We study Efimov physics of three identical bosons with pairwise multichannel interactions for Feshbach resonances of adjustable width. We find that the two-body multichannel nature of the interaction can affect the universal three-body spectrum, especially for resonances of intermediate width. The shifts in this universal spectrum are caused by trimer states in the closed interaction channels that couple to the universal Efimov states. However, in the narrow resonance limit we find that the Efimov spectrum is set by the resonance width parameter $r^*$ only independent of the interaction potential considered. In the broad resonance limit all excited Efimov trimer energies approach the ones from the corresponding single-channel system for the scenarios investigated.
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 nea…
In this Letter we study the effect of Pauli blocking on the Efimov states in a quantum Fermi gas and illustrate that the universal Efimov potential is altered at large distances. We obtain the universal spectrum flow of Efimov trimers when the Fermi density is varied and further consider the effect of scattering of trimers by the Fermi sea. We argue that the universal flow is robust against fluctuating particle-hole pairs that result in an infrared catastrophe in impurity problems.
We have measured the binding energy of $^7$Li Feshbach molecules deep into the non-universal regime by associating free atoms in a Bose-Einstein condensate by modulating the magnetic field. We extract the scattering length from these measurements, correcting for non-universal short-range effects using several different methods. We find that field-dependent effective range corrections agree well with the data. With this more precise determination of the scattering length vs. field we reanalyze our previous data on the location of atom loss features produced by the Efimov effect \cite{PollackSci…
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…
Near a Feshbach resonance, the two-body scattering length can assume any value. When it approaches zero, the next-order term given by the effective range is known to diverge. We consider the question of whether this divergence (and the vanishing of the scattering length) is accompanied by an anomalous solution of the three-boson Schrödinger equation similar to the one found at infinite scattering length by Efimov. Within a simple zero-range model, we find no such solutions, and conclude that higher-order terms do not support Efimov physics.
We study the quantum three-body free space problem of two same-spin-state fermions of mass $m$ interacting with a different particle of mass $M$, on an infinitely narrow Feshbach resonance with infinite s-wave scattering length. This problem is made interesting by the existence of a tunable parameter, the mass ratio $α=m/M$. By a combination of analytical and numerical techniques, we obtain a detailed picture of the spectrum of three-body bound states, within {\sl each} sector of fixed total angular momentum $l$. For $α$ increasing from 0, we find that the trimer states first appear at the $l$…
The 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 the van der Waals interactions, and, more importantly, the multichannel spinor physics. With only minor difference in the atomic masses of the admixtures, the shift in the atom-dimer …
We study three-atom inelastic scattering in ultracold \textsuperscript{39}K near a Feshbach resonance of intermediate coupling strength. The non-universal character of such resonance leads to an abnormally large Efimov absolute length scale and a relatively small effective range $r_e$, allowing the features of the \textsuperscript{39}K Efimov spectrum to be better isolated from the short-range physics. Meticulous characterization of and correction for finite temperature effects ensure high accuracy on the measurements of these features at large-magnitude scattering lengths. For a single Feshba…
Using a combination of bound-state spectroscopy and loss spectroscopy, we pinpoint eight intrastate Feshbach resonances in $^{39}$K, as well as six previously unexplored interstate ones. We also perform a detailed characterization of four of the intrastate resonances and two of the interstate ones. We carry out coupled-channel scattering calculations and find good agreement with experiment. The combination of experiment and theory provides a faithful map of the scattering length $a$ and permits precision measurements of the signatures of Efimov physics across four intermediate-strength resonan…
A powerful experimental technique to study Efimov physics at positive scattering lengths is demonstrated. We use the Feshbach dimers as a local reference for Efimov trimers by creating a coherent superposition of both states. Measurement of its coherent evolution provides information on the binding energy of the trimers with unprecedented precision and yields access to previously inaccessible parameters of the system such as the Efimov trimers' lifetime and the elastic processes between atoms and the constituents of the superposition state. We develop a comprehensive data analysis suitable for…
