies on time-of-flight evolution in a weak harmonic potential. \nThis distribution holds the coherence properties of the gas. \nThe quasi long-range ordered phase manifests itself as a sharp low-momentum peak. \nThe temperature where it forms is identified as the transition temperature. By tuning \nthe temperature and the interaction strength, the phase diagram of the 2D Fermi gas in \nthe BEC-BCS crossover is mapped out. \nThe phase coherence is investigated in a self-interference experiment. Furthermore, \nalgebraic decay of correlations is observed in the trap average of the first order corre- \nlation function, which is obtained from the Fourier transform of the pair momentum \ndistribution. This is in qualitative agreement with predictions of homogeneous theory \nfor the superfluid phase in a 2D gas. \nThe presented results provide a foundation for future experimental and theoretical \nstudies of strongly correlated 2D Fermi gases. They might thus help to elucidate complex \nsystems such as the electron gas in high-Tc superconductors.

DOI
10.11588/heidok.00018107

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This thesis reports on the preparation of a 2D Fermi gas in the BEC-BCS crossover and \nthe observation of the BKT transition into a quasi long-range ordered superfluid phase. \nThe pair momentum distribution of the gas is probed by means of a matter-wave \nfocusing technique which relies on time-of-flight evolution in a weak harmonic potential. \nThis distribution holds the coherence properties of the gas. \nThe quasi long-range ordered phase manifests itself as a sharp low-momentum peak. \nThe temperature where it forms is identified as the transition temperature. By tuning \nthe temperature and the interaction strength, the phase diagram of the 2D Fermi gas in \nthe BEC-BCS crossover is mapped out. \nThe phase coherence is investigated in a self-interference experiment. Furthermore, \nalgebraic decay of correlations is observed in the trap average of the first order corre- \nlation function, which is obtained from the Fourier transform of the pair momentum \ndistribution. This is in qualitative agreement with predictions of homogeneous theory \nfor the superfluid phase in a 2D gas. \nThe presented results provide a foundation for future experimental and theoretical \nstudies of strongly correlated 2D Fermi gases. They might thus help to elucidate complex \nsystems such as the electron gas in high-Tc superconductors.
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.
The condensation of fermion pairs lies at the heart of superfluidity. However, for strongly correlated systems with reduced dimensionality the mechanisms of pairing and condensation are still not fully understood. In our experiment we use ultracold atoms as a generic model system to study the phase transition from a normal to a condensed phase in a strongly interacting quasi-two-dimensional Fermi gas. Using a novel method, we obtain the in situ pair momentum distribution of the strongly interacting system and observe the emergence of a low-momentum condensate at low temperatures. By tuning temperature and interaction strength, we map out the phase diagram of the quasi-2D BEC-BCS crossover.
The condensation of fermion pairs lies at the heart of superfluidity.However, for strongly correlated systems with reduced dimensionality the mechanisms of pairing and condensation are still not fully understood.In our experiment we use ultracold atoms as a generic model system to study the phase transition from a normal to a condensed phase in a strongly interacting quasi-two-dimensional Fermi gas.Using a novel method, we obtain the in situ pair momentum distribution of the strongly interacting system and observe the emergence of a low-momentum condensate at low temperatures.By tuning temperature and interaction strength, we map out the phase diagram of the quasi-2D BEC-BCS crossover.
We experimentally investigate the first-order correlation function of a trapped Fermi gas in the two-dimensional BEC-BCS crossover. We observe a transition to a low-temperature superfluid phase with algebraically decaying correlations. We show that the spatial coherence of the entire trapped system can be characterized by a single temperature-dependent exponent. We find the exponent at the transition to be constant over a wide range of interaction strengths across the crossover. This suggests that the phase transitions in both the bosonic regime and the strongly interacting crossover regime are of Berezinskii-Kosterlitz-Thouless type and lie within the same universality class. On the bosonic side of the crossover, our data are well described by the quantum Monte Carlo calculations for a Bose gas. In contrast, in the strongly interacting regime, we observe a superfluid phase which is significantly influenced by the fermionic nature of the constituent particles.
The problem of the evolution from BCS theory with cooperative Cooper pairing to the formation and condensation of composite bosons has attracted considerable attention for the past several decades. It has gained renewed impetus in the mid-eighties with the discovery of the high-Tc superconductors, which have a coherence length comparable to the interparticle spacing. More recently, this subject has spurred a great deal of research activity in connection with experiments involving dilute atomic gases of fermionic atoms. The initial objective of this work will be to use functional integral techniques to analyze the low-temperature BCS-to-BEC evolution of d-wave superconductors within the saddle point (mean field) approximation for a continuum model. Then, the same mathematical formalism will be applied to the problem of the BCS-to-BEC evolution of fully spin-polarized p-wave Fermi gases in two dimensions. We find that a quantum phase transition occurs for both systems as they are driven from the BCS-like regime of weakly interacting fermionic pairs to the opposite BEC-like regime of strongly interacting bosonic molecules. This is in contrast to the smooth crossover predicted and observed in systems that exhibit s-wave pairing symmetry. We calculate several spectroscopic and thermodynamic properties that signal the occurrence of this phase transition, and suggest some possible experimental realizations. Finally, fluctuations about the saddle point solution are included in the calculations, and the effects of such correction are analyzed in the low (T~0) and high (T~Tc) temperature limits. We conclude that, at high temperatures, the bosonic degrees of freedom that arise from two-particle bound states become essential to describe the strong coupling limit,\nas the saddle point approximation alone becomes unreliable.
This paper addresses the transition from the normal to the superfluid state in strongly correlated two dimensional fermionic superconductors and Fermi gases. We arrive at the Berezinskii-Kosterlitz-Thouless (BKT) temperature TBKTT_{\text{BKT}}TBKT​ as a function of \emph{attractive} pairing strength by associating it with the onset of quasi-condensation in the normal phase. Our approach builds on a criterion for determining the BKT transition temperature for atomic gases which is based on a well established Quantum Monte Carlo analysis of the phase space density. This latter quantity, when derived from BCS-BEC crossover theory for fermions, leads to non-monotonic behavior for TBKTT_{\text{BKT}}TBKT​ as a function of the attractive interaction or inverse scattering length. In Fermi gases, this implies a robust superconducting dome followed by a long tail from the flat BEC asymptote, rather similar to what is observed experimentally. For lattice systems we find that TBKTT_{\text{BKT}}TBKT​ has an absolute maximum of the order of 0.1EF0.1 E_F0.1EF​. We discuss how our results compare with those derived from the Nelson Kosterlitz criterion based on the mean field superfluid density and the approach to the transition from below. While there is agreement in the strict mean-field BCS regime at weak coupling, we find that at moderate pairing strength bosonic excitations cause a substantial increase in TBKTT_\text{BKT}TBKT​ followed by an often dramatic decrease before the system enters the BEC regime.