Strongly interacting two-dimensional Fermi gases

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.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.

arXiv:1408.2737Annual review of cold atoms and moleculesMar 24, 201595 citations

Three-component Fermi gases in quasi-two-dimensional geometries

T. Kirk

This thesis concerns quasi-two-dimensional (quasi-2D) ultracold Fermi systems with short range interactions. Here, quasi-2D geometries are those that lie between two- and three-dimensions. We study few- and many-body systems composed of two or three distinguishable species of fermions. Of principle interest are the bound states that form in these systems and how these bound states are affected by the quasi-2D geometries. In the first research chapter, we focus on the two-dimensional (2D) regime of quasi- 2D. We begin by developing an effective 2D model of this 2D-like geometry. We use this model to analyse a Fermi system consisting of three fermionic species with equal interactions between all distinguishable pairs. Starting with the few-body problem, we show that there is always a three-body bound state (trimer) in the effective 2D model and that these 2D trimers are stable. This is notably different from the extremely unstable ‘Efimov’ trimers found in three-dimensional (3D) systems. Using a low-density expansion and a variational approach, we investigate the fate of the 2D trimers as the system’s density is increased from the three-body limit to the many-body limit. We find that remnants of trimers can persist in the form of strong three-body correlations in the many-body system. In the second research chapter, we analyse a realistic experimental system of three distinguishable fermions confined to quasi-2D. We develop a model that goes beyond the previous chapter in two regards. Firstly, we allow for unequal interactions between the pairs of fermions. Secondly, we use a full quasi-2D model that is not specific to the 2D-like regime. With this general model, we use the scattering and confinement parameters from experiments on ultracold 6Li atoms to calculate the trimer spectrum across the dimensional crossover from 2D to 3D. We show that one state smoothly evolves from an unstable 3D-like trimer to a 2D-like trimer as the attractive interactions are decreased. We furthermore compute the trimer wave function and quantify the stability of the trimer with respect to three-body recombination by determining the probability that three fermions approach each other at short distances. Our results indicate that the lifetime of the trimer can be enhanced by at least an order of magnitude in the quasi-2D geometry. This opens the door to realising long-lifetime trimers in ultracold gas experiments and furthermore, the many-body state of trimers predicted in the preceding chapter. vii In the final research chapter, we examine an alternative approach to accessing quasi-2D geometries by using a system of coupled 2D planes. We study the two-component Fermi gas in this geometry, as a preliminary to studying the three-component gas. We find that the interplanar coupling can be tuned to drive a dimensional crossover from 2D to 3D. We study the effect of this dimensional crossover on the two- and many-body systems. In general, we find that two-body correlations are strengthened by weakening the coupling between 2D planes. In the many-body system, we use mean-field theory to find that the critical temperature of pairing is increased by weakening the coupling between 2D planes. This represents a first step towards a more general representation of quasi-2D geometries, namely: A system of coupled quasi-2D planes.This thesis concerns quasi-two-dimensional (quasi-2D) ultracold Fermi systems with short range interactions. Here, quasi-2D geometries are those that lie between two- and three-dimensions. We study few- and many-body systems composed of two or three distinguishable species of fermions. Of principle interest are the bound states that form in these systems and how these bound states are affected by the quasi-2D geometries. In the first research chapter, we focus on the two-dimensional (2D) regime of quasi- 2D. We begin by developing an effective 2D model of this 2D-like geometry. We use this model to analyse a Fermi system consisting of three fermionic species with equal interactions between all distinguishable pairs. Starting with the few-body problem, we show that there is always a three-body bound state (trimer) in the effective 2D model and that these 2D trimers are stable. This is notably different from the extremely unstable ‘Efimov’ trimers found in three-dimensional (3D) systems. Using a low-density expansion and a variational approach, we investigate the fate of the 2D trimers as the system’s density is increased from the three-body limit to the many-body limit. We find that remnants of trimers can persist in the form of strong three-body correlations in the many-body system. In the second research chapter, we analyse a realistic experimental system of three distinguishable fermions confined to quasi-2D. We develop a model that goes beyond the previous chapter in two regards. Firstly, we allow for unequal interactions between the pairs of fermions. Secondly, we use a full quasi-2D model that is not specific to the 2D-like regime. With this general model, we use the scattering and confinement parameters from experiments on ultracold 6Li atoms to calculate the trimer spectrum across the dimensional crossover from 2D to 3D. We show that one state smoothly evolves from an unstable 3D-like trimer to a 2D-like trimer as the attractive interactions are decreased. We furthermore compute the trimer wave function and quantify the stability of the trimer with respect to three-body recombination by determining the probability that three fermions approach each other at short distances. Our results indicate that the lifetime of the trimer can be enhanced by at least an order of magnitude in the quasi-2D geometry. This opens the door to realising long-lifetime trimers in ultracold gas experiments and furthermore, the many-body state of trimers predicted in the preceding chapter. vii In the final research chapter, we examine an alternative approach to accessing quasi-2D geometries by using a system of coupled 2D planes. We study the two-component Fermi gas in this geometry, as a preliminary to studying the three-component gas. We find that the interplanar coupling can be tuned to drive a dimensional crossover from 2D to 3D. We study the effect of this dimensional crossover on the two- and many-body systems. In general, we find that two-body correlations are strengthened by weakening the coupling between 2D planes. In the many-body system, we use mean-field theory to find that the critical temperature of pairing is increased by weakening the coupling between 2D planes. This represents a first step towards a more general representation of quasi-2D geometries, namely: A system of coupled quasi-2D planes.

