We present the experimental apparatus enabling the observation of the heteronuclear Efimov effect in an optically trapped ultracold mixture of ^6 Li- ^133 Cs with high-resolution control of the interactions. A compact double-species Zeeman slower consisting of four interleaving helical coils allows for a fast-switching between two optimized configurations for either Li or Cs and provides an efficient sequential loading into their respective MOTs. By means of a bichromatic optical trapping scheme based on species-selective trapping we prepare mixtures down to 100 nK of 1× 10^4 Cs atoms and 7× 10^3 Li atoms. Highly stable magnetic fields allow high-resolution atom-loss spectroscopy and enable to resolve splitting in the loss feature of a few tens of milligauss. These features allowed for a detailed study of the Efimov effect.

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 report evidence for spin-rotation coupling in $p$-wave ($N=1$) Feshbach resonances in an ultracold mixture of fermionic $^6$Li and bosonic $^{133}$Cs lifting the commonly observed degeneracy of states with $m_N=\pm1$. By employing magnetic field dependent atom-loss we find a triplet structure of the states with different projections of the pair-rotation angular momentum $N=1$ on the external magnetic field. Comparison with coupled-channel calculations yields a spin-rotation coupling parameter $|\gamma|=0.566(50)\times10^{-3}$, which includes contributions from both spin-spin and spin-rotation interactions at small internuclear distances. The existence of a non-negligible spin-rotation splitting may have consequences for future classifications of $p$-wave superfluid phases in spin-polarized fermions.

We measure higher partial wave Feshbach resonances in an ultracold mixture of fermionic ^6Li and bosonic ^133Cs by magnetic field dependent atom-loss spectroscopy. For the p-wave Feshbach resonances we observe triplet structures corresponding to different projections of the pair rotation angular momentum onto the external magnetic field axis. We attribute the splittings to the spin-spin and spin-rotation couplings by modelling the observation using a full coupled-channel calculation. Comparison with an oversimplified model, estimating the spin-rotation coupling by describing the weakly bound close-channel molecular state with the perturbative multipole expansion, reveals the significant contribution of the molecular wavefunction at short internuclear distances. Our findings highlight the potential of Feshbach resonances in providing precise information on short- and intermediate-range molecular couplings and wavefunctions. The observed d-wave Feshbach resonances allow us to refine the LiCs singlet and triplet ground-state molecular potential curves at large internuclear separations.

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 $^{133}$Cs and fermionic $^6$Li 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.

In this chapter we investigate binary scattering properties of an ultracold mixture of Li and Cs atoms, on which the further exploration of few-body effects throughout the rest of this thesis is based. We start by briefly reiterating basic theoretical concepts of low-energy scattering. It is followed by a description of a typical experimental approach for producing an ultracold mixture of Li and Cs atomic gases. Finally, we present pioneering measurements of weakly bound LiCs Feshbach dimers and obtain LiCs singlet and triplet molecular potential curves with unprecedented accuracy with the help of a coupled-channels calculation. These results provide with currently the most complete knowledge of Li-Cs low-energy scattering properties and Feshbach resonances.

In this chapter we investigate departures from the universal behavior of weakly-bound LiCsCs three-body states due to finite-range effects in the heteronuclear Efimov scenario. The presented Born-Oppenheimer model illuminates the important role of finite-range physics in the heavy-heavy-light system with intuitive clarity. In the following experiments we realize the Li-Cs-Cs Efimov scenario with positive Cs-Cs scattering length for the first time, in this way pioneering the understanding of its influence on the three-body physics. Surprisingly, the resulting Efimov states are almost independent of molecular forces that govern chemical binding of atoms into molecules—the binding of the three atoms is purely quantum-mechanical and the three-body system becomes universal. Finally, we model two-body interactions between individual atoms by van der Waals tails of molecular potentials, and explain the previously observed deviations from the universal behavior.

This chapter investigates the universal behavior of weakly-bound LiCsCs three-body states near a scattering resonance in the s-wave regime, often called the Efimov scenario. We start with a short phenomenological introduction of Efimov physics and follow it up by a detailed mathematical description in the hyperspherical framework. The Efimov effect and its properties emerge naturally as a direct consequence of an effective $$ -1/R^2 $$ potential. Using an improved experimental approach for the preparation of an ultracold Cs-Li mixture, we observe a series of three consecutive Li-Cs-Cs Efimov resonances for the first time. Finally we compare these results with the universal theory and find both—universal behavior and deviations from it.

TheEfimov scenario is a universal three-body effect addressing many areas of modern quantum physics. It plays an important role in the transition between fewand many-body physics and has enabled important breakthroughs in the understanding of the universal few-body theory. We review the basic concepts of the Efimov scenario with specific emphasis on the similarities and differences between homonuclear and heteronuclear systems. In the latter scenario, the existence of a second, independently tunable interaction parameter enables novel few-body phenomena that are universal and have no counterexamples in the homonuclear case. We discuss recent experimental approaches using ultracold atomic gases with magnetically tunable interactions and elucidate the role of short-range interactions in the emergence of universal and non-universal behavior.

We study Efimov resonances via three-body loss in an ultracold two-component gas of fermionic $^{6}\mathrm{Li}$ and bosonic $^{133}\mathrm{Cs}$ atoms close to a Feshbach resonance at 843 G, extending results reported previously [Pires et al., Phys. Rev. Lett. 112, 250404 (2014)] to temperatures around 120 nK. The experimental scheme for reaching lower temperatures is based upon compensating the gravity-induced spatial separation of the mass-imbalanced gases with bichromatic optical dipole traps. We observe the first and second excited Li-Cs-Cs Efimov resonance in the magnetic field dependence of the three-body event rate constant, in good agreement with the universal zero-range theory at finite temperature [Petrov and Werner, Phys. Rev. A 92, 022704 (2015)]. Deviations are found for the Efimov ground state, and the inelasticity parameter $\ensuremath{\eta}$ is found to be significantly larger than those for single-species systems.

