In the atomic Bose-Einstein condensate, the interactions that bring a binary atom system to an intermediate state molecule in the Feshbach resonance create a second condensate component of molecules. The atomic and molecular condensates coherently exchange pairs of atoms. We discuss a signature of the coherent intercondensate exchange: Josephson-like oscillations of the atomic and molecular populations in response to a sudden change of the energy detuning. The dependence of the many-body ground state energy on volume suggests that the on-resonant ground state is a dilute condensate with the liquidlike property of a self-determined density. PACS numbers: 03.75.Fi, 05.30.Jp, 32.80.Pj, 67.90. + z As dilute gases, the atomic Bose-Einstein condensates [1-3] are amenable to atomic manipulation techniques. As superfluids [4], these dilute condensates exhibit an unusual degree of flexibility, promising novel studies of macroscopic quantum coherence. For instance, the notion that external fields can alter the interatomic interactions [5] suggests the study of condensates with interparticle interactions that can be experimentally controlled [6]. Signatures of one of the proposed schemes, the low energy Feshbach resonance [7], have been observed recently [8].In this Letter, we point out that this resonance affects the condensate system more profoundly than altering an effective interparticle interaction: the molecules, formed in the intermediate state of the binary atom resonance, occupy a second condensate component. The atomic and molecular condensates interact in part by coherently exchanging pairs of atoms, implying interesting and unusual properties. Below, we discuss two examples: (i) The molecular condensate, even if it is small in the off-resonant regime, can reveal its presence by means of Josephson-like oscillations of the atomic and molecular populations in response to a sudden change of the detuning. (ii) Close to resonance, the coherent intercondensate tunneling binds the dilute manybody Bose-Einstein condensate (BEC) to a system with the liquidlike property of a self-determined density.In the low energy Feshbach resonance, the hyperfine interaction, V hf , rearranges the spins of two alkali atoms interacting in an external magnetic field B, bringing them to an intermediate quasibound molecular state. In this process, a valence electron spin is "flipped" which, in the magnetic field, raises the continuum of the intermediate spin state jS 0 ͘ by an amount D͑B͒, relative to the continuum of the initial binary atom spin state jS͘. At a resonant magnetic field B B m , the jS͘ continuum lines up with the bound state m of the jS 0 ͘ interatomic potential. Near the resonance, the energy difference e of the initial and intermediate states, which we call "detuning," varies with magnetic field, e ഠ ͑≠D͞≠B͒ 3 ͓B 2 B m ͔. The amplitude of the resonant process is characterized by a ͗S 0 jV hf jS͘ 3 R d 3 r w ‫ء‬ m ͑r͒w͑r͒, where w m denotes the vibrational wave function of the m state and w the continuum (jS͘) wave function...

The zero-temperature system of two dilute overlapping Bose-Einstein condensates is unstable against long wavelength excitations if the interaction strength between the distinguishable bosons exceeds the geometric mean of the like-boson interaction strengths. If the condensates attract each other, the instability is similar to the instability of the negative scattering length condensates. If the condensates repel, they separate spatially into condensates of equal pressure. We estimate the boundary size, surface tension and energy of the phase separated condensate system and we discuss the implications for double condensates in atomic traps. PACS numbers(s):03.75. Fi, 05.30.Jp, 32.80Pj, 67.90.+z Typeset using REVT E X 1

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We show that composite fermi/bose superfluids can be created in coldatom traps by employing a Feshbach resonance or coherent photoassociation. The bosonic molecular condensate created in this way implies a new fermion pairing mechanism associated with the exchange of fermion pairs between the molecular condensate and an atomic fermion superfluid. We predict macroscopically coherent, Josephson-like oscillations of the atomic and molecular populations in response to a sudden change of the molecular energy, and suggest that these oscillations will provide an experimental signature of the pairing. PACS numbers(s):03.75. Fi, 05.30.Jp, 32.80Pj, 67.90.+z Typeset using REVT E X

The description of an impurity atom in a Bose-Einstein condensate can be cast in the form of Fröhlich's polaron Hamiltonian, where the Bogoliubov excitations play the role of the phonons. An expression for the corresponding polaronic coupling strength is derived, relating the coupling strength to the scattering lengths, the trap size and the number of Bose condensed atoms. This allows to identify several approaches to reach the strong-coupling limit for the quantum gas polarons, whereas this limit was hitherto experimentally inaccessible in solids. We apply Feynman's path-integral method to calculate for all coupling strengths the polaronic shift in the free energy and the increase in the effective mass. The effect of temperature on these quantities is included in the description. We find similarities to the acoustic polaron results and indications of a transition between free polarons and self-trapped polarons. The prospects, based on the current theory, of investigating the polaron physics with ultracold gases are discussed for lithium atoms in a sodium condensate.