Physical Review A

P -wave Efimov physics implications at unitarity

Yu-Hsin Chen, Chris H. Greene

Published Mar 27, 2023• 6 citations

Abstract

Equal mass fermionic trimers with two different spin components near the unitary limit are shown to possess a universal van der Waals bound or resonance state near $s$-wave unitarity, when $p$-wave interactions are included between the particles with equal spin. Our treatment uses a single-channel Lennard-Jones interaction with long-range two-body van der Waals potentials. While it is well known that there is no true Efimov effect that would produce an infinite number of bound states in the unitary limit, we demonstrate that another type of universality emerges for the symmetry ${L}^{\mathrm{\ensuremath{\Pi}}}={1}^{\ensuremath{-}}$. The universality is a remnant of Efimov physics that exists in this system at $p$-wave unitarity, and it leads to modified threshold and scaling laws in that limit. Application of our model to the system of three lithium atoms studied experimentally by Du et al. [Phys. Rev. Lett. 102, 250402 (2009)] provides an interpretation of their measured three-body recombination loss rates.

DOI: 10.1103/physreva.107.033329

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Universal trimers with p-wave interactions and the faux-Efimov effect

Yu-Hsin Chen, Chris H. Greene

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Efimov physics implications at p -wave fermionic unitarity

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Universal three-body recombination via resonant d -wave interactions

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Effects of p-wave interactions on Borromean Efimov trimers in heavy–light Fermi systems

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Theoretical Study on Efimov Physics in Ultracold Atoms

晋平遠藤

Mar 24, 20140 citations

Physical Review A

P -wave Efimov physics implications at unitarity

Yu-Hsin Chen, Chris H. Greene

Published Mar 27, 2023• 6 citations

Publisher

Abstract

Equal mass fermionic trimers with two different spin components near the unitary limit are shown to possess a universal van der Waals bound or resonance state near

s

-wave unitarity, when

p

-wave interactions are included between the particles with equal spin. Our treatment uses a single-channel Lennard-Jones interaction with long-range two-body van der Waals potentials. While it is well known that there is no true Efimov effect that would produce an infinite number of bound states in the unitary limit, we demonstrate that another type of universality emerges for the symmetry

{L}^{\mathrm{\ensuremath{\Pi}}}={1}^{\ensuremath{-}}

. The universality is a remnant of Efimov physics that exists in this system at

p

-wave unitarity, and it leads to modified threshold and scaling laws in that limit. Application of our model to the system of three lithium atoms studied experimentally by Du et al. [Phys. Rev. Lett. 102, 250402 (2009)] provides an interpretation of their measured three-body recombination loss rates.

DOI: 10.1103/physreva.107.033329

Related papers

Universal trimers with p-wave interactions and the faux-Efimov effect

Yu-Hsin Chen, Chris H. Greene

Abstract An unusual class of equal mass p-wave universal trimers with symmetry L Π = 1 ± is identified, for both a two-component fermionic trimer with s- and p-wave scattering length close to unitarity and for a one-component fermionic trimer at p-wave unitarity. Moreover, fermionic trimers made of atoms with two internal spin components are found for L Π = 1 ± , when the p-wave interaction between spin-up and spin-down fermions is close to unitarity and/or when the interaction between two spin-up fermions is close to the p-wave unitary limit. The universality of these p-wave universal trimers is tested here by considering van der Waals interactions in a Lennard–Jones potential with different numbers of two-body bound states; our calculations also determine the value of the scattering volume or length where the trimer state hits zero energy and can be observed as a recombination resonance. The faux-Efimov effect appears with trimer symmetry L Π = 1 − when the two fermion interactions are close to p-wave unitarity and the lowest 1 / R 2 coefficient gets modified, thereby altering the usual Wigner threshold law for inelastic processes involving three-body continuum channels.Abstract An unusual class of equal mass p-wave universal trimers with symmetry L Π = 1 ± is identified, for both a two-component fermionic trimer with s- and p-wave scattering length close to unitarity and for a one-component fermionic trimer at p-wave unitarity. Moreover, fermionic trimers made of atoms with two internal spin components are found for L Π = 1 ± , when the p-wave interaction between spin-up and spin-down fermions is close to unitarity and/or when the interaction between two spin-up fermions is close to the p-wave unitary limit. The universality of these p-wave universal trimers is tested here by considering van der Waals interactions in a Lennard–Jones potential with different numbers of two-body bound states; our calculations also determine the value of the scattering volume or length where the trimer state hits zero energy and can be observed as a recombination resonance. The faux-Efimov effect appears with trimer symmetry L Π = 1 − when the two fermion interactions are close to p-wave unitarity and the lowest 1 / R 2 coefficient gets modified, thereby altering the usual Wigner threshold law for inelastic processes involving three-body continuum channels.

