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arXiv:2202.01437 · Physical Review Letters

Universal Tetramer and Pentamer Bound States in Two-Dimensional Fermionic Mixtures

Ruijin Liu, Peng Cheng, Xiaoling Cui

Published Aug 12, 2022• 18 citations
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Abstract

We study the emergence of universal tetramer and pentamer bound states in the two-dimensional (N+1) system, which consists of N identical heavy fermions interacting with a light atom. We show that the critical heavy-light mass ratio to support a (3+1) tetramer below the trimer threshold is 3.38, and to support a (4+1) pentamer below the tetramer threshold is 5.14. While the ground state tetramer and pentamer are both with zero total angular momentum, they exhibit very different density distributions and correlations in momentum space, due to their distinct angular momentum decompositions in the dimer-fermion frame. These universal bound states can be accessible by a number of Fermi-Fermi mixtures now realized in cold atoms laboratories, which also suggest novel few-body correlations dominant in their corresponding many-body systems.

DOI
10.1103/physrevlett.129.073401

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We study the emergence of universal tetramer and pentamer bound states in the two-dimensional (N+1) system, which consists of N identical heavy fermions interacting with a light atom. We show that the critical heavy-light mass ratio to support a (3+1) tetramer below the trimer threshold is 3.38, and to support a (4+1) pentamer below the tetramer threshold is 5.14. While the ground state tetramer and pentamer are both with zero total angular momentum, they exhibit very different density distributions and correlations in momentum space, due to their distinct angular momentum decompositions in the dimer-fermion frame. These universal bound states can be accessible by a number of Fermi-Fermi mixtures now realized in cold atoms laboratories, which also suggest novel few-body correlations dominant in their corresponding many-body systems.
We study universal clusters in quasi-two-dimensions (q2D) that consist of a light (L) atom interacting with two or three heavy (H) identical fermions, forming the trimer or tetramer bound state. The axial confinement in q2D is shown to lift the threefold degeneracy of three-dimensional trimer (tetramer) in p -wave channel and uniquely select the ground state with magnetic angular momentum | m | = 1 ( m = 0 ). By varying the interaction or confinement strength, we explore the dimensional crossover of these clusters from 3D to 2D, characterized by a gradual change of critical H-L mass ratio for their emergence and momentum-space distribution. Importantly, we find that a finite effective range will not alter their critical mass ratios in the weak coupling regime. There, we establish an effective 2D model to quantitatively reproduce the properties of q2D clusters, and further identify the optimal interaction strengths for their detections in experiments. Our results suggest a promising prospect for observing universal clusters and associated high-order correlation effects in realistic q2D ultracold Fermi mixtures. Published by the American Physical Society 2024
We show that four heavy fermions interacting resonantly with a lighter atom (4+1 system) become Efimovian at mass ratio 13.279(2), which is smaller than the corresponding 2+1 and 3+1 thresholds. We thus predict the five-body Efimov effect for this system in the regime where any of its subsystem is non-Efimovian. For smaller mass ratios we show the existence and calculate the energy of a universal 4+1 pentamer state, which continues the series of the 2+1 trimer predicted by Kartavtsev and Malykh and 3+1 tetramer discovered by Blume. We also show that the effective-range correction for the light-heavy interaction has a strong effect on all these states and larger effective ranges increase their tendency to bind.
We calculate the universal spectrum of trimer and tetramer states in heteronuclear mixtures of ultracold atoms with different masses in the vicinity of the heavy-light dimer threshold. To extract the energies, we solve the three- and four-body problem for simple two- and three-body potentials tuned to the universal region using the Gaussian expansion method. We focus on the case of one light particle of mass mmm and two or three heavy bosons of mass MMM with resonant heavy-light interactions. We find that trimer and tetramer cross into the heavy-light dimer threshold at almost the same point and that as the mass ratio M/mM/mM/m decreases, the distance between the thresholds for trimer and tetramer states becomes smaller. We also comment on the possibility of observing exotic three-body states consisting of a dimer and two atoms in this region and compare with previous work.
We consider the problem of NNN identical fermions interacting via a zero-range attractive potential with a lighter atom in one dimension. Using the few-body approach based on the Skorniakov and Ter-Martirosian equation, we determine the energies and the critical mass ratios for the emergence of the tetramer, pentamer, and hexamer. For large NNN, we solve the problem analytically by using the mean-field theory based on the Thomas-Fermi approximation. The system becomes bound when the heavy-to-light mass ratio exceeds a critical value, which grows as N3{N}^{3}N3 at large NNN. We also employ a more sophisticated Hartree-Fock approach, which turns out to be equivalent to the Thomas-Fermi approximation for determining the energies, but provides a better description of the microscopic structure of the clusters.
Polarons can serve as an ideal platform to identify few-body correlations in tackling complex many-body problems. In this work, we reveal various crystalline few-body correlations smoothly emergent from the mass-imbalanced Fermi polarons in two dimensions. A unified variational approach up to three particle-hole excitations allows us to extract the dominant dimer, trimer, or tetramer correlation in a single framework. When the fermion-impurity mass ratio is beyond certain critical value, the Fermi polaron is found to undergo a smooth crossover, instead of a sharp transition, from the polaronic to trimer and tetramer regimes as the fermion-impurity attraction is increased. The emergent trimer and tetramer correlations result in the momentum-space crystallization of particle-hole excitations featuring a stable diagonal or triangular structure, as can be directly probed through the density-density correlation of majority fermions. Our results shed light on the intriguing quantum phases in the mass-imbalanced Fermi-Fermi mixtures beyond the pairing superfluid paradigm.
The universal three-body dynamics in ultra-cold binary Fermi and Fermi–Bose mixtures is studied. Two identical fermions of mass m and a particle of mass m 1 with the zero-range two-body interaction in states of total angular momentum L = 1 are considered. Using the boundary condition model for the s -wave interaction of different particles, both eigenvalue and scattering problems are treated by solving hyper-radial equations, whose terms are derived analytically. The dependences of the three-body binding energies on the mass-ratio m / m 1 for the positive two-body scattering length are calculated; it is shown that the ground and excited states arise at m / m 1 ⩾ λ 1 ≈ 8.172 60 and m / m 1 ⩾ λ 2 ≈ 12.917 43, respectively. For m / m 1 ≲ λ 1 and m / m 1 ≲ λ 2 , the relevant bound states turn to narrow resonances, whose positions and widths are calculated. The 2 + 1 elastic scattering and the three-body recombination near the three-body threshold are studied, and it is shown that a two-hump structure in the mass-ratio dependences of the cross sections is connected with the rise of the bound states.