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Physical Review A

Two heavy impurities immersed in light few-boson systems with noninteger dimensions

R.M. Francisco, D. S. Rosa, T. Frederico

Published Dec 12, 2022• 6 citations
Publisher

Abstract

We investigate the spectrum and structure of two heavy bosonic impurities immersed in a light boson system with noninteger dimensions $D$ by means of the Born-Oppenheimer approximation. The ratio between the energies of two consecutive many-body bound states, which follows an Efimov-type geometrical scaling law when the heavy-light pair has a resonant $s$-wave interaction, is found to be a function of the mass asymmetry, number of light bosons, and effective dimension $D$. Furthermore, the wave function is computed, and its behavior is explored for different system configurations. To exemplify our results, we consider mixtures of two heavy cesium atoms interacting with up to two lithium atoms, which are systems of current experimental interest.

DOI
10.1103/physreva.106.063305

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We investigate the spectrum and structure of two heavy bosonic impurities immersed in a light boson system with noninteger dimensions DDD by means of the Born-Oppenheimer approximation. The ratio between the energies of two consecutive many-body bound states, which follows an Efimov-type geometrical scaling law when the heavy-light pair has a resonant sss-wave interaction, is found to be a function of the mass asymmetry, number of light bosons, and effective dimension DDD. Furthermore, the wave function is computed, and its behavior is explored for different system configurations. To exemplify our results, we consider mixtures of two heavy cesium atoms interacting with up to two lithium atoms, which are systems of current experimental interest.
We investigate the spectrum and structure of two-heavy bosonic impurities immersed in a light-boson system in D dimensions by means of the Born-Oppenheimer approximation. The fractional dimension dependence are associated with squeezed traps. The binding energies follows an Efimov type geometrical scaling law when the heavy-light system has a s-wave resonant interaction and the effective dimension or trap deformation is within a given range. The discrete scaling parameter sss relates two consecutive many-body bound states depending on mass asymmetry, number of light-bosons and effective dimension D. Furthermore, the spectrum and wave-function for finite heavy-light binding energies are computed. To exemplify our results, we consider mixtures of two-heavy caesium atoms interacting with up to two-lithium ones, which are systems of current experimental interest.
Motivated by recent experiments on $^{6}\mathrm{Li}\text{\ensuremath{-}}^{133}\mathrm{Cs}$ atomic mixtures with high mass imbalance, we study the Efimov correlation in an atomic system of two heavy bosons (133Cs^{133}\mathrm{Cs}133Cs) immersed in a bath of light fermions (6Li^{6}\mathrm{Li}6Li). Using the Born-Oppenheimer approximation, we identify two different regimes, depending on the Fermi momentum of light fermions (kF{k}_{F}kF​) and the boson-fermion scattering length as(<0){a}_{s}(<0)as​(<0), where the presence of an underlying Fermi sea plays distinct roles in the Efimov-type binding of bosons. Namely, in the regime ${k}_{F}|{a}_{s}|\ensuremath{\lesssim}1$ (${k}_{F}|{a}_{s}|\ensuremath{\gtrsim}1$), the Fermi sea induces an attractive (repulsive) effective interaction between bosons and thus favors (disfavors) the formation of a bound state, which can be seen as an Efimov trimer dressed by a fermion cloud. Interestingly, this implies nonmonotonic behavior of these bound states as increasing the fermion density (or kF{k}_{F}kF​). Moreover, we establish a generalized universal scaling law for the emergence and variation of such dressed Efimov bound states when incorporating a new scale (kF{k}_{F}kF​) brought on by the Fermi sea. These results can be directly tested in Li-Cs cold-atom experiments by measuring the modified bound-state spectrum and the shifted Efimov resonance, which manifest an emergent nontrivial Efimov correlation in a fermionic many-body environment.
Abstract We study a three-body system, formed by two identical heavy bosons and a light particle, in the Born–Oppenheimer approximation for an arbitrary dimension D . We restrict D to the interval 2 < D < 4, and derive the heavy–heavy D -dimensional effective potential proportional to 1/ R 2 ( R is the relative distance between the heavy particles), which is responsible for the Efimov effect. We found that the Efimov states disappear once the critical strength of the heavy–heavy effective potential 1/ R 2 approaches the limit − ( D − 2 ) 2 / 4 . We obtained the scaling function for the 133 Cs– 133 Cs– 6 Li system as the limit cycle of the correlation between the energies of two consecutive Efimov states as a function of D and the heavy-light binding energy E D 2 . In addition, we found that the energy of the ( N + 1)th excited state reaches the two-body continuum independently of the dimension D when E 2 D / E 3 ( N ) = 0.89 , where E 3 ( N ) is the N th excited three-body binding energy.
We consider the problem of two heavy impurity particles embedded in a gas of weakly interacting light mass bosonic particles in the condensed state. Using the Bogoliubov approach to describe the bosonic gas and the Born-Oppenheimer approximation for the three-body dynamics, we calculate the modification to the heavy-heavy two-body potential due to the presence of the condensate. For the case of resonant interaction between the light bosons and the impurities, we present (semi)-analytical results for the potential in the limit of a large condensate coherence length. In particular, we find a formula for the modification of the Efimov scaling factor due to the presence of a degenerate bosonic gas background.
Abstract In this article, we revisit the heteronuclear Efimov effect in a Bose-Fermi mixture with large mass difference in the Born-Oppenheimer picture. As a specific example, we consider the combination of bosonic 133Cs and fermionic 6Li. In a system consisting of two heavy bosons and one light fermion, the fermion-mediated potential between the two heavy bosons gives rise to an infinite series of three-body bound states. The intraspecies scattering length determines the three-body parameter and the scaling factor between consecutive Efimov states. In a second scenario, we replace the single fermion by an entire Fermi Sea at zero temperature. The emerging interaction potential for the two bosons exhibits long-range oscillations leading to a weakening of the binding and a breakup of the infinite series of Efimov states. In this scenario, the binding energies follow a modified Efimov scaling law incorporating the Fermi momentum. The scaling factor between deeply bound states is governed by the intraspecies interaction, analogous to the Efimov states in vacuum.
We study the Born–Oppenheimer approximation of a mass-imbalanced three-body system made of two heavy particles of mass M and one light particle of mass m for arbitrary angular momentum. In this system, heavy-light pairs interact via a zero-range force. We construct the light-particle Hamiltonian using self-adjoint extensions of the two-center point interaction and show that the corresponding effective potential is regular at the coincidence point of the heavy particles. Consequently, this model presents an alternative method to finite-range, cutoff, or short-distance heavy-heavy regularizations: the necessary three-body input is encoded in the self-adjoint realization of the light-particle Hamiltonian, while the heavy-light interactions remain point-like. In the unitary limit, after fixing the characteristic length scale, we derive an explicit Efimov spectrum. Our results recover the zero-angular-momentum case of [] and provide a sufficient condition ensuring the absence of non-Efimov bound states. Away from unitarity, we show that the spatial size of the shallowest trimer near the threshold is approximately 2.8 times the heavy-light scattering length, in contrast with the common assumption that these two length scales coincide. We also derive a Bargmann-type bound on the number of three-body bound states and obtain an estimate sharper than previous results. Finally, we illustrate the method with numerical results for selected alkali mixtures.