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.

PhysicsJun 8, 20156 citations

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

M. G. Ries

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 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.

Jan 1, 20151 citation

Many-Body Pairing in a Two-Dimensional Fermi Gas

M. Neidig

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.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.

Jan 1, 20170 citations

Excitation Spectrum and Superfluid Gap of an Ultracold Fermi Gas

Hauke Biss, Lennart Sobirey, Niclas Luick +5 more

Ultracold atomic gases are a powerful tool to experimentally study strongly correlated quantum many-body systems. In particular, ultracold Fermi gases with tunable interactions have allowed to realize the famous BEC-BCS crossover from a Bose-Einstein condensate (BEC) of molecules to a Bardeen-Cooper-Schrieffer (BCS) superfluid of weakly bound Cooper pairs. However, large parts of the excitation spectrum of fermionic superfluids in the BEC-BCS crossover are still unexplored. In this work, we use Bragg spectroscopy to measure the full momentum-resolved low-energy excitation spectrum of strongly interacting ultracold Fermi gases. This enables us to directly observe the smooth transformation from a bosonic to a fermionic superfluid that takes place in the BEC-BCS crossover. We also use our spectra to determine the evolution of the superfluid gap and find excellent agreement with previous experiments and self-consistent T-matrix calculations both in the BEC and crossover regime. However, toward the BCS regime a calculation that includes the effects of particle-hole correlations shows better agreement with our data.Ultracold atomic gases are a powerful tool to experimentally study strongly correlated quantum many-body systems. In particular, ultracold Fermi gases with tunable interactions have allowed to realize the famous BEC-BCS crossover from a Bose-Einstein condensate (BEC) of molecules to a Bardeen-Cooper-Schrieffer (BCS) superfluid of weakly bound Cooper pairs. However, large parts of the excitation spectrum of fermionic superfluids in the BEC-BCS crossover are still unexplored. In this work, we use Bragg spectroscopy to measure the full momentum-resolved low-energy excitation spectrum of strongly interacting ultracold Fermi gases. This enables us to directly observe the smooth transformation from a bosonic to a fermionic superfluid that takes place in the BEC-BCS crossover. We also use our spectra to determine the evolution of the superfluid gap and find excellent agreement with previous experiments and self-consistent T-matrix calculations both in the BEC and crossover regime. However, toward the BCS regime a calculation that includes the effects of particle-hole correlations shows better agreement with our data.

arXiv:2105.09820Physical Review LettersMar 8, 202271 citations

BCS–BEC crossover in a quasi-two-dimensional Fermi superfluid

Jing Zhou, Tingting Shi, Xia-Ji Liu +2 more

Abstract We study the crossover from the Bardeen–Cooper–Shrieffer regime to the Bose–Einstein-condensation regime in an anisotropic trapped quantum gas of ultracold fermionic atoms. Using an effective two-dimensional Hamiltonian with renormalized interactions between atoms and dressed molecules, we extend the Gaussian pair fluctuation theory to quasi-two-dimensional systems. The equation of state, pair size and sound velocity as well as the convexity parameters of the Goldstone mode are investigated to show how Fermi superfluidity is affected by reduced dimensionality and Gaussian fluctuations at zero temperature in a wide range of crossover. We compare our results with the recent experiment of 6 L i atomic gases and find good agreements.Abstract We study the crossover from the Bardeen–Cooper–Shrieffer regime to the Bose–Einstein-condensation regime in an anisotropic trapped quantum gas of ultracold fermionic atoms. Using an effective two-dimensional Hamiltonian with renormalized interactions between atoms and dressed molecules, we extend the Gaussian pair fluctuation theory to quasi-two-dimensional systems. The equation of state, pair size and sound velocity as well as the convexity parameters of the Goldstone mode are investigated to show how Fermi superfluidity is affected by reduced dimensionality and Gaussian fluctuations at zero temperature in a wide range of crossover. We compare our results with the recent experiment of 6 L i atomic gases and find good agreements.

arXiv:2211.13406New Journal of PhysicsJul 21, 20230 citations

Strong Pairing in two dimensions: Pseudogap and other phenomena

Xiaoyu Wang, Qijin Chen, K. Levin

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 $T_{\text{BKT}}$ 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 $T_{\text{BKT}}$ 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 $T_{\text{BKT}}$ has an absolute maximum of the order of $0.1 E_F$ . 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 $T_\text{BKT}$ followed by an often dramatic decrease before the system enters the BEC regime.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 $T_{\text{BKT}}$ 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 $T_{\text{BKT}}$ 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 $T_{\text{BKT}}$ has an absolute maximum of the order of $0.1 E_F$. 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 $T_\text{BKT}$ followed by an often dramatic decrease before the system enters the BEC regime.

Jul 13, 20190 citations

T_{\text{BKT}}

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

T_{\text{BKT}}

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

T_{\text{BKT}}

has an absolute maximum of the order of

0.1 E_F

. 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

T_\text{BKT}

followed by an often dramatic decrease before the system enters the BEC regime.