Efimov Resonances Research Articles

Asymmetric Lineshapes of Efimov Resonances in Mass-Imbalanced Ultracold Gases

The resonant profile of the rate coefficient for three-body recombination into a shallow dimer is investigated for mass-imbalanced systems. In the low-energy limit, three atoms collide with zero-range interactions, in a regime where the scattering lengths of the heavy–heavy and the heavy–light subsystems are positive and negative, respectively. For this physical system, the adiabatic hyperspherical representation is combined with a fully semi-classical method and we show that the shallow dimer recombination spectra display an asymmetric lineshape that originates from the coexistence of Efimov resonances with Stückelberg interference minima. These asymmetric lineshapes are quantified utilizing the Fano profile formula. In particular, a closed-form expression is derived that describes the width of the corresponding Efimov resonances and the Fano lineshape asymmetry parameter q. The profile of Efimov resonances exhibits a q-reversal effect as the inter- and intra-species scattering lengths vary. In the case of a diverging asymmetry parameter, i.e., |q|→∞, we show that the Efimov resonances possess zero width and are fully decoupled from the three-body and atom–dimer continua, and the corresponding Efimov metastable states behave as bound levels.

Efimov resonances above four-boson threshold

Four-boson Efimov physics is well known in the negative energy regime but far less above the four-body breakup threshold. The part of this region with negative two-boson scattering length is studied solving rigorous four-particle scattering equations for transition operators in the momentum space. Moving away from the unitary limit the Efimov tetramers evolve from unstable bound states into resonances. Their energies and widths are studied as functions of the two-boson scattering length; a universal behavior is established and given in a dimensionless representation. The Efimov tetramers have finite width in the whole regime; they broaden rapidly in the resonance regime but remain narrower than the associated trimer. The resonant behavior is most clearly seen in the four-particle recombination rate.

Role of the intraspecies scattering length in the Efimov scenario with large mass difference

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.

Testing universality of Efimov physics across broad and narrow Feshbach resonances

Efimov physics is a universal phenomenon arising in quantum three-body systems. For systems with resonant two-body interactions, Efimov predicted an infinite series of three-body bound states with geometric scaling symmetry. These Efimov states were first observed in cold Cs atoms and have since been reported in a variety of atomic systems. While theories predict non-universal behavior for narrow Feshbach resonances, experiments on Efimov resonances are so far consistent with predictions based on universal theories. Here we directly compare the Efimov spectra in a $^6$Li-$^{133}$Cs mixture near two Feshbach resonances which are very different in their resonance strengths but otherwise almost identical. Our result shows a clear dependence of the Efimov resonance positions on Feshbach resonance strength and a clear departure from the universal prediction for the narrow Feshbach resonance.

Isotopic Shift of Atom-Dimer Efimov Resonances in K-Rb Mixtures: Critical Effect of Multichannel Feshbach Physics.

Multichannel Efimov physics is investigated in ultracold heteronuclear admixtures of K and Rb atoms. We observe a shift in the scattering length where the first atom-dimer resonance appears in the ^{41}K-^{87}Rb system relative to the position of the previously observed atom-dimer resonance in the ^{40}K-^{87}Rb system. This shift is well explained by our calculations with a three-body model including van der Waals interactions, and, more importantly, multichannel spinor physics. With only minor differences in the atomic masses of the admixtures, the shift in the atom-dimer resonance positions can be cleanly ascribed to the isolated and overlapping Feshbach resonances in the ^{40}K-^{87}Rb and ^{41}K-^{87}Rb systems, respectively. Our study demonstrates the role of multichannel Feshbach physics in determining Efimov resonances in heteronuclear three-body systems.

Universal Three-Body Physics in Ultracold KRb Mixtures.

