arXiv:1806.10647 · Physical Review A

Exploring universal and nonuniversal regimes of trimers from three-body interactions in one-dimensional lattices

Arthur Christianen, John Sous

Published Jun 4, 2020• 2 citations

Abstract

We investigate the formation of trimers in an infinite one-dimensional lattice model of hard-core particles with single-particle hopping $t$ and and nearest-neighbor two-body $U$ and three-body $V$ interactions of relevance to Rydberg atoms and polar molecules. For sufficiently attractive $U\ensuremath{\le}\ensuremath{-}2t$ and positive $V>0$ a large trimer is stabilized, which persists as $V\ensuremath{\rightarrow}\ensuremath{\infty}$, while both sufficiently attractive $U$ and $V$ bind a small trimer. The excited state above this small trimer is also bound and has a large extent; its behavior as $V\ensuremath{\rightarrow}\ensuremath{-}\ensuremath{\infty}$ resembles that of the large ground-state trimer. These large bound states appear to admit a continuum description. Furthermore, we find that in the limit $V\ensuremath{\gg}t,\phantom{\rule{0.16em}{0ex}}U<\ensuremath{-}2t$ the bound-state behavior qualitatively evolves with larger $|U|$ from a state described by the scattering of three far separated particles to a state of a compact dimer scattering with a single particle.

DOI: 10.1103/physreva.101.063610

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Large Trimers from Three-Body Interactions in One-Dimensional Lattices

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arXiv:1806.10647 · Physical Review A

Exploring universal and nonuniversal regimes of trimers from three-body interactions in one-dimensional lattices

Arthur Christianen, John Sous

Published Jun 4, 2020• 2 citations

arXiv HTML PDF

Abstract

We investigate the formation of trimers in an infinite one-dimensional lattice model of hard-core particles with single-particle hopping

t

and and nearest-neighbor two-body

U

and three-body

V

interactions of relevance to Rydberg atoms and polar molecules. For sufficiently attractive

U\ensuremath{\le}\ensuremath{-}2t

and positive

V>0

a large trimer is stabilized, which persists as

V\ensuremath{\rightarrow}\ensuremath{\infty}

, while both sufficiently attractive

U

and

V

bind a small trimer. The excited state above this small trimer is also bound and has a large extent; its behavior as

V\ensuremath{\rightarrow}\ensuremath{-}\ensuremath{\infty}

resembles that of the large ground-state trimer. These large bound states appear to admit a continuum description. Furthermore, we find that in the limit

V\ensuremath{\gg}t,\phantom{\rule{0.16em}{0ex}}U<\ensuremath{-}2t

the bound-state behavior qualitatively evolves with larger

|U|

from a state described by the scattering of three far separated particles to a state of a compact dimer scattering with a single particle.

DOI: 10.1103/physreva.101.063610

Related papers

Large Trimers from Three-Body Interactions in One-Dimensional Lattices

Arthur Christianen, John Sous

Few-body bound states have been extensively explored in cold atomic gases with a desire to realize large molecular complexes. Here, we investigate the formation of trimers in an infinite one-dimensional lattice with hard-core two- and three-body interactions of relevance to Rydberg atoms and polar molecules in optical lattices, and other physical systems such as the fractional Hall states. We determine the stability regions for attractively and repulsively bound trimers. We discover a regime of large spatially extended trimers that are stabilized by the interplay of attractive two-body, $U$ , and repulsive three-body, $V$ , interactions and persist despite extremely large $V$ . These bound states present a new direction in the search for large few-body complexes in cold atoms.Few-body bound states have been extensively explored in cold atomic gases with a desire to realize large molecular complexes. Here, we investigate the formation of trimers in an infinite one-dimensional lattice with hard-core two- and three-body interactions of relevance to Rydberg atoms and polar molecules in optical lattices, and other physical systems such as the fractional Hall states. We determine the stability regions for attractively and repulsively bound trimers. We discover a regime of large spatially extended trimers that are stabilized by the interplay of attractive two-body, $U$ , and repulsive three-body, $V$ , interactions and persist despite extremely large $V$. These bound states present a new direction in the search for large few-body complexes in cold atoms.