Jul 28, 20180 citations

Zooming in on Fermi gases in two dimensions

Philipp M. Preiss

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.

SPIE Quantum TechnologiesJun 3, 20220 citations

Diffusion Monte Carlo study of strongly interacting two-dimensional Fermi gases

Alexander Galea, Hillary Dawkins, Stefano Gandolfi +1 more

Ultracold atomic Fermi gases have been a popular topic of research, with attention being paid recently to two-dimensional (2D) gases. In this work, we perform $T=0$ ab initio diffusion Monte Carlo calculations for a strongly interacting two-component Fermi gas confined to two dimensions. We first go over finite-size systems and the connection to the thermodynamic limit. After that, we illustrate pertinent 2D scattering physics and properties of the wave function. We then show energy results for the strong-coupling crossover, in between the Bose-Einstein condensation (BEC) and Bardeen-Cooper-Schrieffer (BCS) regimes. Our energy results for the BEC-BCS crossover are parametrized to produce an equation of state, which is used to determine Tan's contact. We carry out a detailed comparison with other microscopic results. Finally, we calculate the pairing gap for a range of interaction strengths in the strong coupling regime, following from variationally optimized many-body wave functions.Ultracold atomic Fermi gases have been a popular topic of research, with attention being paid recently to two-dimensional (2D) gases. In this work, we perform $T=0$ ab initio diffusion Monte Carlo calculations for a strongly interacting two-component Fermi gas confined to two dimensions. We first go over finite-size systems and the connection to the thermodynamic limit. After that, we illustrate pertinent 2D scattering physics and properties of the wave function. We then show energy results for the strong-coupling crossover, in between the Bose-Einstein condensation (BEC) and Bardeen-Cooper-Schrieffer (BCS) regimes. Our energy results for the BEC-BCS crossover are parametrized to produce an equation of state, which is used to determine Tan's contact. We carry out a detailed comparison with other microscopic results. Finally, we calculate the pairing gap for a range of interaction strengths in the strong coupling regime, following from variationally optimized many-body wave functions.

arXiv:1511.05123Physical Review AFeb 1, 201641 citations

Superfluid transition in quasi-two-dimensional Fermi gases

Dmitry S. Petrov, M. A. Baranov, Gora V. Shlyapnikov

We show that atomic Fermi gases in quasi-two-dimensional (2D) geometries are promising for achieving superfluidity. In the regime of BCS pairing for weak attraction, we calculate the critical temperature ${T}_{c}$ and analyze possibilities of increasing the ratio of ${T}_{c}$ to the Fermi energy. In the opposite limit, where a strong coupling leads to the formation of weakly bound quasi-2D dimers, we find that their Bose-Einstein condensate will be stable on a long time scale.We show that atomic Fermi gases in quasi-two-dimensional (2D) geometries are promising for achieving superfluidity. In the regime of BCS pairing for weak attraction, we calculate the critical temperature ${T}_{c}$ and analyze possibilities of increasing the ratio of ${T}_{c}$ to the Fermi energy. In the opposite limit, where a strong coupling leads to the formation of weakly bound quasi-2D dimers, we find that their Bose-Einstein condensate will be stable on a long time scale.

arXiv:cond-mat/0212061Physical Review AMar 11, 2003131 citations

Strongly interacting Fermi gases

Waseem Bakr, Lawrence W. Cheuk, Mark Ku +6 more

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.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.

EPJ Web of ConferencesJan 1, 20133 citations

Ultracold atomic Fermi gases have been a popular topic of research, with attention being paid recently to two-dimensional (2D) gases. In this work, we perform

T=0

ab initio diffusion Monte Carlo calculations for a strongly interacting two-component Fermi gas confined to two dimensions. We first go over finite-size systems and the connection to the thermodynamic limit. After that, we illustrate pertinent 2D scattering physics and properties of the wave function. We then show energy results for the strong-coupling crossover, in between the Bose-Einstein condensation (BEC) and Bardeen-Cooper-Schrieffer (BCS) regimes. Our energy results for the BEC-BCS crossover are parametrized to produce an equation of state, which is used to determine Tan's contact. We carry out a detailed comparison with other microscopic results. Finally, we calculate the pairing gap for a range of interaction strengths in the strong coupling regime, following from variationally optimized many-body wave functions.

{T}_{c}

and analyze possibilities of increasing the ratio of

{T}_{c}

to the Fermi energy. In the opposite limit, where a strong coupling leads to the formation of weakly bound quasi-2D dimers, we find that their Bose-Einstein condensate will be stable on a long time scale.