Ultracold atomic gases have recently become a driving force in few-body physics due to the observation of the Efimov effect. While initially observed in equal mass systems, one expects even richer few-body physics in the heteronuclear case. In previous experiments with ultracold mixtures of potassium and rubidium, an unexpected nonuniversal behavior of Efimov resonances was observed. In contrast, we measure the scattering length dependent three-body recombination coefficient in ultracold heteronuclear mixtures of ^{39}K-^{87}Rb and ^{41}K-^{87}Rb and do not observe any signatures of Efimov resonances for accessible scattering lengths in either mixture. Our results show good agreement with our theoretical model for the scattering dependent three-body recombination coefficient and reestablish universality across isotopic mixtures.

Heteronuclear Efimov Scenario with Positive 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.

Heteronuclear Efimov resonances in ultracold quantum gases

Abstract 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.

Universal three-body recombination and Efimov resonances in an ultracold Li-Cs mixture

We study Efimov resonances via three-body loss in an ultracold two-component gas of fermionic $^6$Li and bosonic $^{133}$Cs atoms close to a Feshbach resonance at 843~G, extending results reported previously [Pires \textit{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 $\eta$ is found to be significantly larger than those for single-species systems.

Finite-temperature effects on a triatomic Efimov resonance in ultracold cesium

We report a thorough investigation of finite-temperature effects on three-body recombination near a triatomic Efimov resonance in an ultracold gas of cesium atoms. Our measurements cover a wide range from a near-ideal realization of the zero-temperature limit to a strongly temperature-dominated regime. The experimental results are analyzed within a recently introduced theoretical model based on a universal zero-range theory. The temperature-induced shift of the resonance reveals a contribution that points to an energy-dependence of the three-body parameter. We interpret this contribution in terms of the finite range of the van der Waals interaction in real atomic systems and we quantify it in an empirical way based on length scale arguments. A universal character of the corresponding resonance shift is suggested by observations related to other Efimov resonances and the comparison with a theoretical finite-temperature approach that explicitly takes the van der Waals interaction into account. Our findings are of importance for the precise determination of Efimov resonance positions from experiments at finite temperatures.

Geometric scaling of Efimov states in a ⁶Li-¹³³Cs mixture.

In few-body physics, Efimov states are an infinite series of three-body bound states that obey universal discrete scaling symmetry when pairwise interactions are resonantly enhanced. Despite abundant reports of Efimov states in recent cold atom experiments, direct observation of the discrete scaling symmetry remains an elusive goal. Here we report the observation of three consecutive Efimov resonances in a heteronuclear Li-Cs mixture near a broad interspecies Feshbach resonance. The positions of the resonances closely follow a geometric series 1, λ, λ². The observed scaling constant λ(exp)=4.9(4) is in good agreement with the predicted value of 4.88.

Generalized Efimov Scenario for Heavy-Light Mixtures

Motivated by recent experimental investigations of Cs-Cs-Li Efimov resonances, this work theoretically investigates the few-body properties of N-1 noninteracting identical heavy bosons, which interact with a light impurity through a large s-wave scattering length. For Cs-Cs-Cs-Li, we predict the existence of universal four-body states with energies E4(n,1) and E4(n,2), which are universally linked to the energy E3(n) of the nth Efimov trimer. For infinitely large (133)Cs-(6)Li and vanishing (133)Cs-(133)Cs scattering lengths, we find (E4(1,1)/E3(1))(1/2)≈1.51 and (E4(1,2)/E3(1))(1/2)≈1.01. The (133)Cs-(6)Li scattering lengths at which these states merge with the four-atom threshold, the dependence of these energy ratios on the mass ratio between the heavy and light atoms, and selected aspects of the generalized Efimov scenario for N>4 are also discussed. Possible implications of our results for ongoing cold atom experiments are presented.

Three-body parameter for Efimov states inLi6

We present a state-of-the-art reanalysis of experimental results on Efimov resonances in the three-fermion system of $^6$Li. We discuss different definitions of the 3-body parameter (3BP) for Efimov states, and adopt a definition that excludes effects due to deviations from universal scaling for low-lying states. We develop a finite-temperature model for the case of three distinguishable fermions and apply it to the excited-state Efimov resonance to obtain the most accurate determination to date of the 3BP in an atomic three-body system. Our analysis of ground-state Efimov resonances in the same system yields values for the three-body parameter that are consistent with the excited-state result. Recent work has suggested that the reduced 3BP for atomic systems is a near-universal quantity, almost independent of the particular atom involved. However, the value of the 3BP obtained for $^6$Li is significantly ($\sim 20$%) different from that previously obtained from the excited-state resonance in Cs. The difference between these values poses a challenge for theory.