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Three-body bound states in a lattice

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Universal trimers of one-dimensional bosons with two- and three-body attractions

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When quantum particles are confined into lower dimensions, an effective three-body interaction inevitably arises and may cause significant consequences. Here we study bosons in one dimension with weak two-body and three-body interactions and predict the existence of two three-body bound states when both interactions are attractive. Their binding energies are universal functions of the two-body and three-body scattering lengths and have direct relevance to a broad range of quasi-one-dimensional systems realized with ultracold atoms.When quantum particles are confined into lower dimensions, an effective three-body interaction inevitably arises and may cause significant consequences. Here we study bosons in one dimension with weak two-body and three-body interactions and predict the existence of two three-body bound states when both interactions are attractive. Their binding energies are universal functions of the two-body and three-body scattering lengths and have direct relevance to a broad range of quasi-one-dimensional systems realized with ultracold atoms.

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Metastable doubly charged Rydberg trimers

Daniel J. Bosworth, Matthew T. Eiles, Peter Schmelcher

We examine an effectively one-electron system with three positive nuclei composed of a Rb * 87 Rydberg atom interacting with a pair of Rb + 87 ions and predict the existence of metastable vibrationally bound states of Rb 3 2 + 87 . These molecules are long-range trimers whose stability rests on the presence of core-shell electrons and favorable scaling of the Rydberg atom's quadrupole moment with the principal quantum number n . Unlike recently observed ion-Rydberg dimers, whose binding is due to internal flipping of the Rydberg atom's dipole moment, the binding of Rb 3 2 + 87 arises from the interaction of the ions with the Rydberg atom's quadrupole moment. The stability of these trimers is highly sensitive to n . For n ≤ 35 , we estimate that the lifetime of the bound states should be limited by intercore tunneling of the Rydberg electron, which creates an instability in the system. However, we predict that the rate of this process decreases significantly with n , such that already for n = 38 it is comparable in magnitude to the rate of spontaneous emission of the Rydberg state. The decreasing depth of the binding potential at larger n will further lead to an increase in the tunneling rate of the vibrational states from the molecular binding potential to dissociative regions of the adiabatic potential energy surface. Nonetheless, at n = 38 , this mechanism is only relevant for the highest-excited vibrational states in the binding potential. Published by the American Physical Society 2024We examine an effectively one-electron system with three positive nuclei composed of a Rb * 87 Rydberg atom interacting with a pair of Rb + 87 ions and predict the existence of metastable vibrationally bound states of Rb 3 2 + 87 . These molecules are long-range trimers whose stability rests on the presence of core-shell electrons and favorable scaling of the Rydberg atom's quadrupole moment with the principal quantum number n . Unlike recently observed ion-Rydberg dimers, whose binding is due to internal flipping of the Rydberg atom's dipole moment, the binding of Rb 3 2 + 87 arises from the interaction of the ions with the Rydberg atom's quadrupole moment. The stability of these trimers is highly sensitive to n . For n ≤ 35 , we estimate that the lifetime of the bound states should be limited by intercore tunneling of the Rydberg electron, which creates an instability in the system. However, we predict that the rate of this process decreases significantly with n , such that already for n = 38 it is comparable in magnitude to the rate of spontaneous emission of the Rydberg state. The decreasing depth of the binding potential at larger n will further lead to an increase in the tunneling rate of the vibrational states from the molecular binding potential to dissociative regions of the adiabatic potential energy surface. Nonetheless, at n = 38 , this mechanism is only relevant for the highest-excited vibrational states in the binding potential. Published by the American Physical Society 2024

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Long-lived trimers in a quasi-two-dimensional Fermi system

