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arXiv:1612.09341 · Physical Review Letters

Five-Body Efimov Effect and Universal Pentamer in Fermionic Mixtures

Betzalel Bazak, Dmitry S. Petrov

Published Feb 23, 2017• 47 citations
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Abstract

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.

DOI
10.1103/physrevlett.118.083002

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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 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.
Motivated by recent experimental investigations of Cs-Cs-Li Efimov resonances, this work theoretically investigates the few-body properties of $N\ensuremath{-}1$ noninteracting identical heavy bosons, which interact with a light impurity through a large sss-wave scattering length. For Cs-Cs-Cs-Li, we predict the existence of universal four-body states with energies E4(n,1){E}_{4}^{(n,1)}E4(n,1)​ and E4(n,2){E}_{4}^{(n,2)}E4(n,2)​, which are universally linked to the energy E3(n){E}_{3}^{(n)}E3(n)​ of the nnnth Efimov trimer. For infinitely large $^{133}\mathrm{Cs}\text{\ensuremath{-}}^{6}\mathrm{Li}$ and vanishing $^{133}\mathrm{Cs}\text{\ensuremath{-}}^{133}\mathrm{Cs}$ scattering lengths, we find $({E}_{4}^{(1,1)}/{E}_{3}^{(1)}{)}^{1/2}\ensuremath{\approx}1.51$ and $({E}_{4}^{(1,2)}/{E}_{3}^{(1)}{)}^{1/2}\ensuremath{\approx}1.01$. The $^{133}\mathrm{Cs}\text{\ensuremath{-}}^{6}\mathrm{Li}$ scattering lengths at which these states merge with the four-atom threshold, the dependence of these energy ratios on the mass ratio between the heavy and light atoms, and selected aspects of the generalized Efimov scenario for N>4N>4N>4 are also discussed. Possible implications of our results for ongoing cold atom experiments are presented.
We examine the physics of two, three, and four heavy fermions interacting with a single light fermion via short-range interactions. Four-particle bosonic Efimov states have proven important experimentally and also been the subject of significant theoretical effort. Similar fermionic systems are just now being investigated. We find that with some simple interactions the four- and five-particle states collapse to the interaction range at smaller mass ratios than the three-body state, and also before larger clusters can collapse. These states and their excitations can be studied in cold atom experiments, providing unique insights into the role of few-body systems in many-body physics.
The number of four-body states known to behave universally is small. This work adds a new class of four-body states to this relatively short list. We predict the existence of a universal four-body bound state for heavy-light mixtures consisting of three identical heavy fermions and a fourth distinguishable lighter particle with a mass ratio κ>/~9.5 and short-range interspecies interaction characterized by a positive s-wave scattering length. The structural properties of these universal states are discussed, and finite-range effects are analyzed. The bound states can be experimentally realized and probed by utilizing ultracold atom mixtures.
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.