Equation of State of Ultracold Fermions in the 2D BEC-BCS Crossover Region

Abstract

We report the experimental measurement of the equation of state of a two-dimensional Fermi gas with attractive s-wave interactions throughout the crossover from a weakly coupled Fermi gas to a Bose gas of tightly bound dimers as the interaction strength is varied. We demonstrate that interactions lead to a renormalization of the density of the Fermi gas by several orders of magnitude. We compare our data near the ground state and at finite temperature to predictions for both fermions and bosons from Quantum Monte Carlo simulations and Luttinger-Ward theory. Our results serve as input for investigations of close-to-equilibrium dynamics and transport in the two-dimensional system. The rich phenomenology of fermionic many-body systems reveals itself on very different scales of energy, ranging from solid state materials and ultracold quantum gases to heavy-ion collisions and neutron stars. Understanding the underlying mechanisms promises substantial advances both on a fundamental and technological level. Ultracold quantum gases provide a platform for the exploration of the macroscopic phases and thermodynamic properties of fermionic many-body Hamiltonians in a highly controlled manner [1]. In particular, using strongly anisotropic traps, it is possible to enter the 2D regime [2][3][4][5][6][7] which is of large interest to the condensed matter community [8,9].The thermodynamic properties of a many-body system are encapsulated in its equation of state (EOS) n(µ, T, {g i }), which expresses the density n as a function of chemical potential µ, temperature T , and further system parameters {g i } characterizing, for instance, the interactions between particles. For ultracold atoms with short-range attraction, the only additional parameter is the s-wave scattering length a. This universality allows one to describe different atomic species by the same EOS n(µ, T, a). The equilibrium EOS is also the basis for studying dynamics close to thermal equilibrium.In this Letter, we report the experimental determination of the EOS of two-component fermions with attractive short-range interactions in the 2D BEC-BCS crossover regime. We tune the interaction strength using a Feshbach resonance to connect the well-known limits of a weakly attractive Fermi gas and a Bose gas of tightly bound dimers. We report the measurement of the finite temperature EOS in the intermediate, strongly correlated region and compare with theoretical predictions.Our experimental setup consists of a populationbalanced mixture of N ∼ 100, 0006 Li-atoms in the lowest two hyperfine states, which we denote by |1 and |2 . The interactions between both species can be tuned by means of a magnetic Feshbach resonance [10,11]. The atoms are trapped in a highly anisotropic trapping potential, which is radially symmetric to a high degree in the xy-plane and provides a tight confinement along the z-direction with the aspect ratio of frequencies ω x : ω y : ω z ≈ 1 : 1 : 310. A detailed description of the experiment is given in [7]. This strong anisotropy induces a quantu...

Fermions in Two Dimensions: Scattering and Many-Body Properties

“…The dotted vertical line corresponds to the interaction strength (η ≈ 0.65) where the chemical potential changes sign. Comparing our results with experimentally extracted values of the chemical potential [34,51], we find a nice match in the deep BEC regime. Differences become more significant in the BCS limit, probably due to finite-temperature and quasi-2D effects in the experiment.…”

“…A rich area of study subject to ongoing investigation is that of low dimensionality [16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38]. These dilute cold atomic gases have been trapped using anisotropic potentials, resulting in a quasi-2D pancake-shape gas cloud.…”

Second-order virial expansion for an atomic gas in a harmonic waveguide

“…This permits one to achieve one-dimensional (1D) or two-dimensional (2D) systems in the limit where all the characteristic energies, including the temperature, are lower than the atomic zero-point energy of the tight direction(s) of the trap [30]. In this way the 2D EOS for a two-component resonant Fermi gas has been measured [31,32]. On the theoretical side, highly anisotropic traps can be modeled by considering harmonic atomic waveguides where interatomic collisions are well known in the low energy limit [33][34][35].…”

Response Functions for the Two-Dimensional Ultracold Fermi Gas: Dynamical BCS Theory and Beyond

“…An array of ground state properties in 2D have already been measured, both theoretically and experimentally [7,8,9,10,11,12,13,14,15,16], although much less is available in 2D compared to 3D systems. Exact calculations have been recently achieved using auxiliary-field quantum Monte Carlo (AFQMC) methodologies both for ground state properties [17] and excited states [18].…”