arXiv:2408.08993Journal of Physics B Atomic Molecular and Optical PhysicsNov 28, 20245 citations

Efimov physics implications at p -wave fermionic unitarity

Yu-Hsin Chen, Chris H. Greene

Efimov physics at $p$ -wave unitarity for three equal mass fermions in multiple symmetries interacting via Lennard-Jones potentials is predicted to modify the long-range interaction potential energy, but without producing a true Efimov effect. This analysis treats the total orbital angular momenta and parities, ${J}^{\mathrm{\ensuremath{\Pi}}}={0}^{+},{1}^{+},{1}^{\ensuremath{-}}$, and ${2}^{\ensuremath{-}}$, for either three spin-polarized fermions ($\ensuremath{\uparrow}\ensuremath{\uparrow}\ensuremath{\uparrow}$) or two spin-up and one spin-down fermion ($\ensuremath{\downarrow}\ensuremath{\uparrow}\ensuremath{\uparrow}$). Our results for the long-range interaction in some of those cases agree with previous work by Werner and Castin and by Blume et al., namely, in cases where the $s$ -wave scattering length goes to infinity. The present results extend those calculated interaction energies to small and intermediate hyperradii comparable to the van der Waals length, and we consider additional unitarity scenarios where the $p$ -wave scattering volume approaches infinity. The crucial role of the diagonal hyperradial adiabatic correction term is identified and characterized.Efimov physics at $p$-wave unitarity for three equal mass fermions in multiple symmetries interacting via Lennard-Jones potentials is predicted to modify the long-range interaction potential energy, but without producing a true Efimov effect. This analysis treats the total orbital angular momenta and parities, ${J}^{\mathrm{\ensuremath{\Pi}}}={0}^{+},{1}^{+},{1}^{\ensuremath{-}}$, and ${2}^{\ensuremath{-}}$, for either three spin-polarized fermions ($\ensuremath{\uparrow}\ensuremath{\uparrow}\ensuremath{\uparrow}$) or two spin-up and one spin-down fermion ($\ensuremath{\downarrow}\ensuremath{\uparrow}\ensuremath{\uparrow}$). Our results for the long-range interaction in some of those cases agree with previous work by Werner and Castin and by Blume et al., namely, in cases where the $s$-wave scattering length goes to infinity. The present results extend those calculated interaction energies to small and intermediate hyperradii comparable to the van der Waals length, and we consider additional unitarity scenarios where the $p$-wave scattering volume approaches infinity. The crucial role of the diagonal hyperradial adiabatic correction term is identified and characterized.

