This article reviews theoretical and experimental advances in Efimov physics, an array of quantum few-body and many-body phenomena arising for particles interacting via short-range resonant interactions, that is based on the appearance of a scale-invariant three-body attraction theoretically discovered by Vitaly Efimov in 1970. This three-body effect was originally proposed to explain the binding of nuclei such as the triton and the Hoyle state of carbon-12, and later considered as a simple explanation for the existence of some halo nuclei. It was subsequently evidenced in trapped ultra-cold atomic clouds and in diffracted molecular beams of gaseous helium. These experiments revealed that the previously undetermined three-body parameter introduced in the Efimov theory to stabilise the three-body attraction typically scales with the range of atomic interactions. The few- and many-body consequences of the Efimov attraction have been since investigated theoretically, and are expected to be observed in a broader spectrum of physical systems.

By performing high-resolution two-color photoassociation spectroscopy, we have successfully determined the binding energies of several of the last bound states of the homonuclear dimers of six different isotopes of ytterbium. These spectroscopic data are in excellent agreement with theoretical calculations based on a simple model potential, which very precisely predicts the s-wave scattering lengths of all 28 pairs of the seven stable isotopes. The s-wave scattering lengths for collision of two atoms of the same isotopic species are 13.33 (18) nm for 168 Yb, 3.38(11) nm for 170 Yb, −0.15(19) nm for 171 Yb, −31.7(3.4) nm for 172 Yb, 10.55(11) nm for 173 Yb, 5.55(8) nm for 174 Yb, and −1.28(23) nm for 176 Yb. The coefficient of the lead term of the long-range van der Waals potential of the Yb2 molecule is C6 = 1932(30) atomic units (E h a 6 0 ≈ 9.573 × 10 −26 J nm 6 ).

With ultracold 88Sr in a 1D magic wavelength optical lattice, we performed narrow-line photoassociation spectroscopy near the 1S0 - 3P1 intercombination transition. Nine least-bound vibrational molecular levels associated with the long-range 0u and 1u potential energy surfaces were measured and identified. A simple theoretical model accurately describes the level positions and treats the effects of the lattice confinement on the line shapes. The measured resonance strengths show that optical tuning of the ground state scattering length should be possible without significant atom loss.

We report on the direct conversion of laser-cooled 41K and 87Rb atoms into ultracold 41K87Rb molecules in the rovibrational ground state via photoassociation followed by stimulated Raman adiabatic passage. High-resolution spectroscopy based on the coherent transfer revealed the hyperfine structure of weakly bound molecules in an unexplored region. Our results show that a rovibrationally pure sample of ultracold ground-state molecules is achieved via the all-optical association of laser-cooled atoms, opening possibilities to coherently manipulate a wide variety of molecules.

We observed an enhanced atom-dimer loss due to the existence of Efimov states in a three-component mixture of 6Li atoms. We measured the magnetic-field dependence of the atom-dimer loss in the mixture of atoms in state |1> and dimers formed in states |2> and |3>, and found two peaks corresponding to the degeneracy points of the energy levels of |23> dimers and the ground and first excited Efimov trimers. We found that the locations of these peaks disagree with universal theory predictions, in a way that cannot be explained by nonuniversal two-body properties. We constructed theoretical models that characterize the nonuniversal three-body physics of three-component 6Li atoms in the low-energy domain.

