Comparing models for the ground state energy of a trapped one-dimensional Fermi gas with a single impurity

Abstract

We discuss the local density approximation approach to calculating the ground state energy of a one-dimensional Fermi gas containing a single impurity, and compare the results with exact numerical values that we have for up to 11 particles for general interaction strengths and up to 30 particles in the strongly interacting case. We also calculate the contact coefficient in the strongly interacting regime. The different theoretical predictions are compared to recent experimental results with few-atom systems. Firstly, we find that the local density approximation suffers from great ambiguity in the few-atom regime, yet it works surprisingly well for some models. Secondly, we find that the strong interaction theories quickly break down when the number of particles increase or the interaction strength decreases.

10 pages, 4 figures, 2 tables, final version

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• SU(N) Fermions in a One-Dimensional Harmonic Trap
• Universal Tan relations for quantum gases in one dimension
• Comparing numerical and analytical approaches to strongly interacting two-component mixtures in one dimensional traps
• An interpolatory ansatz captures the physics of one-dimensional confined Fermi systems
• Exact results for polaron and molecule in one-dimensional spin-1/2 Fermi gas
• Momentum reconstruction and contact of the one-dimensional Bose-Fermi mixture
• Numerical methods and analytic results for one-dimensional strongly interacting spinor gases
• Several fermions strongly interacting with a heavy mobile impurity in a one-dimensional harmonic trap