arXiv:2209.06181Physical Review AJan 12, 20227 citations

Efimov physics implications at $p$ -wave fermionic unitarity

Chen, Yu-Hsin, Chris H. Greene

Efimov physics at $p$ -wave unitarity for three equal mass fermions in multiple symmetries interacting via Lennard-Jones potentials is predicted to modify the long range interaction potential energy, but without producing a true Efimov effect. This analysis treats the following total orbital angular momenta and parities, $J^Π=0^{+}, 1^{+}, 1^{-}$ and $2^{-}$ , for either three spin-polarized fermions ($\uparrow \uparrow \uparrow $), or two spin-up and one spin-down fermion ($ \downarrow \uparrow \uparrow $). Our results for the long range interaction in some of those cases agree with previous work by Werner and Castin and by Blume {\it et al.}, namely in cases where the $s$ -wave scattering length goes to infinity. The present results extend those calculated interaction energies to small and intermediate hyperradii comparable to the van der Waals length, and we consider additional unitarity scenarios where the $p$ -wave scattering volume approaches infinity. The crucial role of the diagonal hyperradial adiabatic correction term is identified and characterized.Efimov physics at $p$-wave unitarity for three equal mass fermions in multiple symmetries interacting via Lennard-Jones potentials is predicted to modify the long range interaction potential energy, but without producing a true Efimov effect. This analysis treats the following total orbital angular momenta and parities, $J^Π=0^{+}, 1^{+}, 1^{-}$ and $2^{-}$, for either three spin-polarized fermions ($\uparrow \uparrow \uparrow $), or two spin-up and one spin-down fermion ($\downarrow \uparrow \uparrow $). Our results for the long range interaction in some of those cases agree with previous work by Werner and Castin and by Blume {\it et al.}, namely in cases where the $s$-wave scattering length goes to infinity. The present results extend those calculated interaction energies to small and intermediate hyperradii comparable to the van der Waals length, and we consider additional unitarity scenarios where the $p$-wave scattering volume approaches infinity. The crucial role of the diagonal hyperradial adiabatic correction term is identified and characterized.

arXiv:2109.13311Sep 27, 20210 citations

Universal three-body recombination via resonant d -wave interactions

Jia Wang, José Paulo D'Incao, Yujun Wang +1 more

For a system of three identical bosons interacting via short-range forces, when two of the atoms are about to form a two-body $s$ -wave dimer, the Efimov effect takes place leading to the formation of an infinite number of three-body (Efimov) states. The lowest Efimov state crosses the three-body break-up threshold when the $s$ -wave two-body scattering length is $a\ensuremath{\approx}\ensuremath{-}9.73{r}_{\mathrm{vdW}}$, ${r}_{\mathrm{vdW}}$ being the van der Waals length. This article focuses on a generalized version of this Efimov scenario, where two of the atoms are about to form a two-body $d$ -wave dimer, resulting in strong $d$ -wave interactions. In his paper [Phys. Rev. A 62, 050702(R) (2000)], Bo Gao predicted that for broad resonances the $d$ -wave dimer is always formed when $a\ensuremath{\approx}0.956{r}_{\mathrm{vdW}}$. Here we find that a single universal three-body state associated with the $d$ -wave dimer is also formed near the three-body breakup threshold at $a\ensuremath{\approx}1.09{r}_{\mathrm{vdW}}$, or alternatively ${a}_{2}=0.902{r}_{\mathrm{vdW}}$ , where ${a}_{2}$ is the two-body $d$ -wave scattering length. The signature of such a universal three-body state is signaled experimentally by an enhancement of the three-body recombination rate. The three-body effective potential curves that are crucial for understanding the recombination dynamics are also calculated and analyzed. An improved method to calculate the couplings, effective potential curves, and recombination rate coefficients is presented.For a system of three identical bosons interacting via short-range forces, when two of the atoms are about to form a two-body $s$-wave dimer, the Efimov effect takes place leading to the formation of an infinite number of three-body (Efimov) states. The lowest Efimov state crosses the three-body break-up threshold when the $s$-wave two-body scattering length is $a\ensuremath{\approx}\ensuremath{-}9.73{r}_{\mathrm{vdW}}$, ${r}_{\mathrm{vdW}}$ being the van der Waals length. This article focuses on a generalized version of this Efimov scenario, where two of the atoms are about to form a two-body $d$-wave dimer, resulting in strong $d$-wave interactions. In his paper [Phys. Rev. A 62, 050702(R) (2000)], Bo Gao predicted that for broad resonances the $d$-wave dimer is always formed when $a\ensuremath{\approx}0.956{r}_{\mathrm{vdW}}$. Here we find that a single universal three-body state associated with the $d$-wave dimer is also formed near the three-body breakup threshold at $a\ensuremath{\approx}1.09{r}_{\mathrm{vdW}}$, or alternatively ${a}_{2}=0.902{r}_{\mathrm{vdW}}$, where ${a}_{2}$ is the two-body $d$-wave scattering length. The signature of such a universal three-body state is signaled experimentally by an enhancement of the three-body recombination rate. The three-body effective potential curves that are crucial for understanding the recombination dynamics are also calculated and analyzed. An improved method to calculate the couplings, effective potential curves, and recombination rate coefficients is presented.

