Abstract. Three interacting particles form a system which is well known for its complex physical behavior. A landmark theoretical result in few-body quantum physics is Efimov's prediction of a universal set of weakly bound trimer states appearing for three identical bosons with a resonant two-body interaction [1,2]. Surprisingly, these states even exist in the absence of a corresponding two-body bound state and their precise nature is largely independent of the particular type of the two-body interaction potential. Efimov's scenario has attracted great interest in many areas of physics; an experimental test however has not been achieved. We report the observation of an Efimov resonance in an ultracold thermal gas of cesium atoms [3]. The resonance occurs in the range of large negative two-body scattering lengths and arises from the coupling of three free atoms to an Efimov trimer. We observe its signature as a giant three-body recombination loss when the strength of the two-body interaction is varied near a Feshbach resonance. This resonance develops into a continuum resonance at non-zero collision energies, and we observe a shift of the resonance position as a function of temperature. We also report on a minimum in the recombination loss for positive scattering lengths, indicating destructive interference of decay pathways. Our results confirm central theoretical predictions of Efimov physics and represent a starting point from which to explore the universal properties of resonantly interacting few-body systems. Efimov's treatment of three identical bosons [1,2] is closely linked to the concept of universality [4] in systems with a resonant two-body interaction, where the s-wave scattering length a fully characterizes the two-body physics. When |a| greatly exceeds the characteristic range ℓ of the two-body interaction potential, details of the short-range interaction become irrelevant because of the long-range nature of the wave function. Universality then leads to a generic behavior in three-body physics, reflected in the energy spectrum of weakly bound Efimov trimer states. Up to now, in spite of their great fundamental importance, these states could not be observed experimentally. An observation in the realm of nuclear physics, as originally proposed by Efimov, is hampered by the presence of the Coulomb interaction, and only two-neutron halo systems with a spinless core are likely to feature Efimov states [5]. In molecular physics, the helium trimer [6] is predicted to have an excited state with Efimov character [7]. The existence of this state could so far not be confirmed [8]. A different approach to experimentally study the physics of Efimov states is based on the unique properties of ultracold atomic Keywords

Control over all internal and external degrees of freedom of molecules at the level of single quantum states will enable a series of fundamental studies in physics and chemistry 1, 2 .In particular, samples of ground-state molecules at ultralow temperatures and high number densities will allow novel quantum-gas studies 3 and future applications in quantum information science 4 . However, high phase-space densities for molecular samples are not readily attainable as efficient cooling techniques such as laser cooling are lacking. Here we produce an ultracold and dense sample of molecules in a single hyperfine level of the rovibronic ground state with each molecule individually trapped in the motional ground state of an optical lattice well. Starting from a zero-temperature atomic Mott-insulator state 5 with optimized double-site occupancy 6 , weakly-bound dimer molecules are efficiently associated on a Feshbach resonance 7 and subsequently transferred to the rovibronic ground state by a stimulated four-photon process with >50% efficiency. The molecules are trapped in the lattice and have a lifetime of 8 s. Our results present a crucial step towards Bose-Einstein condensation 1 arXiv:0909.4700v1 [cond-mat.quant-gas] 25 Sep 2009 of ground-state molecules and, when suitably generalized to polar heteronuclear molecules, the realization of dipolar quantum-gas phases in optical lattices 8-10 . Recent years have seen spectacular advances in the field of atomic quantum gases. Ultracold atomic samples have been loaded into optical lattice potentials, allowing the realization of strongly-correlated many-body systems and enabling the direct observation of quantum phase transitions with full control over the entire parameter space 5 . Molecules with their increased complexity are expected to play a crucial role in future generation quantum gas studies. For example, the long-range dipole-dipole force between polar molecules gives rise to nearest-neighbour and next-nearest-neighbour interaction terms in the extended Bose-Hubbard Hamiltonian and should thus lead to novel many-body states in optical lattices in the form of striped, checkerboard, and supersolid phases 8-10 .An important prerequisite for all proposed molecular quantum gas experiments is the capability to fully control all internal and external quantum degrees of freedom of the molecules. For radiative and collisional stability, the molecules need to be prepared in their rovibronic ground state, i.e. the lowest vibrational and rotational level of the lowest electronic state, and preferably in its energetically lowest hyperfine sublevel. As a starting point for the realization of novel quantum phases, the molecular ensemble should be in the ground state of the many-body system. Such state control is only possible at ultralow temperatures and sufficiently high particle densities. While versatile non-optical cooling and slowing techniques have recently been developed for molecular ensembles 11 , the achievable molecular phase-space densities are still far away from

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