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arXiv:2202.07639 · Scientific Reports

Unconventional pairing in few-fermion systems at finite temperature

Daniel Pęcak, Tomasz Sowiński

Published Oct 19, 2022• 6 citations
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Abstract

Attractively interacting two-component mixtures of fermionic particles confined in a one-dimensional harmonic trap are investigated. Properties of balanced and imbalanced systems are systematically explored with the exact diagonalization approach, focusing on the finite-temperature effects. Using single- and two-particle density distributions, specific non-classical pairing correlations are analyzed in terms of the noise correlations-quantity directly accessible in state-of-the-art experiments with ultra-cold atoms. It is shown that along with increasing temperature, any imbalanced system hosting Fulde-Ferrel-Larkin-Ovchinnikov pairs crossovers to a standard Bardeen-Cooper-Schrieffer one characterized by zero net momentum of resulting pairs. By performing calculations for systems with different imbalances, the approximate boundary between the two phases on a phase diagram is determined.

DOI
10.1038/s41598-022-22411-w

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Attractively interacting two-component mixtures of fermionic particles confined in a one-dimensional harmonic trap are investigated. Properties of balanced and imbalanced systems are systematically explored with the exact diagonalization approach, focusing on the finite-temperature effects. Using single- and two-particle density distributions, specific non-classical pairing correlations are analyzed in terms of the noise correlations-quantity directly accessible in state-of-the-art experiments with ultra-cold atoms. It is shown that along with increasing temperature, any imbalanced system hosting Fulde-Ferrel-Larkin-Ovchinnikov pairs crossovers to a standard Bardeen-Cooper-Schrieffer one characterized by zero net momentum of resulting pairs. By performing calculations for systems with different imbalances, the approximate boundary between the two phases on a phase diagram is determined.
We study the ground-state properties of a two-component one-dimensional system of a few ultra-cold fermions with attractive interactions. We show that, by ramping up an external potential barrier felt by one of the components, it is possible to induce regions of exotic superfluid phases, characterized by a tunable finite net momentum of the Cooper pair, without changing the overall spin populations. We show that these phases, which are the few-body analogs of the celebrated Fulde-Ferrell-Larkin-Ovchinnikov state, can be distinguished by analyzing a specific two-particle correlation encoded in the noise correlation function. Our theoretical results can be addressed in current experiments with cold atoms confined in spin-selective optical traps.
We study the ground-state properties of a two-component fermionic mixture effectively confined in a one-dimensional harmonic trap. We consider scenarios when numbers of particles in components are the same but particles have different masses. We examine whether it is possible to detect signatures of an unconventional pairing between opposite-spin fermions in the presence of attractive interactions. For this purpose, we perform the exact diagonalization of the many-body Hamiltonian and study the two-particle reduced density matrix. In agreement with expectations, we confirm that the many-body ground state is dominated by conventional pairs with a negligible total momentum for a small mass imbalance. Furthermore, we show that for sufficiently large mass ratios the domination of fundamentally different pairs is established and the Fulde-Ferrell-Larkin-Ovchinnikov phase is supported. Finally, we argue that the two mechanisms can coexist in the regime of moderate mass ratios. Due to the current experimental progress in obtaining ultracold fermionic systems in a few-body regime, our predictions may have some importance for the upcoming experiments.
We present a systematic investigation of attractive binary mixtures in the presence of both spin- and mass-imbalance in one-dimensional setups described by the Hubbard model. After discussing typical cold atomic experimental realizations and the relation between microscopic and effective parameters, we study several many-body features of trapped Fermi-Fermi and Bose-Bose mixtures such as density profiles, momentum distributions, and correlation functions by means of density-matrix-renormalization-group and quantum Monte Carlo simulations. In particular, we focus on the stability of Fulde-Ferrell-Larkin-Ovchinnikov, dimer, and trimer fluids in inhomogeneous situations, as typically realized in cold gas experiments due to the harmonic confinement. We finally consider possible experimental signatures of these phases both in the presence of a finite polarization and of a finite temperature.
Using exact continuous quantum Monte Carlo techniques, we study the zero- and finite-temperature properties of a system of harmonically trapped one-dimensional spin-12\frac{1}{2}21​ 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.
Pairing in a population-imbalanced Fermi system in a two-dimensional optical lattice is studied using determinant quantum Monte Carlo simulations and mean-field calculations. The approximation-free numerical results show a wide range of stability of the Fulde-Ferrell-Larkin-Ovchinnikov phase. Contrary to claims of fragility with increased dimensionality, we find that this phase is stable across a wide range of values for the polarization, temperature, and interaction strength. Both homogeneous and harmonically trapped systems display pairing with finite center-of-mass momentum, with clear signatures either in momentum space or real space, which could be observed in cold-atomic gases loaded in an optical lattice. We also use the harmonic level basis in the confined system and find that pairs can form between particles occupying different levels, which can be seen as the analog of the finite center-of-mass momentum pairing in the translationally invariant case. Finally, we perform mean-field calculations for the uniform and confined systems and show the results to be in good agreement with quantum Monte Carlo. This leads to a simple picture of the different pairing mechanisms, depending on the filling and confining potential.