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arXiv:1910.07365 · Physical Review A

Dimensional crossover in ultracold Fermi gases from functional renormalization

Bruno M. Faigle-Cedzich, Jan Martin Pawlowski, CHRISTOF WETTERICH

Published Mar 22, 2021• 6 citations
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Abstract

We investigate the dimensional crossover from three to two dimensions in an ultracold Fermi gas across the whole BCS-BEC crossover. Of particular interest is the strongly interacting regime as strong correlations and pair fluctuations are more pronounced in reduced dimensions. Our results are obtained from first principles within the framework of the functional renormalization group (FRG). Here, the confinement of the transverse direction is imposed by means of periodic boundary conditions. We calculate the equation of state, the gap parameter at zero temperature, and the superfluid transition temperature across a wide range of transversal confinement length scales. Particular emphasis is put on the determination of the finite-temperature phase diagram for different confinement length scales. In the end, our results are compared with recent experimental observations and we discuss them in the context of other theoretical works.

DOI
10.1103/physreva.103.033320

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We investigate the dimensional crossover from three to two dimensions in an ultracold Fermi gas across the whole BCS-BEC crossover. Of particular interest is the strongly interacting regime as strong correlations and pair fluctuations are more pronounced in reduced dimensions. Our results are obtained from first principles within the framework of the functional renormalization group (FRG). Here, the confinement of the transverse direction is imposed by means of periodic boundary conditions. We calculate the equation of state, the gap parameter at zero temperature, and the superfluid transition temperature across a wide range of transversal confinement length scales. Particular emphasis is put on the determination of the finite-temperature phase diagram for different confinement length scales. In the end, our results are compared with recent experimental observations and we discuss them in the context of other theoretical works.
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We investigate thermodynamics and phase structure of ultracold Fermi gases, which can be realized and measured in the laboratory with modern trapping techniques. We approach the subject from a both theoretical and experimental perspective. Central to the analysis is the systematic comparison of the BCS-BEC crossover of two-component fermions in both three and two dimensions. A dimensional reduction can be achieved in experiments by means of highly anisotropic traps. The Functional Renormalization Group (FRG) allows for a description of both cases in a unified theoretical framework. In three dimensions we discuss with the FRG the influence of high momentum particles onto the density, extend previous approaches to the Unitary Fermi Gas to reach quantitative precision, and study the breakdown of superfluidity due to an asymmetry in the population of the two fermion components. In this context we also investigate the stability of the Sarma phase. For the two-dimensional system scattering theory in reduced dimension plays an important role. We present both the theoretically as well as experimentally relevant aspects thereof. After a qualitative analysis of the phase diagram and the equation of state in two dimensions with the FRG we describe the experimental determination of the phase diagram of the two-dimensional BCS-BEC crossover in collaboration with the group of S. Jochim at PI Heidelberg.
In this thesis we study the dimensional crossover of a nonrelativistic Bose gas with pointlike repulsive interactions. Our focus is on the dimensional crossover from two to three dimensions, which is of particular relevance in ultracold experiments. Both the two-dimensional and the three-dimensional Bose gas feature a phase transition to a superfluid state. We investigate how the phase transition temperature changes as a function of the spatial extent of the transverse dimension, which is confined in a potential well with periodic boundary conditions. For these calculations we employ Functional Renormalization Group equations. Further, we relate the 3D and 2D s-wave scattering lengths and show how the lower-dimensional system inherits its properties from the higher-dimensional system during the renormalization group flow. In these calculations we introduce the crossover function, which is of central importance in the dimensional crossover. We also investigate other compactifications. We calculate the crossover function for a box confinement and introduce approximate flow equations for a confinement in a harmonic trap.
The role of fluctuations is enhanced in lower dimensionality systems: in a two dimensions offdiagonal long-range order is destroyed by the fluctuations at any finite temperature, drastically modifying the critical properties with respect to the three-dimensional counterpart.Recently two-dimensional systems of interacting fermions have been the subject of Montecarlo studies and experimental investigations, in particular an ultracold gas of attractive fermions with a widely tunable interaction due to a Feshbach resonance has been realized and the Berezinskii-Kosterlitz-Thouless transition has been observed.The present work deals with the theoretical description of an ultracold Fermi gas: we discuss the role of Gaussian fluctuations of the order parameter in the equation of state, in particular we take into account the first sound velocity, showing that the inclusion of order parameter fluctuations is needed in order to get the correct composite-boson limit in the strong-coupling regime.The theory is also compared with experimental data.Finally we focus on the superfluid density in the weak-coupling, intermediate and strong-coupling regimes at finite temperature, through which the Berezinskii-Kosterlitz-Thouless critical temperature is obtained.
The method of functional renormalization is applied to the theoretical investigation of ultracold quantum gases. Flow equations are derived for a Bose gas with approximately pointlike interaction, for a Fermi gas with two (hyperfine) spin components in the Bardeen-Cooper-Schrieffer (BCS) to Bose-Einstein condensation (BEC) crossover and for a Fermi gas with three components. The solution of the flow equations determine the properties of these systems both in the few-body regime and in thermal equilibrium. For the Bose gas this covers the quantum phase diagram, the condensate and superfluid fraction, the critical temperature, the correlation length, the specific heat or sound propagation. The properties are discussed both for three and two spatial dimensions. The discussion of the Fermi gas in the BCS-BEC crossover concentrates on the effect of particle-hole fluctuations but addresses the complete phase diagram. For the three component fermions, the flow equations in the few-body regime show a limit-cycle scaling and the Efimov tower of three-body bound states. Applied to the case of Lithium they explain recently observed three-body loss features. Extending the calculations by continuity to nonzero density, it is found that a new trion phase separates a BCS and a BEC phase for three component fermions close to a common resonance. More formal is the derivation of a new exact flow equation for scale dependent composite operators. This equation allows for example a better treatment of bound states.
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.