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 Efimov scenario is a universal three-body effect addressing many areas of modern quantum physics.It plays an important role in the transition between few- and many-body physics and has enabled important breakthroughs in the understanding of the universal few-body theory.We review the basic concepts of the Efimov scenario with specific emphasis on the similarities and differences between homonuclear and heteronuclear systems.In the latter scenario,the existence of a second,independently tunable interaction parameter enables novel few-body phenomena that are universal and have no counterexamples in the homonuclear case.We discuss recent experimental approaches using ultracold atomic gases with magnetically tunable interactions and elucidate the role of short-range interactions in the emergence of universal and non-universal behavior.

We study the interspecies scattering properties of ultracold Li–Cs mixtures in their two energetically lowest spin channels in the magnetic field range between 800 and 1000 G. Close to two broad Feshbach resonances (FR) we create weakly bound LiCs dimers by radio-frequency association and measure the dependence of their binding energy on the external magnetic field strength. Based on the binding energies and complementary atom loss spectroscopy of three other Li–Cs s-wave FRs we construct precise molecular singlet and triplet electronic ground state potentials using a coupled-channels calculation. We extract the Li–Cs interspecies scattering length as a function of the external field and obtain almost a ten-fold improvement in the precision of the values for the pole positions and widths of the s-wave FRs as compared to our previous work (Pires et al 2014 Phys. Rev. Lett. 112 250404). We discuss implications on the Efimov scenario and the universal geometric scaling for LiCsCs trimers.

We observe two consecutive heteronuclear Efimov resonances in an ultracold Li-Cs mixture by measuring three-body loss coefficients as a function of magnetic field near a Feshbach resonance. The first resonance is detected at a scattering length of a_((0))=-320(10)a_((0)), corresponding to ∼7(∼3) times the Li-Cs (Cs-Cs) van der Waals range. The second resonance appears at 5.8(1.0)a_((0)), close to the unitarity-limited regime at the sample temperature of 450 nK. Indication of a third resonance is found in the atom loss spectra. The scaling of the resonance positions is close to the predicted universal scaling value of 4.9 for zero temperature. Deviations from universality might be caused by finite-range and temperature effects, as well as magnetic field-dependent Cs-Cs interactions.

We provide a comprehensive comparison of a coupled channels calculation, the asymptotic bound state model (ABM), and the multichannel quantum defect theory (MQDT). Quantitative results for $^6$Li -$^{133}$Cs are presented and compared to previously measured $^6$Li -$^{133}$Cs Feshbach resonances (FRs) [M. Repp et al., Phys. Rev. A 87 010701(R) (2013)]. We demonstrate how the accuracy of the ABM can be stepwise improved by including magnetic dipole-dipole interactions and coupling to a non-dominant virtual state. We present a MQDT calculation, where magnetic dipole-dipole and second order spin-orbit interactions are included. A frame transformation formalism is introduced, which allows the assignment of measured FRs with only three parameters. All three models achieve a total rms error of < 1G on the observed FRs. We critically compare the different models in view of the accuracy for the description of FRs and the required input parameters for the calculations.

We report on the observation of 19 interspecies Feshbach resonances in an optically trapped ultracold Bose-Fermi mixture of Cs-133 and Li-6 in the two energetically lowest spin states. We assign the resonances to s- and p-wave molecular channels by a coupled-channels calculation, resulting in an accurate determination of LiCs ground-state potentials. Fits of the resonance position based on the undressed asymptotic bound state model do not provide the same level of accuracy as the coupled-channels calculation. Several broad s-wave resonances provide prospects to create fermionic LiCs molecules with a large dipole moment via Feshbach association followed by stimulated Raman passage. Two of the s-wave resonances overlap with a zero crossing of the Cs scattering length, which offers prospects for the investigation of polarons in an ultracold Li-Cs mixture. DOI: 10.1103/PhysRevA.87.010701

We report on the observation of 19 interspecies Feshbach resonances in an optically trapped ultracold Bose-Fermi mixture of ${}^{133}\text{Cs}$ and ${}^{6}\text{Li}$ in the two energetically lowest spin states. We assign the resonances to $s$- and $p$-wave molecular channels by a coupled-channels calculation, resulting in an accurate determination of LiCs ground-state potentials. Fits of the resonance position based on the undressed asymptotic bound state model do not provide the same level of accuracy as the coupled-channels calculation. Several broad $s$-wave resonances provide prospects to create fermionic LiCs molecules with a large dipole moment via Feshbach association followed by stimulated Raman passage. Two of the $s$-wave resonances overlap with a zero crossing of the Cs scattering length, which offers prospects for the investigation of polarons in an ultracold Li-Cs mixture.

We revisit transit time broadening for one of the typical experiment designs in molecular spectroscopy, that of a collimated supersonic beam of particles crossing a focused Gaussian laser beam. In particular, we consider a Doppler-free arrangement of a collimated supersonic beam of Na-2 molecules crossing two counterpropagating laser beams that excite a two-photon transition in a three-level ladder scheme. We propose an analytical two-level model with a virtual intermediate level to show that the excitation line shape is described by a Voigt profile and provide the validity range of this model with respect to significant experimental parameters. The model also shows that line broadening due to the curvature of laser field wave fronts on the particle beam path is exactly compensated by increased transit time of particles farther away from the beam axis, such that the broadening is determined solely by the size of the laser beam waist. The analytical model is validated by comparing it with numerical simulations of density-matrix equations of motion using a split propagation technique and with experimental results.