We measure the critical scattering length for the appearance of the first three-body bound state, or Efimov three-body parameter, at seven different Feshbach resonances in ultracold 39K atoms. We study both intermediate and narrow resonances, where the three-body spectrum is expected to be determined by the non-universal coupling of two scattering channels. We observe instead approximately the same universal relation of the three-body parameter with the two-body van der Waals radius already found for broader resonances, which can be modeled with a single channel. This unexpected observation su…
We calculate the spectrum of three-body Efimov bound states near a Feshbach resonance within a model which accounts both for the finite range of interactions and the presence of background scattering. The latter may be due to direct interactions in an open channel or a second overlapping Feshbach resonance. It is found that background scattering gives rise to substantial changes in the trimer spectrum as a function of the detuning away from a Feshbach resonance, in particular in the regime where the background channel supports Efimov states on its own. Compared to the situation with negligible…
In the vicinity of a narrow Feshbach resonances Efimov features are expected to be characterized by the resonance's properties rather than the van der Waals length of the interatomic potential. Although this theoretical prediction is well-established by now, it still lacks experimental confirmation. Here, we apply our recently developed three-channel model [Yudkin and Khaykovich, Phys. Rev. A 103, 063303 (2021)] to the experimental result obtained in a mass-imbalanced $^6$Li-$^{133}$Cs mixture in the vicinity of the narrowest resonance explored to date [Johansen at. al. Nat. Phys. 13, 731 (201…
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 G and 1000 G. Close to two broad Feshbach resonances we create weakly bound LiCs dimers by radio-frequency association and measure the dependence of the 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 Feshbach resonances we construct precise molecular singlet and triplet electronic ground state potentials using a coupled-channe…
While Efimov physics in ultracold atoms is usually modeled with an isolated Feshbach resonance many real world resonances appear in close vicinity to each other and are therefore overlapping. Here we derive a realistic model based on the mutual coupling of an open channel and two closed molecular channels while neglecting short-range physics as permitted by the narrow character of the considered resonances. The model is applied to three distinct scenarios with experimental relevance. We show that the effect of overlapping resonances is manifested most strikingly at a narrow resonance in whose …
We provide an exact solution of the Efimov spectrum in ultracold gases within the standard two-channel model for Feshbach resonances. It is shown that the finite range in the Feshbach coupling makes the introduction of an adjustable three-body parameter obsolete. The solution explains the empirical relation between the scattering length a_- where the first Efimov state appears at the atom threshold and the van der Waals length l_vdw for open channel dominated resonances. There is a continuous crossover to the closed channel dominated limit, where the scale in the energy level diagram as a func…
We present a multichannel quantum-defect theory for magnetic Feshbach resonances in the interaction of two heteronuclear group I atoms. The theory provides a unified and a uniform description of resonances in all partial waves, and enables the characterization of large number of resonances in terms of very few parameters. For the sample system of $^6$Li$^{40}$K, we present descriptions of all resonances in $aa$, $ab$, and $ba$ channels, in partial waves $s$ ($l=0$) through $h$ ($l=5$), and in a magnetic field of 0 through 1000 Gauss. All resonances, including those in nonzero partial waves, ar…
Motivated by the prospect of observing Efimov and Bose polaron physics in ultracold mixtures of bosonic atoms with large mass imbalance, this work investigates the magnetic Feshbach resonances between $^{7}\text{Li}$ and $^{133}\text{Cs}$. The resonances are predicted at the 1 gauss level using the model of Pires et al. [Phys. Rev. A, 90, 012710] obtained from experimental observations of resonances between $^{6}\text{Li}$ and $^{133}\text{Cs}$. It is found that a few resonances in a practical range of magnetic field intensity could be used to tune the scattering length between $^{7}\text{Li}$…