Observation of Efimov resonances in a mixture with extreme mass imbalance.

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.

Tests of universal three-body physics in an ultracold bose-fermi mixture.

Recent measurements of Efimov resonances for a number of ultracold atom species have revealed an unexpected universality, in which three-body scattering properties are determined by the van der Waals length of the two-body interaction potential. To investigate whether this universality extends to heteronuclear mixtures, we measure loss rate coefficients in an ultracold trapped gas of 40K and 87Rb atoms. We find an Efimov-like resonance in the rate of inelastic collisions between 40K87Rb Feshbach molecules and 87Rb atoms. However, we do not observe any Efimov-related resonances in the rates of inelastic collisions between three atoms. These observations are compared to previous measurements by the LENS group of Efimov resonances in a 41K and 87Rb mixture as well as to recent predictions.

Efimov Resonances in Ultracold Quantum Gases

Ultracold atomic gases have developed into prime systems for experimental studies of Efimov three-body physics and related few-body phenomena, which occur in the universal regime of resonant interactions. In the last few years, many important breakthroughs have been achieved, confirming basic predictions of universal few-body theory and deepening our understanding of such systems. We review the basic ideas along with the fast experimental developments of the field, focussing on ultracold cesium gases as a well-investigated model system. Triatomic Efimov resonances, atom-dimer Efimov resonances, and related four-body resonances are discussed as central observables. We also present some new observations of such resonances, supporting and complementing the set of available data.

Universality of the Three-Body Parameter for Efimov States in Ultracold Cesium

We report on the observation of triatomic Efimov resonances in an ultracold gas of cesium atoms. Exploiting the wide tunability of interactions resulting from three broad Feshbach resonances in the same spin channel, we measure magnetic-field dependent three-body recombination loss. The positions of the loss resonances yield corresponding values for the three-body parameter, which in universal few-body physics is required to describe three-body phenomena and, in particular, to fix the spectrum of Efimov states. Our observations show a robust universal behavior with a three-body parameter that stays essentially constant.

Study of Efimov physics in two nuclear-spin sublevels of 7Li

Efimov physics in two nuclear-spin sublevels of bosonic lithium is studied and it is shown that the positions and widths of recombination minima and Efimov resonances are identical for both states within the experimental errors which indicates that the short-range physics is nuclear-spin independent. We also find that the Efimov features are universally related across Feshbach resonances. These results crucially depend on careful mapping between the scattering length and the applied magnetic field which we achieve by characterization of the two broad Feshbach resonances in the different states by means of rf-spectroscopy of weakly bound molecules. By fitting the binding energies numerically with a coupled channels calculation we precisely determine the absolute positions of the Feshbach resonances and the values of the singlet and triplet scattering lengths.

Nuclear-Spin-Independent Short-Range Three-Body Physics in Ultracold Atoms

We investigate three-body recombination loss across a Feshbach resonance in a gas of ultracold 7Li atoms prepared in the absolute ground state and perform a comparison with previously reported results of a different nuclear-spin state [N. Gross, Phys. Rev. Lett. 103, 163202 (2009)]. We extend the previously reported universality in three-body recombination loss across a Feshbach resonance to the absolute ground state. We show that the positions and widths of recombination minima and Efimov resonances are identical for both states which indicates that the short-range physics is nuclear-spin independent.

Erratum: Observation of Heteronuclear Atomic Efimov Resonances [Phys. Rev. Lett.103, 043201 (2009)

Erratum: Observation of Heteronuclear Atomic Efimov Resonances [Phys. Rev. Lett.<b>103</b>, 043201 (2009)