One dimensional trapped fermions with attractive contact interactions

ChangMo Yang

Pino D’Amico, Massimo Rontani

We provide an accurate calculation of the energy spectrum of three atoms interacting through a contact force in a one-dimensional harmonic trap, considering both spinful fermions and spinless bosons. We use fermionic energies as a benchmark for the exact-diagonalization technique (also known as full configuration interaction), which is found to slowly converge in the case of strong inter-atomic attraction.

Seth Grable, Noah Kamm, Harsh Mathur

Oleksandr V. Marchukov, Dmitri V. Fedorov, Aksel S. Jensen +2 more

Michele Casula, David M. Ceperley, Erich J. Mueller

Using exact continuous quantum Monte Carlo techniques, we study the zero- and finite-temperature properties of a system of harmonically trapped one-dimensional spin-$\frac{1}{2}$ fermions with short-range interactions. Motivated by experimental searches for modulated Fulde-Ferrel-Larkin-Ovchinikov states, we systematically examine the impact of a spin imbalance on the density profiles. We quantify the accuracy of the Thomas-Fermi approximation, finding that for sufficiently large particle numbers $(N\ensuremath{\gtrsim}100)$ it quantitatively reproduces most features of the exact density profile. The Thomas-Fermi approximation fails to capture small Friedel-like spin and density oscillations and overestimates the size of the fully paired region in the outer shell of the trap. Based on our results, we suggest a range of experimentally tunable parameters to maximize the visibility of the double-shell structure of the system and the Fulde-Ferrel-Larkin-Ovchinikov state in the one-dimensional harmonic trap. Furthermore, we analyze the fingerprints of the attractive contact interactions in the features of the momentum and pair momentum distributions.

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