We convert a strongly interacting ultracold Bose gas into a mixture of atoms and molecules by sweeping the interactions from resonant to weak. By analyzing the decay dynamics of the molecular gas, we show that in addition to Feshbach dimers it contains Efimov trimers. Typically around 8\% of the total atomic population is bound into trimers, identified by their density-independent lifetime of about 100~$μ$s. The lifetime of the Feshbach dimers shows a density dependence due to inelastic atom-dimer collisions, in agreement with theoretical calculations. We also vary the density of the gas acros…
Ultracold atomic gases are an important testing ground for understanding few-body physics. In particular, these systems enable a detailed study of the Efimov effect. We use ultracold $^{39}\mathrm{K}$ to investigate the temperature dependence of an Efimov resonance. The shape and position of the observed resonance are analyzed by employing an empirical fit, and universal finite-temperature zero-range theory. Both procedures suggest that the resonance position shifts towards lower absolute scattering lengths when approaching the zero-temperature limit. We extrapolate this shift to obtain an est…
We develop a full multichannel spin model in momentum space to investigate three-body recombination of identical alkali-metal atoms colliding in a magnetic field. The model combines the exact three-atom spin structure and realistic pairwise atom-atom interactions. By neglecting the interaction between two particles when the spectating particle is not in its initial spin state we arrive at an approximate model. With this approximate model we achieve excellent agreement with the recent precise measurement of the ground Efimov resonance position in potassium-39 close to 33.58 G [Chapurin $et$ $al…
Recent experiment has observed Feshbach resonances between alkaline and alkaline-earth atoms. These Feshbach resonances are insensitive to the nuclear spin of alkaline-earth atoms. Ultilizing this feature, we propose to take this system as a candidate to perform quantum simulation of the Kondo effect. An alkaline atom can form a molecule with an alkaline-earth atom with different nuclear spins, which plays the role of spin-exchange scattering responsible for the Kondo effect. Furthermore, we point out that the existence of three-body bound state and atom-molecule resonance due to the Efimov ef…
The "avalanche mechanism" has been used to relate Efimov trimer states to certain enhanced atom loss features observed in ultracold atom gas experiments. These atom loss features are argued to be a signature of resonant atom-molecule scattering that occurs when an Efimov trimer is degenerate with the atom-molecule scattering threshold. However, observation of these atom loss features has yet to be combined with the direct observation of atom-molecule resonant scattering for any particular atomic species. In addition, recent Monte-Carlo simulations were unable to reproduce a narrow loss feature…
We calculate shallow three-body bound states in the universal regime, defined by Efimov, with inclusion of both scattering length and effective range parameters. The universal spectrum is recovered for the least bound states, whereas for larger binding energies we find corrections to the universal scaling laws. We recover known results for broad Feshbach resonances with small effective range, whereas in the case of narrow resonances we find a distinct non-monotonic behavior of the threshold at which the lowest Efimov trimer merges with the three-body continuum. To address the issue of the phys…
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 W…
Recent measurements of Efimov resonances in 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 $^{40}$K and $^{87}$Rb atoms. We find an Efimov-like resonance in the rate of inelastic collisions between $^{40}$K$^{87}$Rb Feshbach molecules and $^{87}$Rb atoms. However, we do not observe any Efimov-related res…
Recent cold atom experiments report a surprising universal scaling of the first Efimov resonance position a_{-}^1 by the two-body van der Waals length r_{vdW}. The ratio C=-a_{-}^1/r_{vdW}=8.5~9.5 for identical particles appears to be a constant regardless of the atomic spin configuration, the Feshbach resonance employed to tune the scattering length, and even the atomic species, with K-39 being the only exception. This result indicates that the Efimov energy structure is insensitive to the details of the short range potential. We suggest that the universality results from the quantum reflecti…
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 $1$, $λ$, $λ^2$. The observed scaling constant $λ_…
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 st…
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 thre…
We discuss our recent observation of an atom-dimer Efimov resonance in an ultracold mixture of Cs atoms and Cs_2 Feshbach molecules [Nature Phys. 5, 227 (2009)]. We review our experimental procedure and present additional data involving a non-universal g-wave dimer state, to contrast our previous results on the universal s-wave dimer. We resolve a seeming discrepancy when quantitatively comparing our experimental findings with theoretical results from effective field theory.
