The Photo Response Function of Universal Trimers

-wave components. These oscillations are the fingerprints of universal Efimov physics. We discuss the relevance of this effect to contemporary experiments in ultracold atoms.

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Photoreactions with universal trimers

Betzalel Bazak, Nir Barnea

Considering one-body and two-body currents, we study the photoassociation and photodissociation of universal bosonic trimers. Analyzing the relative importance of these currents, we identify two physical scenarios: (i) normal hierarchy, where naive power counting holds and the one-body current dominates, and (ii) strong hierarchy, where the one-body current is suppressed. For both scenarios we observe that at the high-frequency tail, the response function exhibits log-periodic oscillations in transition to or from any continuum state regardless of the reaction partial-wave channel. In contrast, near-threshold log-periodic oscillations appear only in the leading $s$ -wave components. These oscillations are the fingerprints of universal Efimov physics. We discuss the relevance of this effect to contemporary experiments in ultracold atoms.Considering one-body and two-body currents, we study the photoassociation and photodissociation of universal bosonic trimers. Analyzing the relative importance of these currents, we identify two physical scenarios: (i) normal hierarchy, where naive power counting holds and the one-body current dominates, and (ii) strong hierarchy, where the one-body current is suppressed. For both scenarios we observe that at the high-frequency tail, the response function exhibits log-periodic oscillations in transition to or from any continuum state regardless of the reaction partial-wave channel. In contrast, near-threshold log-periodic oscillations appear only in the leading $s$-wave components. These oscillations are the fingerprints of universal Efimov physics. We discuss the relevance of this effect to contemporary experiments in ultracold atoms.

arXiv:1305.4368Physical Review AMar 21, 20143 citations

Photoassociation of universal Efimov trimers

Betzalel Bazak, Nir Barnea

Abstract In view of recent experiments in ultracold atomic systems, the photoassociation of Efimov trimers, composed of three identical bosons, is studied utilizing the multipole expansion. We study both the normal hierarchy case, where one-body current is dominant, and the strong hierarchy case, relevant for photoassociation in ultracold atoms, where two-body current is dominant. For identical particles in the normal hierarchy case, the leading contribution comes from the r 2 s -mode operator and from the quadrupole d -mode operator. The s -mode reaction is found to be dominant at low temperature, while as the temperature increases the d -mode becomes as significant. For the strong hierarchy case, the leading contribution comes from a 2-body s -wave δ operator. In both cases log periodic oscillations are found in the cross section. For large but finite scattering length the amplitude of the oscillations becomes larger in comparison to infinite scattering length case. We apply our theory to photoassociation of 7 Li ultracold atoms and show a good fit to the available experimental results.Abstract In view of recent experiments in ultracold atomic systems, the photoassociation of Efimov trimers, composed of three identical bosons, is studied utilizing the multipole expansion. We study both the normal hierarchy case, where one-body current is dominant, and the strong hierarchy case, relevant for photoassociation in ultracold atoms, where two-body current is dominant. For identical particles in the normal hierarchy case, the leading contribution comes from the r 2 s -mode operator and from the quadrupole d -mode operator. The s -mode reaction is found to be dominant at low temperature, while as the temperature increases the d -mode becomes as significant. For the strong hierarchy case, the leading contribution comes from a 2-body s -wave δ operator. In both cases log periodic oscillations are found in the cross section. For large but finite scattering length the amplitude of the oscillations becomes larger in comparison to infinite scattering length case. We apply our theory to photoassociation of 7 Li ultracold atoms and show a good fit to the available experimental results.

arXiv:1502.07119Journal of Physics B Atomic Molecular and Optical PhysicsAug 5, 20150 citations

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

Few-boson system with a single impurity: Universal bound states tied to Efimov trimers

