We investigate the appearance of a four-boson limit cycle in Hamiltonian systems at the unitarity limit. The model interaction incorporates two-, three-, and four-body short-range potentials, which allow us to disentangle the interwoven dynamics of three- and four-boson energy levels. Through numerical evidence, we observe a correlation between the energies of two successive universal tetramer levels for a fixed weakly bound trimer, which is found to be largely model independent. Interestingly, this correlation cycle is consistent with the findings of Hadizadeh et al. [Phys. Rev. Lett. 107, 135304 (2011)] using a zero-range model.We investigate the appearance of a four-boson limit cycle in Hamiltonian systems at the unitarity limit. The model interaction incorporates two-, three-, and four-body short-range potentials, which allow us to disentangle the interwoven dynamics of three- and four-boson energy levels. Through numerical evidence, we observe a correlation between the energies of two successive universal tetramer levels for a fixed weakly bound trimer, which is found to be largely model independent. Interestingly, this correlation cycle is consistent with the findings of Hadizadeh et al. [Phys. Rev. Lett. 107, 135304 (2011)] using a zero-range model.

arXiv:2303.14952Physical Review ASep 5, 20235 citations

Binding and structure of tetramers in the scaling limit

M. R. Hadizadeh, Marcelo Takeshi Yamashita, Lauro Tomio +2 more

The momentum-space structure of the Faddeev-Yakubovsky (FY) components of weakly bound tetramers is investigated at the unitary limit using a renormalized zero-range two-body interaction. The results, obtained by considering a given trimer level with binding energy ${B}_{3}$ , provide further support to a universal scaling function relating the binding energies of two successive tetramer states. The correlated scaling between the tetramer energies comes from the sensitivity of the four-boson system to a short-range four-body scale. Each excited $N$ th tetramer energy ${B}_{4}^{(N)}$ moves as the short-range four-body scale changes, while the trimer properties are kept fixed, with the next excited tetramer ${B}_{4}^{(N+1)}$ emerging from the atom-trimer threshold for a universal ratio ${B}_{4}^{(N)}/{B}_{3}={B}_{4}^{(N)}/{B}_{4}^{(N+1)}\ensuremath{\simeq}4.6$, which does not depend on $N$ . We show that both channels of the FY decomposition [atom-trimer ( $K$ type) and dimer-dimer ( $H$ type)] present high-momentum tails that reflect the short-range four-body scale. We also found that the $H$ channel is favored over the $K$ channel at low momentum, when the four-body momentum scale largely overcomes the three-body scale.The momentum-space structure of the Faddeev-Yakubovsky (FY) components of weakly bound tetramers is investigated at the unitary limit using a renormalized zero-range two-body interaction. The results, obtained by considering a given trimer level with binding energy ${B}_{3}$, provide further support to a universal scaling function relating the binding energies of two successive tetramer states. The correlated scaling between the tetramer energies comes from the sensitivity of the four-boson system to a short-range four-body scale. Each excited $N$th tetramer energy ${B}_{4}^{(N)}$ moves as the short-range four-body scale changes, while the trimer properties are kept fixed, with the next excited tetramer ${B}_{4}^{(N+1)}$ emerging from the atom-trimer threshold for a universal ratio ${B}_{4}^{(N)}/{B}_{3}={B}_{4}^{(N)}/{B}_{4}^{(N+1)}\ensuremath{\simeq}4.6$, which does not depend on $N$. We show that both channels of the FY decomposition [atom-trimer ($K$ type) and dimer-dimer ($H$ type)] present high-momentum tails that reflect the short-range four-body scale. We also found that the $H$ channel is favored over the $K$ channel at low momentum, when the four-body momentum scale largely overcomes the three-body scale.