arXiv:1209.4553Physical Review ADec 20, 201237 citations

Effects of p-wave interactions on Borromean Efimov trimers in heavy–light Fermi systems

Cai-Yun Zhao, Hui-Li Han, Ting-Yun Shi

Abstract We investigate the effects of p-wave interactions on Efimov trimers in systems comprising two identical heavy fermions and a light particle, with mass ratios larger than 13.6. Our focus lies on the Borromean regime where the ground-state trimer exists in the absence of dimers. Using pair-wise Lennard–Jones potentials and concentrating on the L π = 1 − symmetry, we explore the critical value of the interspecies s-wave scattering length a c at which the Borromean state appears in several two-component particle systems. Our exploration encompasses the universal properties of a c and the influence of p-wave fermion–fermion interactions on its value. We find that, in the absence of p-wave fermion–fermion interactions, a c is determined universally by the van der Waals radius and mass ratio. However, the introduction of p-wave fermion–fermion interactions unveiled a departure from this universality. Our calculations show that the critical interspecies scattering length a c now depends on the details of the fermion–fermion p-wave interaction. And, the presence of p-wave fermion–fermion interactions favors the formation of the Borromean state. Additionally, our investigation reveals that Efimov effect in the 1 − symmetry persist even when the fermion–fermion interaction reaches the p-wave unitary limit.Abstract We investigate the effects of p-wave interactions on Efimov trimers in systems comprising two identical heavy fermions and a light particle, with mass ratios larger than 13.6. Our focus lies on the Borromean regime where the ground-state trimer exists in the absence of dimers. Using pair-wise Lennard–Jones potentials and concentrating on the L π = 1 − symmetry, we explore the critical value of the interspecies s-wave scattering length a c at which the Borromean state appears in several two-component particle systems. Our exploration encompasses the universal properties of a c and the influence of p-wave fermion–fermion interactions on its value. We find that, in the absence of p-wave fermion–fermion interactions, a c is determined universally by the van der Waals radius and mass ratio. However, the introduction of p-wave fermion–fermion interactions unveiled a departure from this universality. Our calculations show that the critical interspecies scattering length a c now depends on the details of the fermion–fermion p-wave interaction. And, the presence of p-wave fermion–fermion interactions favors the formation of the Borromean state. Additionally, our investigation reveals that Efimov effect in the 1 − symmetry persist even when the fermion–fermion interaction reaches the p-wave unitary limit.

arXiv:2307.12598Journal of Physics B Atomic Molecular and Optical PhysicsMay 23, 20243 citations

