Ab initioLattice Results for Fermi Polarons in Two Dimensions

Abstract

We investigate the attractive Fermi polaron problem in two dimensions using non-perturbative Monte Carlo simulations. We introduce a new Monte Carlo algorithm called the impurity lattice Monte Carlo method. This algorithm samples the path integral in a computationally efficient manner and has only small sign oscillations for systems with a single impurity. As a benchmark of the method, we calculate the universal polaron energy in three dimensions in the scale-invariant unitarity limit and find agreement with published results. We then present the first fully non-perturbative calculations of the polaron energy in two dimensions and density correlations between the impurity and majority particles in the limit of zero range interactions. We find evidence for a smooth crossover transition from fermionic quasiparticle to molecular state as a function of interaction strength.PACS numbers: 67.85. Lm, 02.70.Ss, One of the most interesting and fundamental problems in quantum many-body physics is the polaron problem, where a mobile impurity interacts with a bath of particles. With the advent of trapped ultracold atomic gases, the polaron problem can now be realized for both bosonic and fermionic baths, and also in the universal limit where the range of the particle interactions are negligible [1]. In a fermionic medium, the impurity can undergo a transition and change its quantum statistics by binding fermions from the surrounding Fermi gas [2,3]. The impurity is dressed by fluctuations of the Fermi sea forming a quasiparticle or polaron state. But with increasing particle interaction strength, molecules will form by capturing one or even two particles from the Fermi sea, and this behavior has been shown to depend on the mass ratio of the two components of the Fermi gas for the 3D case [2][3][4][5][6][7][8][9][10]. In 1D, the exact analytical solution for equal masses shows that the polaron-molecule transition is a smooth crossover [11,12].In 2D the Fermi polaron properties have been studied using different theoretical and experimental approaches, and these have predicted various scenarios for the existence or absence of a polaron-molecule transition [13][14][15][16][17][18][19][20][21]. The Fermi polaron system has been studied using diagrammatic Monte Carlo (diag MC) [20,21]. The diag MC method uses a worm algorithm to stochastically sample Feynman diagrams to high orders in the coupling constant. In this work we introduce a non-perturbative ab initio approach called impurity lattice Monte Carlo (ILMC) [22] to investigate highlyimbalanced Fermi gases. Unlike diag MC, impurity lattice Monte Carlo directly samples the path integral and so is a fully non-perturbative calculation. We present calculations for the energy of the 2D polaron and density correlations between the impurity and majority particles as a function of interaction strength. Our results show evidence for a smooth crossover from polaron to molecule.Impurity lattice Monte Carlo method. The impurity lattice Monte Carlo method is a hybrid of two Monte Carlo al...

Fermi gases in the two-dimensional to quasi-two-dimensional crossover

“…where q = ǫ F /E b . This analytic result interpolates between the molecular regime (neglecting the molecular mean field) at magnetic fields well below the Feshbach resonance and agrees with the Fermi polaron approximation [22] and recent QMC predictions [39] at and above the Feshbach resonance, where our data is taken. The red solid curves in the spectra of Fig.…”

Repulsive Fermi polarons and their induced interactions in binary mixtures of ultracold atoms

“…As a result exotic quantum phases and itinerant ferromagnetism [26][27][28][29][30][31][32][33] could be explored. While for finite impurity mass Fermi polarons constitute well-defined quasiparticles in these higher dimensional systems [34][35][36], the quasiparticle picture is shown to be ill-defined in the thermodynamic limit of one-dimensional (1D) settings [37][38][39]. However, important aspects of the physics in this limit have been identified in few-body experiments evading such difficulties [40,41].…”

Impurity lattice Monte Carlo for hypernuclei

“…[16] in the context of a Hamiltonian theory of spin-up and spin-down fermions, and applied to the intrinsically non-perturbative physics of Fermi polarons in two dimensions in Ref. [17]. The ILMC method is particularly useful for the case where only one fermion (of either species) is immersed in a "sea" of the other species.…”