We study the use of an optical Feshbach resonance to modify the p-wave interaction between ultracold polarized Yb-171 spin-1/2 fermions. A laser exciting two colliding atoms to the 1S_0 + 3P_1 channel can be detuned near a purely-long-range excited molecular bound state. Such an exotic molecule has an inner turning point far from the chemical binding region and thus three-body-recombination in the Feshbach resonance will be highly suppressed in contrast to that typically seen in a ground state p-wave magnetic Feshbach resonance. We calculate the excited molecular bound-state spectrum using a m…
We numerically study the problem of two fermions in a three dimensional optical lattice interacting via a zero-range Feshbach resonance, and display the dispersions of the bound states as a two-particle band structure with unique features compared to typical single-particle band structures. We show that the exact two-particle solutions of a projected Hamiltonian may be used to define an effective two-channel, few-band model for the low energy, low density physics of many fermions at arbitrary s-wave scattering length. Our method applies to resonances of any width, and can be adapted to multich…
High partial-wave ($l\ge2$) Feshbach resonance (FR) in an ultracold mixture of $^{85}$Rb-$^{87}$Rb atoms is investigated experimentally aided by a partial-wave insensitive analytic multichannel quantum-defect theory (MQDT). Two "broad" resonances from coupling between d-waves in both the open and closed channels are observed and characterized. One of them shows a fully resolved triplet structure with splitting ratio well explained by the perturbation to the closed channel due to interatomic spin-spin interaction. These tunable "broad" d-wave resonances, especially the one in the lowest-energy …
We report on the detection of extremely narrow Feshbach resonances by employing a Mott-insulating state for cesium atoms in a three-dimensional optical lattice. The Mott insulator protects the atomic ensemble from high background three-body losses in a magnetic field region where a broad Efimov resonance otherwise dominates the atom loss in bulk samples. Our technique reveals three ultra-narrow and previously unobserved Feshbach resonances in this region with widths below $\approx 10\,μ$G, measured via Landau-Zener-type molecule formation and confirmed by theoretical predictions. For comparati…
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…
We use a minimal zero-range model for describing the bound state spectrum of three-body states consisting of two Cesium and one Lithium atom. Using a broad Feshbach resonance model for the two-body interactions, we show that recent experimental data can be described surprisingly well for particular values of the three-body parameter that governs the short-range behavior of the atomic potentials and is outside the scope of the zero-range model. Studying the spectrum as a function of the three-body parameter suggests that the lowest state seen in experiment could be influenced by finite range co…
In this paper we discuss the recent discovery of the universality of the three-body parameter (3BP) from Efimov physics. This new result was identified by recent experimental observations in ultracold quantum gases where the value of the s-wave scattering length, $a=a_-$, at which the first Efimov resonance is created was found to be nearly the same for a range of atomic species --- if scaled as $a_-/r_{\rm vdW}$, where $r_{\rm vdW}$ is the van der Waals length. Here, we discuss some of the physical principles related to these observations that emerge from solving the three-body problem with v…
We use an effective-field-theory framework to analyze the Efimov effect in heteronuclear three-body systems consisting of two species of atoms with a large interspecies scattering length. In the leading-order description of this theory, various three-body observables in heteronuclear mixtures can be universally parameterized by one three-body parameter. We present the next-to-leading corrections, which include the effects of the finite interspecies effective range and the finite intraspecies scattering length, to various three-body observables. We show that only one additional three-body param…
We have analyzed our recently-measured three-body loss rate coefficient for a Bose-Einstein condensate of spin-polarized metastable triplet 4He atoms in terms of Efimov physics. The large value of the scattering length for these atoms, which provides access to the Efimov regime, arises from a nearby potential resonance. We find the loss coefficient to be consistent with the three-body parameter (3BP) found in alkali-metal experiments, where Feshbach resonances are used to tune the interaction. This provides new evidence for a universal 3BP, the first outside the group of alkali-metal elements.…
Under certain circumstances, three or more interacting particles may form bound states. While the general few-body problem is not analytically solvable, the so-called Efimov trimers appear for a system of three particles with resonant two-body interactions. The binding energies of these trimers are predicted to be universally connected to each other, independent of the microscopic details of the interaction. By exploiting a Feshbach resonance to widely tune the interactions between trapped ultracold lithium atoms, we find evidence for two universally connected Efimov trimers and their associat…
We observe new Feshbach resonances in ultracold mixtures of $^{85}$Rb and $^{87}$Rb atoms in the $^{85}$Rb$|2, +2\rangle$+$^{87}$Rb$|1, +1\rangle$ and $^{85}$Rb$|2, -2\rangle$+$^{87}$Rb$|1, -1\rangle$ scattering channels. The positions and properties of the resonances are predicted and characterized using the semi-analytic multichannel quantum-defect theory by Gao. Of particular interest, a number of broad entrance-channel dominated p-wave resonances are identified, implicating exciting opportunities for studying a variety of p-wave interaction dominated physics.
