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arXiv:1801.04663 · Physical Review A

Atom-dimer scattering in a heteronuclear mixture with a finite intraspecies scattering length

Chao Gao, Peng Zhang

Published Apr 2, 2018• 10 citations
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Abstract

We study the three-body problem of two ultracold identical bosonic atoms (denoted by $B$) and one extra atom (denoted by $X$), where the scattering length ${a}_{BX}$ between each bosonic atom and atom $X$ is resonantly large and positive. We calculate the scattering length ${a}_{\mathrm{ad}}$ between one bosonic atom and the shallow dimer formed by the other bosonic atom and atom $X$, and investigate the effect induced by the interaction between the two bosonic atoms. We find that even if this interaction is weak (i.e., the corresponding scattering length ${a}_{BB}$ is of the same order of the van der Waals length ${r}_{\mathrm{vdW}}$ or even smaller), it can still induce a significant effect for the atom-dimer scattering length ${a}_{\mathrm{ad}}$. Explicitly, an atom-dimer scattering resonance can always occur when the value of ${a}_{BB}$ varies in the region with $|{a}_{BB}|\ensuremath{\lesssim}{r}_{\mathrm{vdW}}$. As a result, both the sign and the absolute value of ${a}_{\mathrm{ad}}$, as well as the behavior of the ${a}_{\mathrm{ad}}\text{\ensuremath{-}}{a}_{BX}$ function, depends sensitively on the exact value of ${a}_{BB}$. Our results show that, for a good quantitative theory, the intraspecies interaction is required to be taken into account for this heteronuclear system, even if this interaction is weak.

