Session U7: Few-body Physics

Atom Loss Resonances in a Bose-Einstein Condensate

Atom loss resonances in ultracold trapped atoms have been observed at scattering lengths near atom-dimer resonances, at which Efimov trimers cross the atom-dimer threshold, and near 2-dimer resonances, at which universal tetramers cross the dimer-dimer threshold. We propose a new mechanism for these loss resonances in a Bose-Einstein condensate of atoms. The process of creating a large scattering length, at which the atom loss rate is measured, can form a condensate of shallow dimers. The coexisting atom and dimer condensates can be described by a low-energy effective field theory with universal coefficients that are determined by matching exact results from few-body physics. The classical field equations for the atom and dimer condensates predict narrow enhancements in the atom loss rate near atom-dimer resonances and near 2-dimer resonances from inelastic dimer collisions.   

Universal three-body recombination via resonant d-wave interactions

For a system of three identical bosons interacting via short-range forces, when two of the atoms are about to form a two-body $s$-wave dimer, the Efimov effect takes place leading to the formation of an infinite number of three-body (Efimov) states. The present study focuses on a generalized version of this Efimov scenario, where two of the atoms are about to form a two-body $d$-wave dimer, resulting in strong $d$-wave interactions. Our results demonstrate that a single universal three-body state associated with the $d$-wave dimer is also formed near the three-body break-up threshold. Such a universal three-body state is signaled by an enhancement of the three-body recombination rate.   

Three-body recombination in a quasi-two-dimensional quantum gas

Collisional properties of interacting particles can dramatically change when the dimensionality of the system is reduced. One intriguing example is the disappearance of the weakly bound trimers known as Efimov states in two dimensions. Many open questions remain about the details of the crossover from three to two dimensions and how the Efimov-related three-body recombination losses are affected. We use ultracold cesium atoms trapped tightly in a harmonic potential along one spatial direction to realize a quasi-two-dimensional system with tunable confinement and tunable interactions. In our latest results, we succeed to trace a smooth transition of the three-body recombination rate from a three-dimensional to a nearly two-dimensional system, in good agreement with recent theoretical models.   

Origin of the Universal Three-body Parameter in Atomic Efimov Physic

Several experiments [1] with different kinds of ultra-cold atoms have revealed that the three-body parameter that fixes the Efimov spectrum of few-atom systems near broad Feshbach resonances is universally determined by the atoms' van der Waals length. Using model potential calculations we find that the three-body parameter originates from a deformation of the three-atom system due to universal two-body correlations at separations on the order of the van der Waals length scale [3]. This simple physical picture is consistent with the universality of the three-body parameter observed in the experiments [1], as well as previous numerical calculations [2]. It explains why the low-energy physics of three bosonic atoms near a broad resonance is solely determined by their two-body parameters.\\[4pt] [1] F. Ferlaino, A. Zenesini, M. Berninger, B. Huang, H.-C. N\"agerl, R. Grimm, Few-Body Syst 51: 113-133 (2011).\\[0pt] [2] J.Wang, J.P.D'Incao, B.D.Esry, and C.H.Greene, Phys. Rev. Lett. 108, 263001 (2012).\\[0pt] [3] P. Naidon, S. Endo, M. Ueda, arXiv:1208.3912 (2012).   

Two-dimensional Bose gases near resonance: Competing two and three body interactions

We report in this Letter the results of our investigation of 2D Bose gases beyond the dilute limit emphasizing the role played by three-body scattering events. We demonstrate that a competition between three-body attractive interactions and two-body repulsive forces results in the chemical potential of 2D Bose gases to exhibit a maximum at a critical scattering length beyond which these quantum gases possess a negative compressibility. For larger scattering lengths, the increasingly prominent role played by three-body attractive interactions leads to an onset instability at a second critical value. The three-body effects studied here are universal, fully characterized by the effective 2D scattering length $a_{2D}$ (or the size of the 2D bound states) and are, in comparison to the 3D case, independent of three-body ultraviolet physics. We find, within our approach, the ratios of the contribution to the chemical potential due to three-body interactions to the one due to two-body to be 0.27 near the maximum of the chemical potential and 0.73 in the vicinity of the onset instability.   

Scattering properties of three ultracold atoms in a cylindrical waveguide geometry

In the ultracold regime the de Broglie wavelength is much larger than the van der Waals length, and the true atom-atom potential can be replaced by a simple model potential. Using a short-range Gaussian interaction model, the scattering properties of three atoms in a cylindrical waveguide geometry are analyzed using two independent and complementary approaches: the finite element method and an explicitly correlated Gaussian basis set. We integrate over the coordinates associated with the tight confinement direction and calculate the effective potential curves as a function of the hyperradius, which is defined in terms of the particle coordinates parallel to the axis of the waveguide. The scattering properties are determined by solving the coupled set of hyperradial equations.   

Non-universal bound states of two identical heavy fermions and one light particle

We study a system of two identical heavy fermions of mass M and light particle of mass m. The interspecies interaction is modeled using a short-range two-body potential with positive $s$-wave scattering length. We impose a short-range boundary condition on the logarithmic derivative of the hyperradial wavefunction and show that, in the regime where Efimov states are absent, a non-universal three-body state ``cuts through'' the universal three-body states previously described by Kartavtsev and Malykh [O. I. Kartavtsev and A. V. Malykh, J. Phys. B 40, 1429 (2007)]. We study the effect of the non-universal state on the behavior of the universal states and use a simple quantum defect theory, utilizing hyperspherical coordinates, to explain the existence of the non-universal state. An empirical two-state model is employed to quantify the coupling of the non-universal state to the universal states.   

Three-body parameter for ultracold atoms

The recent experimental observations of a universal three-body parameter near broad Feshbach resonances in ultracold gases have attracted great interests in the study of the fundamental physics behind. By employing multichannel two-body interactions, we numerically study the extent of the universality in the three-body parameter for atoms near Feshbach resonances with arbitrary widths. In particular, we show the role of the resonance width and the background scattering length in determining the three-body parameter and the general scaling of three-body recombination. Previous results based on the the effective-range modeling of Feshbach resonance parameters are also compared with our present study. By varying the background state in the open channel and the resonant state in the closed channel, we predict the range of the resonance parameters where the three-body parameter and/or the three-body recombination rate should be universal. The knowledge of such universality will greatly benefit the experimental manipulations of ultracold atoms near an arbitrary Feshbach resonance.   

Optical control of Efimov state properties via blue-shielding

In this work we explore the use of optical field to control fundamental properties of Efimov states. In the regime in which an external laser field is blue-detuned from an $S$-$P$ transition, the repulsive interaction between ground ($S$) and excited ($P$) atoms can be used in order to shield the short-range effects in the three-body physics. As a result, one could expect an improvement of the lifetime of Efimov states as well as collision properties involving three ground state atoms. We develop a hyperspherical adiabatic representation in combination with the Floquet formalism, leading to a clear physical picture of the relevant atomic processes.   

Universal Relation for the Inelastic Two-Atom Loss Rate

For a strongly-interacting system consisting of particles that interact through a large scattering length, there are universal relations that express many of its central properties in terms of the contact, which measures the number of pairs with small separations. We use the operator product expansion of quantum field theory to derive the universal relation for the inelastic 2-body loss rate, which is proportional to the contact. We verify the universal relation explicitly by direct calculations in the low-density limit as a function of temperature. This universal relation can be tested experimentally using ultracold quantum gases of atoms in hyperfine states that have an inelastic spin-relaxation channel.