Theoretical Study on Efimov Physics in Ultracold Atoms

晋平遠藤

The Efimov states are three-body bound states, which appear universally when the s-wave scattering length between the particles is resonantly large.Since the Efimov states and their characteristic discrete scale invariance have recently been observed in ultracold atoms, the Efimov states and their associated few-body phenomena have attracted widening interest both theoretically and experimentally.In this thesis, I theoretically study the Efimov physics and related phenomena, focusing on the following three topics: (i) Universal three-body physics for a mass-imbalanced Fermi system (Chapter 3).For a system of two identical spinless (i.e., spin-polarized) fermions and one distinguishable particle which interact via a short-range potential with a large s-wave scattering length, two classes of universal three-body bound states have been known to appear in different regimes of the mass ratio: the Efimov trimers and the Kartavtsev-Malykh trimers, which feature the discrete and continuous scale invariance, respectively.I have found the third class of universal three-body bound states, which I call the "crossover trimers".The crossover trimers show neither the discrete nor continuous scale invariance.I have identified the regions of these three classes of trimers as a function of the mass ratio and the s-wave scattering length, and shown that the Kartavtsev-Malykh trimers and the Efimov trimers can continuously transform into each other via the crossover trimers as the mass ratio and the s-wave scattering length are varied.Owing to the presence of the crossover trimers, the Kartavtsev-Malykh trimers dissociate into a particle and a dimer when the s-wave scattering length is varied, inducing resonances in the particle-dimer scattering.I have calculated the elastic particle-dimer scattering lengths in arbitrary angular-momentum channels, and shown that the particle-dimer resonances indeed occur.From the resonance positions, I have found accurate values of the critical mass ratios at which the Kartavtsev-Malykh trimers in the higher angular-momentum channels appear. (ii) Universal three-body parameter (Chapter 4).In the Efimov physics, the three-body parameter fixes the short-range three-body phase and hence the scale of the energy spectrum.Until quite recently, it has been widely held that the threebody parameter should depend on the short-range part of the inter-atomic potential, and hence vary almost randomly between different atomic species and hyperfine states.However, mounting evidence in recent experiments suggests otherwise.While some theoretical studies have succeeded in reproducing the universal behavior in the three-body parameter, the underlying physical mechanism has remained unclear and controversial.In this thesis, I elucidate the physical origin of the universal three-body parameter.I propose that a non-adiabatic deformation of the three-body wave function induced by a universal two-body correlation results in a universal three-body repulsion, which prevents three particles from coming close and renders the three-body parameter universal.This mechanism is verified by reproducing the universal three-body repulsion with a simple model wave function.The mechanism found here suggests that the three-body parameter would also be universal for non-van der Waals types of potentials.For various classes of deep two-body potentials, it is shown that the effective range is the relevant length scale to characterize the two-body correlation and sets the three-body parameter.Depending on the shape of the two-body correlation, thereThe Efimov states are three-body bound states, which appear universally when the s-wave scattering length between the particles is resonantly large.Since the Efimov states and their characteristic discrete scale invariance have recently been observed in ultracold atoms, the Efimov states and their associated few-body phenomena have attracted widening interest both theoretically and experimentally.In this thesis, I theoretically study the Efimov physics and related phenomena, focusing on the following three topics: (i) Universal three-body physics for a mass-imbalanced Fermi system (Chapter 3).For a system of two identical spinless (i.e., spin-polarized) fermions and one distinguishable particle which interact via a short-range potential with a large s-wave scattering length, two classes of universal three-body bound states have been known to appear in different regimes of the mass ratio: the Efimov trimers and the Kartavtsev-Malykh trimers, which feature the discrete and continuous scale invariance, respectively.I have found the third class of universal three-body bound states, which I call the "crossover trimers".The crossover trimers show neither the discrete nor continuous scale invariance.I have identified the regions of these three classes of trimers as a function of the mass ratio and the s-wave scattering length, and shown that the Kartavtsev-Malykh trimers and the Efimov trimers can continuously transform into each other via the crossover trimers as the mass ratio and the s-wave scattering length are varied.Owing to the presence of the crossover trimers, the Kartavtsev-Malykh trimers dissociate into a particle and a dimer when the s-wave scattering length is varied, inducing resonances in the particle-dimer scattering.I have calculated the elastic particle-dimer scattering lengths in arbitrary angular-momentum channels, and shown that the particle-dimer resonances indeed occur.From the resonance positions, I have found accurate values of the critical mass ratios at which the Kartavtsev-Malykh trimers in the higher angular-momentum channels appear. (ii) Universal three-body parameter (Chapter 4).In the Efimov physics, the three-body parameter fixes the short-range three-body phase and hence the scale of the energy spectrum.Until quite recently, it has been widely held that the threebody parameter should depend on the short-range part of the inter-atomic potential, and hence vary almost randomly between different atomic species and hyperfine states.However, mounting evidence in recent experiments suggests otherwise.While some theoretical studies have succeeded in reproducing the universal behavior in the three-body parameter, the underlying physical mechanism has remained unclear and controversial.In this thesis, I elucidate the physical origin of the universal three-body parameter.I propose that a non-adiabatic deformation of the three-body wave function induced by a universal two-body correlation results in a universal three-body repulsion, which prevents three particles from coming close and renders the three-body parameter universal.This mechanism is verified by reproducing the universal three-body repulsion with a simple model wave function.The mechanism found here suggests that the three-body parameter would also be universal for non-van der Waals types of potentials.For various classes of deep two-body potentials, it is shown that the effective range is the relevant length scale to characterize the two-body correlation and sets the three-body parameter.Depending on the shape of the two-body correlation, there