arXiv:1110.5214Physical Review AFeb 8, 201233 citations

A coherent superposition of dimers and trimers

Yaakov Yudkin, Roy Elbaz, Panagiotis Giannakeas +2 more

Bulletin of the American Physical SocietyMay 29, 20190 citations

Interwoven limit cycles in the spectra of mass imbalanced many-boson system

W. de Paula, A. Delfino, T. Frederico +1 more

The independence between few-body scales beyond the van der Waals universality is demonstrated for the extreme mass-imbalanced case of a specific many-boson system. This finding generalizes the scaling properties of universal tetramers to a broader class of heterogeneous few-boson systems. We assume two heavy atoms interacting with $(N-2)-$ lighter ones at the unitary limit, using a particular case where no interactions are active between identical particles, by investigating the interwoven spectra of this many-body system for an arbitrary number of light bosons. A large mass-ratio between the particles allows us to treat this $N-$ body system analytically, by solving an effective inverse-squared long-range interaction which is stablished for the two heavy bosons. For a cluster with $N-2$ light bosons ( $N\ge 4$ ), we discuss the implications of the corresponding long-range potentials associated with different subsystem thresholds, implying in independent interwoven limit cycles for the correlation between the energies of excited $N-$ body system. Our study with extreme mass-imbalanced few-boson bound states provides a fundamental understanding of the scaling behavior of their interwoven spectra. The novel insights enlarge the well-known Efimov physics paradigm and show the existence of different limit cycles, which could be probed by new experiments.The independence between few-body scales beyond the van der Waals universality is demonstrated for the extreme mass-imbalanced case of a specific many-boson system. This finding generalizes the scaling properties of universal tetramers to a broader class of heterogeneous few-boson systems. We assume two heavy atoms interacting with $(N-2)-$lighter ones at the unitary limit, using a particular case where no interactions are active between identical particles, by investigating the interwoven spectra of this many-body system for an arbitrary number of light bosons. A large mass-ratio between the particles allows us to treat this $N-$body system analytically, by solving an effective inverse-squared long-range interaction which is stablished for the two heavy bosons. For a cluster with $N-2$ light bosons ($N\ge 4$), we discuss the implications of the corresponding long-range potentials associated with different subsystem thresholds, implying in independent interwoven limit cycles for the correlation between the energies of excited $N-$body system. Our study with extreme mass-imbalanced few-boson bound states provides a fundamental understanding of the scaling behavior of their interwoven spectra. The novel insights enlarge the well-known Efimov physics paradigm and show the existence of different limit cycles, which could be probed by new experiments.

arXiv:1903.10321Mar 25, 20191 citation

{B}_{3}

, provide further support to a universal scaling function relating the binding energies of two successive tetramer states. The correlated scaling between the tetramer energies comes from the sensitivity of the four-boson system to a short-range four-body scale. Each excited

N

th tetramer energy

{B}_{4}^{(N)}

moves as the short-range four-body scale changes, while the trimer properties are kept fixed, with the next excited tetramer

{B}_{4}^{(N+1)}

emerging from the atom-trimer threshold for a universal ratio ${B}_{4}^{(N)}/{B}_{3}={B}_{4}^{(N)}/{B}_{4}^{(N+1)}\ensuremath{\simeq}4.6$, which does not depend on

N

. We show that both channels of the FY decomposition [atom-trimer (

K

type) and dimer-dimer (

H

type)] present high-momentum tails that reflect the short-range four-body scale. We also found that the

H

channel is favored over the

K

channel at low momentum, when the four-body momentum scale largely overcomes the three-body scale.

(N-2)-

lighter ones at the unitary limit, using a particular case where no interactions are active between identical particles, by investigating the interwoven spectra of this many-body system for an arbitrary number of light bosons. A large mass-ratio between the particles allows us to treat this

N-

body system analytically, by solving an effective inverse-squared long-range interaction which is stablished for the two heavy bosons. For a cluster with

N-2

light bosons (

N\ge 4

), we discuss the implications of the corresponding long-range potentials associated with different subsystem thresholds, implying in independent interwoven limit cycles for the correlation between the energies of excited

N-

body system. Our study with extreme mass-imbalanced few-boson bound states provides a fundamental understanding of the scaling behavior of their interwoven spectra. The novel insights enlarge the well-known Efimov physics paradigm and show the existence of different limit cycles, which could be probed by new experiments.