The universal three-fermion bound states arising at a p-wave Feshbach resonance when the three particles are confined in two dimensions are studied, and a universal effective potential that is responsible for the scaling of these states is identified.
A new kind of "super-Efimov" states of binding energies scaling as ln∣En∣∼−e3nπ/4 were predicted by a field theory calculation for three fermions with resonant p-wave interactions in two dimensions [Phys. Rev. Lett. \textbf{110}, 235301 (2013)]. However, the universality of these "super-Efimov" states has not been proved independently. In this Letter, we study the three fermion system through the hyperspherical formalism. Within the adiabatic approximation, we find that at p-wave resonances, the low energy physics of states of angular momentum ℓ=±1 crucially depends on the value of an emergent dimensionless parameter Y determined by the detail of the inter-particle potential. Only if Y is exactly zero, the predicted "super-Efimov" states exist. If Y>0, the scaling of the bound states changes to ln∣En∣∼−(nπ)2/2Y, while there are no shallow bound states if Y<0.
A class of universal ``three-body'' bound states has been recently predicted theoretically for identical fermions interacting at p-wave resonance in two dimensions. This phenomenon is called the super Efimov effect since the binding energies of the states follow a intriguing double exponential scaling. However, experimental resolution of this scaling is expected to meet formidable challenges. In this work, we introduce a thermodynamic quantity, the three-body contact ${C}_{\ensuremath{\theta}}$, to quantify three-body correlations in a two-dimensional gas composed of the resonantly interacting fermions; the contact ${C}_{\ensuremath{\theta}}$ is the consequence of the underlying universal super Efimov effect in the many-body context. We show how ${C}_{\ensuremath{\theta}}$ affects physical observables such as the radio-frequency spectrum, the momentum distribution, and the atom loss rate. The signature of the elusive super Efimov effect can be pinned down by the detection of the three-body contact ${C}_{\ensuremath{\theta}}$ via these observables in the many-body system.
We study a system of spinless fermions in two dimensions with a short-range interaction fine-tuned to a p-wave resonance. We show that three such fermions form an infinite tower of bound states of orbital angular momentum $\ensuremath{\ell}=\ifmmode\pm\else\textpm\fi{}1$ and their binding energies obey a universal doubly exponential scaling ${E}_{3}^{(n)}\ensuremath{\propto}\mathrm{exp}(\ensuremath{-}2{e}^{3\ensuremath{\pi}n/4+\ensuremath{\theta}})$ at large n. This ``super Efimov effect'' is found by a renormalization group analysis and confirmed by solving the bound state problem. We also provide an indication that there are $\ensuremath{\ell}=\ifmmode\pm\else\textpm\fi{}2$ four-body resonances associated with every three-body bound state at ${E}_{4}^{(n)}\ensuremath{\propto}\mathrm{exp}(\ensuremath{-}2{e}^{3\ensuremath{\pi}n/4+\ensuremath{\theta}\ensuremath{-}0.188})$. These universal few-body states may be observed in ultracold atom experiments and should be taken into account in future many-body studies of the system.
The Efimov effect was first predicted for three particles interacting at an s-wave resonance in three dimensions. A subsequent study showed that the same effect can be realized by considering two-body and three-body interactions in mixed dimensions. In this work, we consider the three-body problem of two bosonic A atoms interacting with another single B atom in mixed dimensions: The A atoms are confined in a space of dimension dA and the B atom in a space of dimension dB, and there is an interspecies s-wave interaction in a dint-codimensional space accessible to both species. We find that when the s-wave interaction is tuned on resonance, there emerge an infinite series of universal three-body bound states for dA,dB,dint=2,2,0 and 2,3,1. Going beyond the Efimov paradigm, the binding energies of these states follow the scaling $ln|{E}_{n}{|\ensuremath{\sim}\ensuremath{-}s(n\ensuremath{\pi}\ensuremath{-}\ensuremath{\theta})}^{2}/4$, with the scaling factor s being unity for the former case and mB(2mA+mB)/(mA+mB) for the latter. We discuss the possibility of realizing our mixed-dimensional systems in a cold-atom experiment and how the effects of these universal three-body bound states may be detected.
We study two species of particles in two dimensions interacting by isotropic short-range potentials with the interspecies potential fine-tuned to a p-wave resonance. Their universal low-energy physics can be extracted by analyzing a properly constructed low-energy effective field theory with the renormalization group method. Consequently, a three-body system consisting of two particles of one species and one of the other is shown to exhibit the super Efimov effect, the emergence of an infinite tower of three-body bound states with orbital angular momentum $\ensuremath{\ell}=\ifmmode\pm\else\textpm\fi{}1$ whose binding energies obey a doubly exponential scaling, when the two particles are heavier than the other by a mass ratio greater than 4.034 04 for identical bosons and 2.414 21 for identical fermions. With increasing the mass ratio, the super Efimov spectrum becomes denser which would make its experimental observation easier. We also point out that the Born-Oppenheimer approximation is incapable of reproducing the super Efimov effect, the universal low-energy asymptotic scaling of the spectrum.
Inspired by the narrow Feshbach resonance in systems with the two-body interaction, we propose a two-channel model of three-component fermions with a three-body interaction that takes into account finite-range effects in low dimensions. Within this model, the p -wave Efimov-like effect in the four-body sector is predicted in fractional dimensions between d=1 and d=2 . The impact of the finite-range interaction on the formation of the four-body bound states in d=1 is also discussed in detail. Published by the American Physical Society 2024