In 1970 V. Efimov predicted a puzzling quantummechanical effect that is still of great interest today. He found that three particles subjected to a resonant pairwise interaction can join into an infinite number of loosely bound states even though each particle pair cannot bind. Interestingly, the properties of these aggregates, such as the peculiar geometric scaling of their energy spectrum, are universal, i.e. independent of the microscopic details of their components. Despite an extensive search in many different physical systems, including atoms, molecules and nuclei, the characteristic spectrum of Efimov trimer states still eludes observation. Here we report on the discovery of two bound trimer states of potassium atoms very close to the Efimov scenario, which we reveal by studying three-particle collisions in an ultracold gas. Our observation provides the first evidence of an Efimov spectrum and allows a direct test of its scaling behaviour, shedding new light onto the physics of few-body systems.From nuclei, atoms and molecules up to galaxies, our complex world is made up of many kinds of aggregates whose properties depend on the details of the interactions between their components. This scenario is expected to drastically change as one moves to the world of few neutral quantum particles. The physics of these systems is typically dominated by two-body interactions, which in the limit of vanishing collision energies can be described by a single parameter, namely the s-wave scattering length, independently from the nature of the particles and of the microscopic shape of their interaction 1,2 . If the two-body scattering length becomes resonantly large, the binding of few such particles into larger aggregates is predicted to become universal, in the sense that its properties depend only on the scattering length and few other global parameters 3 .These expectations have been so far verified only for twobody bound states 2 , and even the seemingly simple case of three particles is still under investigation. In this frame, a landmark theoretical result was obtained in 1970 by Efimov 4,5 . He extended previous studies 6 to show that three identical bosons with large two-body scattering length a, even without two-body bound states, can form weakly bound trimer states with size greatly exceeding the characteristic range r 0 of the two-body potential. The binding properties of such states follow a universal behaviour, regardless of the microscopic peculiarities of their components and of their interaction. Efimov indeed identified an effective three-particle interaction potential of the form -(s 0 2 +1/4)/R 2 , where R is the overall size of the three-body system and s 0 1.00624 is a universal parameter 4 . This simple potential is known to support an infinite number of bound states whose energy spectrum exhibits a peculiar geometric scaling where two consecutive states are linked by the relation E n =E n-1 exp(-2/s 0 ). This perfect scaling is predicted to apply only for the special case of a system with infinite...

We demonstrate the operation of an atom interferometer based on a weakly interacting Bose-Einstein condensate. We strongly reduce the interaction induced decoherence that usually limits interferometers based on trapped condensates by tuning the s-wave scattering length almost to zero via a magnetic Feshbach resonance. We employ a 39 K condensate trapped in an optical lattice, where Bloch oscillations are forced by gravity. The fine-tuning of the scattering length down to 0:1 a 0 and the micrometric sizes of the atomic sample make our system a very promising candidate for measuring forces with high spatial resolution. Our technique can be in principle extended to other measurement schemes opening new possibilities in the field of trapped atom interferometry. [2,3]. Unfortunately in high density trapped condensed clouds, interaction induces phase diffusion [4] and can cause systematic frequency shifts due to uncontrolled atomic density gradient, thus seriously limiting the performances of a BEC atom interferometer. In order to avoid the deleterious effect of interaction, atom interferometers for high precision measurement use free falling dilute samples of nondegenerate atoms [5]. The main drawbacks are the limited interrogation time (0.5 s) due to the finite size of the apparatus and the poor spatial resolution of this type of sensors. Using fermionic atoms instead of bosons represents one possibility to have access to trapped interferometry with a degenerate gas [6]. In fact, because of the Pauli exclusion principle, the atomic scattering cross section at sufficiently low temperatures is fully suppressed. However, the quantum pressure limits the spatial resolution, and the momentum spread reduces the interference contrast. Another way to reduce the effect of the interaction is to realize a number squeezed splitting [7,8]. In this way, coherence times are increased at the expense of the interference signal visibility. Despite the fundamental limit represented by interaction induced decoherence, several groups are performing experiments with trapped BECs [7][8][9][10], in the challenging search for the ''ideal'' interferometer.In this Letter, we demonstrate the conceptually simplest solution to the long-standing problem of interaction induced decoherence in BEC interferometers. We show how, by properly tuning the interaction strength in a quantum degenerate gas of 39 K [11] by means of a broad magnetic Feshbach resonance [12], we can greatly increase the coherence time of an atom interferometer. By achieving almost vanishing values of the s-wave scattering length, we demonstrate trapped atom interferometry with a weakly interacting BEC.The interferometer we adopted, commonly known as Bloch oscillations interferometer, is based on a multiple well scheme [2,6,13,14]. The condensate is adiabatically loaded in a sinusoidal potential with period =2, realized with an optical standing wave of wavelength . In the presence of an external force F, the macroscopic wave function of the condensate can be described as a cohere...

We study the three-body problem for three atomic fermions, in the same spin state, experiencing a resonant interaction in the p-wave channel via a Feshbach resonance represented by a two-channel model. The rate of inelastic processes due to recombination to deeply bound dimers is then estimated from the three-body solution using a simple prescription. We obtain numerical and analytical predictions for most of the experimentally relevant quantities that can be extracted from the threebody solution: the existence of weakly bound trimers and their lifetime, the low-energy elastic and inelastic scattering properties of an atom on a weakly bound dimer (including the atom-dimer scattering length and scattering volume), and the recombination rates for three colliding atoms towards weakly bound and deeply bound dimers. The effect of "background" non-resonant interactions in the open channel of the two-channel model is also calculated and allows to determine which three-body quantities are 'universal' and which on the contrary depend on the details of the model.