The Efimov effect can be induced by means of an external deformed one-body field that effectively reduces the allowed spatial dimensions to less than three. To understand this new mechanism, conceptually and practically, we employ a formulation using non-integer dimension, which is equivalent to the strength of an external oscillator field. The effect most clearly appears when the crucial two-body systems are unbound in three, but bound in two, dimensions. We discuss energy variation, conditions for occurrence, and number of Efimov states, as functions of the dimension. We use practical exampl…
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 $a_-^{(1)}=-320(10)~a_0$ corresponding to $\sim 7 $ ($\sim 3$) times the Li-Cs (Cs-Cs) van der Waals range. The second resonance appears at $5.8(1.0) a_-^{(1)}$ 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 t…
We explore the scattering properties of ultracold ground-state Cs atoms at magnetic fields between 450 G (45 mT) and 1000 G. We identify 17 new Feshbach resonances, including two very broad ones near 549 G and 787 G. We measure the binding energies of several different dimer states by magnetic field modulation spectroscopy. We use least-squares fitting to these experimental results, together with previous measurements at lower field, to determine a new 6-parameter model of the long-range interaction potential, designated M2012. Coupled-channels calculations using M2012 provide an accurate mapp…
Two-particle scattering in graphene is a multichannel problem, where the energies of the identical or opposite-helicity channels lie in disjoint energy segments. Due to the absence of Galilean invariance, these segments depend on the total momentum $Q$. The dispersion relations for the two opposite-helicity scattering channels are analogous to those of two one-dimensional tight-binding lattices with opposite dispersion relations, which are known to easily bind states at their edges. When an $s$-wave separable interaction potential is assumed, those bound states reveal themselves as three Feshb…
Feshbach resonances in ultracold collisions often result from an interplay between many collision channels. Simple two-channel models can be introduced to capture the basic features, but cannot fully reproduce the situation when several resonances from different closed channels contribute to the scattering process. Using the formalism of multichannel quantum defect theory we develop an analytical model of overlapping Feshbach resonances. We find a general formula for the variation of the scattering length with magnetic field in the vicinity of an arbitrary number of resonances, characterized b…
We perform precise studies of two- and three-body interactions near an intermediate-strength Feshbach resonance in $^{39}\mathrm{K}$ at $33.5820(14)\thinspace$G. Precise measurement of dimer binding energies, spanning three orders of magnitude, enables the construction of a complete two-body coupled-channel model for determination of the scattering lengths with an unprecedented low uncertainty. Utilizing an accurate scattering length map, we measure the precise location of the Efimov ground state to test van der Waals universality. Precise control of the sample's temperature and density ensure…
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 et.al., 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-s…
The multichannel Na-Cs interactions are characterized by a series of measurements using two atoms in an optical tweezer, along with a multichannel quantum defect theory (MQDT). The triplet and singlet scattering lengths are measured by performing Raman spectroscopy of the Na-Cs motional states and least-bound molecular state in the tweezer. Magnetic Feshbach resonances are observed for only two atoms at fields which agree well with the MQDT. Our methodology, which promotes the idea of an effective theory of interaction, can be a key step towards the understanding and the description of more co…
Using potential models we analyze range corrections to the universal law dictated by the Efimov theory of three bosons. In the case of finite-range interactions we have observed that, at first order, it is necessary to supplement the theory with one finite-range parameter, $Γ_n^3$, for each specific $n$-level [Kievsky and Gattobigio, Phys. Rev. A {\bf 87}, 052719 (2013)]. The value of $Γ_n^3$ depends on the way the potentials is changed to tune the scattering length toward the unitary limit. In this work we analyze a particular path in which the length $r_B=a-a_B$, measuring the difference bet…