Emma Laird, Thomas Kirk, Meera M. Parish +1 more

We consider the problem of three distinguishable fermions confined to a quasi-two-dimensional (quasi-2D) geometry, where there is a strong harmonic potential in one direction. We go beyond previous theoretical work and investigate the three-body bound states (trimers) for the case where the two-body short-range interactions between fermions are unequal. Using the scattering parameters from experiments on ultracold $^{6}\mathrm{Li}$ atoms, we calculate the trimer spectrum throughout the crossover from two to three dimensions. We find that the deepest Efimov trimer in the $^{6}\mathrm{Li}$ system is unaffected by realistic quasi-2D confinements, while the first excited trimer smoothly evolves from a three-dimensional-like Efimov trimer to an extended 2D-like trimer as the attractive interactions are decreased. We furthermore compute the excited trimer wave function and quantify the stability of the trimer against decay into a dimer and an atom by determining the probability that three fermions approach each other at short distances. Our results indicate that the lifetime of the trimer can be enhanced by at least an order of magnitude in the quasi-2D geometry, thus opening the door to realizing long-lived trimers in three-component Fermi gases.We consider the problem of three distinguishable fermions confined to a quasi-two-dimensional (quasi-2D) geometry, where there is a strong harmonic potential in one direction. We go beyond previous theoretical work and investigate the three-body bound states (trimers) for the case where the two-body short-range interactions between fermions are unequal. Using the scattering parameters from experiments on ultracold $^{6}\mathrm{Li}$ atoms, we calculate the trimer spectrum throughout the crossover from two to three dimensions. We find that the deepest Efimov trimer in the $^{6}\mathrm{Li}$ system is unaffected by realistic quasi-2D confinements, while the first excited trimer smoothly evolves from a three-dimensional-like Efimov trimer to an extended 2D-like trimer as the attractive interactions are decreased. We furthermore compute the excited trimer wave function and quantify the stability of the trimer against decay into a dimer and an atom by determining the probability that three fermions approach each other at short distances. Our results indicate that the lifetime of the trimer can be enhanced by at least an order of magnitude in the quasi-2D geometry, thus opening the door to realizing long-lived trimers in three-component Fermi gases.

arXiv:1803.02529Physical Review AApr 30, 20185 citations

We investigate the formation of trimers in an infinite one-dimensional lattice model of hard-core particles with single-particle hopping

t

and and nearest-neighbor two-body

U

and three-body

V

interactions of relevance to Rydberg atoms and polar molecules. For sufficiently attractive

U\ensuremath{\le}\ensuremath{-}2t

and positive

V>0

a large trimer is stabilized, which persists as

V\ensuremath{\rightarrow}\ensuremath{\infty}

, while both sufficiently attractive

U

and

V

bind a small trimer. The excited state above this small trimer is also bound and has a large extent; its behavior as

V\ensuremath{\rightarrow}\ensuremath{-}\ensuremath{\infty}

resembles that of the large ground-state trimer. These large bound states appear to admit a continuum description. Furthermore, we find that in the limit

V\ensuremath{\gg}t,\phantom{\rule{0.16em}{0ex}}U<\ensuremath{-}2t

the bound-state behavior qualitatively evolves with larger

|U|

from a state described by the scattering of three far separated particles to a state of a compact dimer scattering with a single particle.

U

, and repulsive three-body,

V

, interactions and persist despite extremely large

V

. These bound states present a new direction in the search for large few-body complexes in cold atoms.

^{6}\mathrm{Li}

atoms, we calculate the trimer spectrum throughout the crossover from two to three dimensions. We find that the deepest Efimov trimer in the

^{6}\mathrm{Li}

system is unaffected by realistic quasi-2D confinements, while the first excited trimer smoothly evolves from a three-dimensional-like Efimov trimer to an extended 2D-like trimer as the attractive interactions are decreased. We furthermore compute the excited trimer wave function and quantify the stability of the trimer against decay into a dimer and an atom by determining the probability that three fermions approach each other at short distances. Our results indicate that the lifetime of the trimer can be enhanced by at least an order of magnitude in the quasi-2D geometry, thus opening the door to realizing long-lived trimers in three-component Fermi gases.