Fermions in Two Dimensions: Scattering and Many-Body Properties

Abstract

Ultracold atomic Fermi gases in two-dimensions (2D) are an increasingly popular topic of research. The interaction strength between spin-up and spindown particles in two-component Fermi gases can be tuned in experiments, allowing for a strongly interacting regime where the gas properties are yet to be fully understood. We have probed this regime for 2D Fermi gases by performing T = 0 ab initio diffusion Monte Carlo (DMC) calculations. The many-body dynamics are largely dependent on the two-body interactions, therefore we start with an in-depth look at scattering theory in 2D. We show the partial-wave expansion and its relation to the scattering length and effective range. Then we discuss our numerical methods for determining these scattering parameters. We close out this discussion by illustrating the details of bound states in 2D. Transitioning to the many-body system, we use variationally optimized wave functions to calculate ground-state properties of the gas over a range of interaction strengths. We show results for the energy per particle and parametrize an equation of state. We then proceed to determine the chemical potential for the strongly interacting gas.

Pairing in two-dimensional Fermi gases with a coordinate-space potential

“…These results inticate that the choices of k F r e 's used in our DMC calculations (in Refs. [42,44] and below) are small enough to get meaningful results.…”

“…In earlier works, we have employed Diffusion Monte Carlo [42,44] (DMC) to evaluate two-dimensional coldgas properties such as the equation of state and the pairing gap. These involved, first, the use of a finiterange two-particle interaction and, second, the use of only N = 26 particles in a periodic area.…”

Analytical treatment of the interaction quench dynamics of two bosons in a two-dimensional harmonic trap

“…Also and in contrast to the one-dimensional case, there are bound states |Ψ ν0 in both interaction regimes. The presence of these bound states can be attributed to the existence of the centripetal term − 1 4r 2 , in the 2D radial Schrödinger equation [55], which supports a bound state even for weakly attractive potentials, in contrast to the 3D case [12,59]. To further appreciate the influence of these bound states we also provide in the insets of Fig.…”

Cold Atoms Beyond Atomic Physics

“…Since the seminal work with the unitary Fermi gas [37] and properties calculated across the BCS-BEC crossover [38,39], QMC methods have been applied to investigate several other aspects of two-component Fermi gases [40][41][42][43]. A few examples include the following: effects of the effective range of the interaction [44,45], truly zero-range calculations [46][47][48], the contact parameter [49], two-dimensional systems [50,51], the excitation of vortices in 3D [52,53] and 2D [54] systems, and mass imbalance systems, for example 6 Li-40 K, between the two species [55].…”