The binding energy of an Efimov trimer state was precisely determined via radio-frequency association. It is found that the measurement results significantly shift with temperature, but that the shift can be made negligible at the lowest temperature in our experiment. The obtained trimer binding energy reveals a significant deviation from the nonuniversal theory prediction based on a three-body parameter with a monotonic energy dependence.About forty years ago, V. Efimov predicted that the existence of universal trimer states known as the Efimov states, in a three-body system with resonant short-range interactions [1]. Such universal states are characterized only by the two-body scattering lengths for each pair of particles and a three-body parameter fixed by short-range physics. Owing to magnetic Feshbach resonances [2], ultracold atomic systems turned out to be the first systems where the Efimov effect was observed conclusively. Since the first experimental evidence in an ultracold cesium gas [3], general properties of few-body systems near unitarity such as the universal scaling laws [4] were confirmed in many ultracold bosonic systems [5-9] and a three-component fermionic gas of 6 Li [10][11][12][13][14], via the inelastic collision enhancements and minima occurring at particular intensities of an externally-applied magnetic field. Although these features are qualitatively explained by Efimov's universal theory (UT) [4], their relative positions of loss features are shifted significantly from universal predictions. For example, the shift of the atom-dimer loss peaks from that expected from the three-body loss peaks [5,13,14] and the notable discrepancies in properties of the Efimov resonances between regions of positive and negative scattering lengths [8] do not seem to be consistent with a fixed three-body parameter. Therefore, the precise determination of the three-body parameter is crucial to understand these systems.To understand the atom-dimer loss feature in the threecomponent gas of 6 Li, we constructed a nonuniversal model by taking into account the energy dependence of the scattering length due to finite-range corrections [13]. This two-body physics correction still does not explain the atom-dimer loss feature that we observed experimentally. We then introduced an energy-dependent three-body parameter Λ which phenomenologically reproduces all the experimental data of the three-body loss and the atomdimer loss in the three-component mixture of 6 Li atoms. [13,15]. However, these three-body and atom-dimer loss measurements provide information on Λ only at the points where the trimer energy level vanishes upon dissociation or meets a dimer energy level. Thus, it has been desirable to directly measure the binding energy of the Efimov trimers to fully determine the three-body parameter and the validity of the model. Recently, T. Lompe et.al.[16] demonstrated a radiofrequency (RF) association of the Efimov trimer state in the three-component mixture of 6 Li atoms. This method constitutes the most direct o...

The low-energy spectrum of three particles interacting via nearly resonant two-body interactions in the Efimov regime is set by the so-called three-body parameter. We show that the three-body parameter is essentially determined by the zero-energy two-body correlation. As a result, we identify two classes of two-body interactions for which the three-body parameter has a universal value in units of their effective range. One class involves the universality of the three-body parameter recently found in ultracold atom systems. The other is relevant to short-range interactions that can be found in nuclear physics and solid-state physics.The Efimov effect is a universal low-energy quantum phenomenon, which was originally predicted in nuclear physics [1] and has rekindled considerable interest since its experimental confirmation with ultracold atoms . It is also expected to occur in solid-state physics [23,24]. This universality stems from the effective three-body attraction that occurs between particles interacting with nearly resonant short-range interactions. As a result of this attraction, three particles may bind even when the interaction is not strong enough to bind two particles. Furthermore, an infinite series of such three-body bound states exists near the unitary point where the interaction is resonant, i.e. where a two-body bound state appears and the s-wave scattering a length diverges. The typical three-body energy spectrum for such systems is represented in Fig. 1 in units of inverse length. Near zero energy and large scattering lengths, the three-body spectrum is invariant under a discrete scaling transformation by a universal factor e π/s0 ≈ 22.7 for identical bosons, where s 0 ≈ 1.00624 characterises the strength of the three-body attraction.A notable consequence of the Efimov effect is the existence of another physical scale beyond the two-body scattering length to fix the low-energy properties of the system. This scale is known as the three-body parameter. In zero-range models, it manifests itself as the necessity to introduce a momentum cutoff or a three-body boundary condition. It can be characterised, for instance, by the scattering length a − at which a trimer appears or by its binding wave number κ at unitarity, as indicated in Fig. 1. Because of the discrete scaling invariance, it is defined up to a power of e π/s0 . In this Letter, we will focus on the ground Efimov state, which slightly deviates from the discrete-scaling-invariant structure, but is more easily observed and computed, and still reveals the essence of the physics behind the three-body parameter.Three important questions can be raised concerning the three-body parameter. Is there a simple mechanism that determines the three-body parameter from the microscopic interactions? What is the microscopic length scale which determines the three-body parameter? Finally, if there is such a length scale, what are the conditions for the three-body parameter to be related to that length scale through a universal dimensionless constant,

At ultracold temperatures, the Pauli exclusion principle suppresses collisions between identical fermions. This has motivated the development of atomic clocks with fermionic isotopes. However, by probing an optical clock transition with thousands of lattice-confined, ultracold fermionic strontium atoms, we observed density-dependent collisional frequency shifts. These collision effects were measured systematically and are supported by a theoretical description attributing them to inhomogeneities in the probe excitation process that render the atoms distinguishable. This work also yields insights for zeroing the clock density shift.