D. Blume

Small weakly bound droplets determine a number of properties of ultracold Bose and Fermi gases. For example, Efimov trimers near the atom-atom-atom and atom-dimer thresholds lead to enhanced losses from bosonic clouds. Generalizations to four- and higher-body systems have also been considered. Moreover, Efimov trimers have been predicted to play a role in the Bose polaron with large boson-impurity scattering length. Motivated by these considerations, the present work provides a detailed theoretical analysis of weakly bound $N$ -body clusters consisting of $N\ensuremath{-}1$ identical bosons (denoted by ``B'') of mass $m$ that interact with a single distinguishable impurity particle (denoted by ``X'') of mass $M$ . The system properties are analyzed as a function of the mass ratio $\ensuremath{\kappa}$ (values from $\ensuremath{\kappa}=1$ to 50 are considered), where $\ensuremath{\kappa}$ is equal to $m/M$ , and the two-body $s$ -wave scattering length ${a}_{\text{BX}}$ between the bosons and the impurity. To reach the universal Efimov regime in which the size of the BBX trimer as well as those of larger clusters is much larger than the length scales of the underlying interaction model, three different approaches are considered: resonance states are determined in the absence of BB and BBX interactions, bound states are determined in the presence of repulsive three-body boson-boson-impurity interactions, and bound states are determined in the presence of repulsive two-body boson-boson interactions. The universal regime, in which the details of the underlying interaction model become irrelevant, is identified.Small weakly bound droplets determine a number of properties of ultracold Bose and Fermi gases. For example, Efimov trimers near the atom-atom-atom and atom-dimer thresholds lead to enhanced losses from bosonic clouds. Generalizations to four- and higher-body systems have also been considered. Moreover, Efimov trimers have been predicted to play a role in the Bose polaron with large boson-impurity scattering length. Motivated by these considerations, the present work provides a detailed theoretical analysis of weakly bound $N$-body clusters consisting of $N\ensuremath{-}1$ identical bosons (denoted by ``B'') of mass $m$ that interact with a single distinguishable impurity particle (denoted by ``X'') of mass $M$. The system properties are analyzed as a function of the mass ratio $\ensuremath{\kappa}$ (values from $\ensuremath{\kappa}=1$ to 50 are considered), where $\ensuremath{\kappa}$ is equal to $m/M$, and the two-body $s$-wave scattering length ${a}_{\text{BX}}$ between the bosons and the impurity. To reach the universal Efimov regime in which the size of the BBX trimer as well as those of larger clusters is much larger than the length scales of the underlying interaction model, three different approaches are considered: resonance states are determined in the absence of BB and BBX interactions, bound states are determined in the presence of repulsive three-body boson-boson-impurity interactions, and bound states are determined in the presence of repulsive two-body boson-boson interactions. The universal regime, in which the details of the underlying interaction model become irrelevant, is identified.

arXiv:1901.03542Physical Review AJan 16, 201912 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

Efimov physics and universal trimers in spin-orbit-coupled ultracold atomic mixtures

Zhe-Yu Shi, Hui Zhai, Xiaoling Cui

We study the two-body and three-body bound states in ultracold atomic mixtures with one of the atoms subjected to an isotropic spin-orbit (SO) coupling. We consider a system of two identical fermions interacting with one SO-coupled atom. It is found that there can exist two types of three-body bound states, Efimov trimers and universal trimers. The Efimov trimers are energetically less favored by the SO coupling, which will finally merge into the atom-dimer threshold as increasing the SO-coupling strength. Nevertheless, these trimers exhibit a discrete scaling law incorporating the SO-coupling effect. On the other hand, the universal trimers are more favored by the SO coupling. They can be induced at negative $s$ -wave scattering lengths and with smaller mass ratios than those without SO coupling. These results are obtained by both the Born-Oppenheimer approximation and exact solutions from three-body equations.We study the two-body and three-body bound states in ultracold atomic mixtures with one of the atoms subjected to an isotropic spin-orbit (SO) coupling. We consider a system of two identical fermions interacting with one SO-coupled atom. It is found that there can exist two types of three-body bound states, Efimov trimers and universal trimers. The Efimov trimers are energetically less favored by the SO coupling, which will finally merge into the atom-dimer threshold as increasing the SO-coupling strength. Nevertheless, these trimers exhibit a discrete scaling law incorporating the SO-coupling effect. On the other hand, the universal trimers are more favored by the SO coupling. They can be induced at negative $s$-wave scattering lengths and with smaller mass ratios than those without SO coupling. These results are obtained by both the Born-Oppenheimer approximation and exact solutions from three-body equations.

arXiv:1411.7488Physical Review AFeb 18, 201514 citations

s

-wave components. These oscillations are the fingerprints of universal Efimov physics. We discuss the relevance of this effect to contemporary experiments in ultracold atoms.

s

-wave components. These oscillations are the fingerprints of universal Efimov physics. We discuss the relevance of this effect to contemporary experiments in ultracold atoms.

N

-body clusters consisting of $N\ensuremath{-}1$ identical bosons (denoted by ``B'') of mass

m

that interact with a single distinguishable impurity particle (denoted by ``X'') of mass

M

. The system properties are analyzed as a function of the mass ratio $\ensuremath{\kappa}$ (values from $\ensuremath{\kappa}=1$ to 50 are considered), where $\ensuremath{\kappa}$ is equal to

m/M

, and the two-body

s

-wave scattering length

{a}_{\text{BX}}

between the bosons and the impurity. To reach the universal Efimov regime in which the size of the BBX trimer as well as those of larger clusters is much larger than the length scales of the underlying interaction model, three different approaches are considered: resonance states are determined in the absence of BB and BBX interactions, bound states are determined in the presence of repulsive three-body boson-boson-impurity interactions, and bound states are determined in the presence of repulsive two-body boson-boson interactions. The universal regime, in which the details of the underlying interaction model become irrelevant, is identified.

s

-wave scattering lengths and with smaller mass ratios than those without SO coupling. These results are obtained by both the Born-Oppenheimer approximation and exact solutions from three-body equations.