DOI
10.1103/physreva.97.042701

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We study the three-body problem of two ultracold identical bosonic atoms (denoted by BBB) and one extra atom (denoted by XXX), where the scattering length aBX{a}_{BX}aBX​ between each bosonic atom and atom XXX is resonantly large and positive. We calculate the scattering length aad{a}_{\mathrm{ad}}aad​ between one bosonic atom and the shallow dimer formed by the other bosonic atom and atom XXX, and investigate the effect induced by the interaction between the two bosonic atoms. We find that even if this interaction is weak (i.e., the corresponding scattering length aBB{a}_{BB}aBB​ is of the same order of the van der Waals length rvdW{r}_{\mathrm{vdW}}rvdW​ or even smaller), it can still induce a significant effect for the atom-dimer scattering length aad{a}_{\mathrm{ad}}aad​. Explicitly, an atom-dimer scattering resonance can always occur when the value of aBB{a}_{BB}aBB​ varies in the region with ∣aBB∣\ensuremath≲rvdW|{a}_{BB}|\ensuremath{\lesssim}{r}_{\mathrm{vdW}}∣aBB​∣\ensuremath≲rvdW​. As a result, both the sign and the absolute value of aad{a}_{\mathrm{ad}}aad​, as well as the behavior of the aad\ensuremath-aBX{a}_{\mathrm{ad}}\text{\ensuremath{-}}{a}_{BX}aad​\ensuremath-aBX​ function, depends sensitively on the exact value of aBB{a}_{BB}aBB​. Our results show that, for a good quantitative theory, the intraspecies interaction is required to be taken into account for this heteronuclear system, even if this interaction is weak.
We use the zero-range approximation to study a system of two identical bosons interacting resonantly with a third particle. The method is derived from effective field theory. It reduces the three-body problem to an integral equation which we then solve numerically. We also develop an alternative approach which gives analytic solutions of the integral equation in coordinate representation in the limit of vanishing total energy. The atom-dimer scattering length, the rates of atom-dimer relaxation, and the three-body recombination to shallow and to deep molecular states are calculated either analytically or numerically with a well-controlled accuracy for various energies as functions of the mass ratio, scattering length, and three-body parameter. We discuss in detail the relative positions of the recombination loss peaks, which in the universal limit depend only on the mass ratio. Our results have implications for ongoing and future experiments on Bose-Bose and Bose-Fermi atomic mixtures.
We experimentally and theoretically study the effect of the intraspecies scattering length onto the heteronuclear Efimov scenario, following up on our earlier observation of Efimov resonances in an ultracold Cs-Li mixture for negative [Pires et al., Phys. Rev. Lett. 112, 250404 (2014)] and positive Cs-Cs scattering length [Ulmanis et al., Phys. Rev. Lett. 117, 153201 (2016)]. Three theoretical models of increasing complexity are employed to quantify its influence on the scaling factor and the three-body parameter: a simple Born-Oppenheimer picture, a zero-range theory, and a spinless van der Waals model. These models are compared to Efimov resonances observed in an ultracold mixture of bosonic 133Cs^{133}\mathrm{Cs}133Cs and fermionic 6Li^{6}\mathrm{Li}6Li atoms close to two Cs-Li Feshbach resonances located at 843 G and 889 G, characterized by different sign and magnitude of the Cs-Cs interaction. By changing the sign and magnitude of the intraspecies scattering length different scaling behaviors of the three-body loss rate are identified, in qualitative agreement with theoretical predictions. The three-body loss rate is strongly influenced by the intraspecies scattering length.
We investigate theoretically and experimentally the heteronuclear Efimov scenario for a three-body system that consists of two bosons and one distinguishable particle with positive intraspecies scattering lengths. The three-body parameter at the three-body scattering threshold and the scaling factor between consecutive Efimov resonances are found to be controlled by the scattering length between the two bosons, approximately independent of short-range physics. We observe two excited-state Efimov resonances in the three-body recombination spectra of an ultracold mixture of fermionic ^{6}Li and bosonic ^{133}Cs atoms close to a Li-Cs Feshbach resonance, where the Cs-Cs interaction is positive. Deviation of the obtained scaling factor of 4.0(3) from the universal prediction of 4.9 and the absence of the ground state Efimov resonance shed new light on the interpretation of the universality and the discrete scaling behavior of heteronuclear Efimov physics.
The three-body parameter (3BP) ${a}_{\ensuremath{-}}^{(1)}$ is crucial for understanding Efimov physics, and a universal 3BP has been shown in experiments and theory in ultracold homonuclear gases. The 3BP of heteronuclear systems has been predicted to possess much richer properties than its homonuclear counterparts due to the larger parameter space. In this work, we investigate the universal properties of ${a}_{\ensuremath{-}}^{(1)}$ for heavy-heavy-light (HHL) systems with a negative intraspecies scattering length aHH{a}_{HH}aHH​. We find that ${a}_{\ensuremath{-}}^{(1)}$ follows a universal behavior determined by the van der Waals (vdW) interaction and the mass ratio. A linear fit of ${a}_{\ensuremath{-}}^{(1)}$ for large ∣aHH∣|{a}_{HH}|∣aHH​∣ leads to a simple formula, which gives the general dependence of ${a}_{\ensuremath{-}}^{(1)}$ on the mass ratio and the vdW length rvdW{r}_{vdW}rvdW​. In a special case, when the two heavy atoms are in resonance, ${a}_{\ensuremath{-}}^{(1)}$ is approximately constant: ${a}_{\ensuremath{-}}^{(1)}=\ensuremath{-}(6.3\ifmmode\pm\else\textpm\fi{}0.6){r}_{vdW,HL}$.
We study the three-body problem for both fermionic and bosonic cold-atom gases in a parabolic transverse trap of length scale ${a}_{\ensuremath{\perp}}$. For this quasi-one-dimensional (quasi-1D) problem, there is a two-body bound state (dimer) for any sign of the 3D scattering length aaa and a confinement-induced scattering resonance. The fermionic three-body problem is universal and characterized by two atom-dimer scattering lengths aad{a}_{\mathit{ad}}aad​ and bad{b}_{\mathit{ad}}bad​. In the tightly bound ``dimer limit'' ${a}_{\ensuremath{\perp}}∕a\ensuremath{\rightarrow}\ensuremath{\infty}$, we find bad=0{b}_{\mathit{ad}}=0bad​=0 and aad{a}_{\mathit{ad}}aad​ is linked to the 3D atom-dimer scattering length. In the weakly bound ``BCS limit'' ${a}_{\ensuremath{\perp}}∕a\ensuremath{\rightarrow}\ensuremath{-}\ensuremath{\infty}$, a connection to the Bethe ansatz is established, which allows for exact results. The full crossover is obtained numerically. The bosonic three-body problem, however, is nonuniversal: aad{a}_{\mathit{ad}}aad​ and bad{b}_{\mathit{ad}}bad​ depend both on ${a}_{\ensuremath{\perp}}∕a$ and on a parameter R∗{R}^{*}R∗ related to the sharpness of the resonance. Scattering solutions are qualitatively similar to fermionic ones. We predict the existence of a single confinement-induced three-body bound state (trimer) for bosons.
We consider collisional properties of weakly bound heteronuclear molecules (dimers) formed in a two-species mixture of atoms with a large mass difference. We focus on dimers containing light fermionic atoms as they manifest collisional stability due to an effective dimer-dimer repulsion originating from the exchange of the light atoms. In order to solve the dimer-dimer scattering problem we develop a theoretical approach, which provides a physically transparent and quantitative description of this four-atom system in terms of three- and two-body observables. We calculate the elastic scattering amplitude and the rates of inelastic processes such as the trimer formation and the relaxation of dimers into deeply bound molecular states. Irrespective of whether the heavy atoms are bosons or fermions, the inelastic rate can be significantly lower than the rate of elastic collisions. Moreover, the measurement of the inelastic rate which is a four-body observable, can be an efficient and precise tool for determining three-body observables such as the three-body parameter, positions of Efimov states, and their lifetimes.