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Since the early days of quantum physics, the complex behavior of three interacting particles has been the subject of numerous experimental and theoretical studies. In a recent Letter to Nature, Kraemer et al. [Nature (London) 440, 315 (2006)] report on experimental ``evidence for Efimov quantum states in an ultracold gas of cesium atoms. Such quantum states refer to an infinite series of energy levels of three identical Bose particles, accumulating at the threshold for dissociation as the scattering length of each pair is tuned to infinity. Whereas the existence of a single Efimov state has been predicted for three helium atoms, earlier experimental studies concluded that this elusive state had not been found. In this paper we show by an intuitive argument and full numerical calculations that the helium and cesium experiments actually provide evidence of the same, ground state of this trimer spectrum, which the helium experimentalists and pioneering theoretical studies had not associated with Efimovs effect. Unlike the helium trimer, the observed 133Cs_3 resonance refers to a Borromean molecular state. We discuss how as yet unobserved, excited Efimov quantum states might be detected in ultracold gases of 85Rb and of 133Cs at magnetic field strengths in the vicinity of 0.08 T (800 G).
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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.
Feshbach resonances are the essential tool to control the interaction between atoms in ultracold quantum gases. They have found numerous experimental applications, opening up the way to important breakthroughs. This Review broadly covers the phenomenon of Feshbach resonances in ultracold gases and their main applications. This includes the theoretical background and models for the description of Feshbach resonances, the experimental methods to find and characterize the resonances, a discussion of the main properties of resonances in various atomic species and mixed atomic species systems, and an overview of key experiments with atomic Bose-Einstein condensates, degenerate Fermi gases, and ultracold molecules.
The field of few-body physics has originally been motivated by understanding nuclear matter. New model systems to experimentally explore few-body quantum systems can now be realized in ultracold gases with tunable interactions. Albeit the vastly different energy regimes of ultracold and nuclear matter (peV as compared to MeV), few-body phenomena are universal for near-resonant two-body interactions. Efimov states represent a paradigm for universal three-body states, and evidence for their existence has been obtained in measurements of three-body recombination in an ultracold gas of caesium atoms. Interacting samples of halo dimers can provide further information on universal few-body phenomena. Here we study interactions in an optically trapped mixture of such halo dimers with atoms, realized in a caesium gas at nanokelvin temperatures. We observe an atom-dimer scattering resonance, which we interpret as being due to a trimer state hitting the atom-dimer threshold. We discuss the close relation of this observation to Efimovs scenario, and in particular to atom-dimer Efimov resonances.
Systems of three interacting particles are notorious for their complex physical behavior. A landmark theoretical result in few-body quantum physics is Efimovs prediction of a universal set of bound trimer states appearing for three identical bosons with a resonant two-body interaction. Counterintuitively, these states even exist in the absence of a corresponding two-body bound state. Since the formulation of Efimovs problem in the context of nuclear physics 35 years ago, it has attracted great interest in many areas of physics. However, the observation of Efimov quantum states has remained an elusive goal. Here we report the observation of an Efimov resonance in an ultracold gas of cesium atoms. The resonance occurs in the range of large negative two-body scattering lengths, arising from the coupling of three free atoms to an Efimov trimer. Experimentally, we observe its signature as a giant three-body recombination loss when the strength of the two-body interaction is varied. We also detect 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 with which to explore the universal properties of resonantly interacting few-body systems. While Feshbach resonances have provided the key to control quantum-mechanical interactions on the two-body level, Efimov resonances connect ultracold matter to the world of few-body quantum phenomena.
A review on superfluidity and the BEC-BCS crossover in ultracold Fermi gases.
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