Highly polarized Fermi gases: One-dimensional case

Abstract

We consider the problem of a single particle interacting with $N$ identical fermions, at zero temperature and in one dimension. We calculate the binding energy as well as the effective mass of the single particle. We use an approximate method developed in the three-dimensional case, where the Hilbert space for the excited states of the $N$ fermions is restricted to have at most two particle-hole pairs. When the mass of the single particle is equal to the fermion mass, we find an excellent agreement with the exact results of McGuire. When the mass of the single particle is infinite, we solve exactly the problem and find again excellent agreement between approximate results and exact ones. This overall agreement in one dimension gives a strong validation for the approximate method applied in three dimensions. Moreover it shows that our approximate treatment is excellent for the one dimensional problem in the general case with respect to the mass of the single particle.

9 pages, 13 figures

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• Entanglement of an Impurity in a Few-Body One-Dimensional Ideal Bose System
• Exact results for polaron and molecule in one-dimensional spin-1/2 Fermi gas
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• Mobile impurity in a one-dimensional gas at finite temperatures
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• Two-dimensional composite solitons in a spin-orbit-coupled Fermi gas in free space
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• Highly polarized one-dimensional Fermi gases near a narrow $p-$wave resonance
• Polar molecules in bilayers with high population imbalance
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• Momentum Evolution Numerics of an Impurity in a Quantum Quench