Mar 24, 20140 citations

Equal mass fermionic trimers with two different spin components near the unitary limit are shown to possess a universal van der Waals bound or resonance state near

s

-wave unitarity, when

p

{L}^{\mathrm{\ensuremath{\Pi}}}={1}^{\ensuremath{-}}

. The universality is a remnant of Efimov physics that exists in this system at

p

Efimov physics at

p

-wave unitarity for three equal mass fermions in multiple symmetries interacting via Lennard-Jones potentials is predicted to modify the long-range interaction potential energy, but without producing a true Efimov effect. This analysis treats the total orbital angular momenta and parities, ${J}^{\mathrm{\ensuremath{\Pi}}}={0}^{+},{1}^{+},{1}^{\ensuremath{-}}$, and ${2}^{\ensuremath{-}}$, for either three spin-polarized fermions ($\ensuremath{\uparrow}\ensuremath{\uparrow}\ensuremath{\uparrow}$) or two spin-up and one spin-down fermion ($\ensuremath{\downarrow}\ensuremath{\uparrow}\ensuremath{\uparrow}$). Our results for the long-range interaction in some of those cases agree with previous work by Werner and Castin and by Blume et al., namely, in cases where the

s

-wave scattering length goes to infinity. The present results extend those calculated interaction energies to small and intermediate hyperradii comparable to the van der Waals length, and we consider additional unitarity scenarios where the

p

-wave scattering volume approaches infinity. The crucial role of the diagonal hyperradial adiabatic correction term is identified and characterized.

Efimov physics at

p

-wave unitarity for three equal mass fermions in multiple symmetries interacting via Lennard-Jones potentials is predicted to modify the long range interaction potential energy, but without producing a true Efimov effect. This analysis treats the following total orbital angular momenta and parities,

J^Π=0^{+}, 1^{+}, 1^{-}

and

2^{-}

, for either three spin-polarized fermions ($\uparrow \uparrow \uparrow

), or two spin-up and one spin-down fermion (

\downarrow \uparrow \uparrow $). Our results for the long range interaction in some of those cases agree with previous work by Werner and Castin and by Blume {\it et al.}, namely in cases where the

s

p

-wave scattering volume approaches infinity. The crucial role of the diagonal hyperradial adiabatic correction term is identified and characterized.

For a system of three identical bosons interacting via short-range forces, when two of the atoms are about to form a two-body

s

-wave dimer, the Efimov effect takes place leading to the formation of an infinite number of three-body (Efimov) states. The lowest Efimov state crosses the three-body break-up threshold when the

s

-wave two-body scattering length is $a\ensuremath{\approx}\ensuremath{-}9.73{r}_{\mathrm{vdW}}$,

{r}_{\mathrm{vdW}}

being the van der Waals length. This article focuses on a generalized version of this Efimov scenario, where two of the atoms are about to form a two-body

d

-wave dimer, resulting in strong

d

-wave interactions. In his paper [Phys. Rev. A 62, 050702(R) (2000)], Bo Gao predicted that for broad resonances the

d

-wave dimer is always formed when $a\ensuremath{\approx}0.956{r}_{\mathrm{vdW}}$. Here we find that a single universal three-body state associated with the

d

-wave dimer is also formed near the three-body breakup threshold at $a\ensuremath{\approx}1.09{r}_{\mathrm{vdW}}$, or alternatively

{a}_{2}=0.902{r}_{\mathrm{vdW}}

, where

{a}_{2}

is the two-body

d

-wave scattering length. The signature of such a universal three-body state is signaled experimentally by an enhancement of the three-body recombination rate. The three-body effective potential curves that are crucial for understanding the recombination dynamics are also calculated and analyzed. An improved method to calculate the couplings, effective potential curves, and recombination rate coefficients is presented.