Quasi-one-dimensional (quasi-1d) two-component Fermi gases with effectively attractive and repulsive interactions are characterized for arbitrary interaction strength. The ground-state properties of the gas confined in highly elongated harmonic traps are determined within the local density approximation. For strong attractive effective interactions the existence of a molecular TonksGirardeau gas is predicted. The frequency of the lowest breathing mode is calculated as a function of the coupling strength for both attractive and repulsive interactions. PACS numbers:The study of cold quasi-1d atomic quantum gases presents a very active area of research. So far, most of the experimental [1] and theoretical [2,3,4,5,6] investigations have been devoted to quasi-1d Bose gases and, in particular, to the strongly-interacting Tonks-Girardeau gas, which can be mapped to a gas of non-interacting fermions [2,7,8]. Quasi-1d atomic Fermi gases have not been realized experimentally yet.The role of interactions in quasi-1d atomic Fermi gases has been studied mainly in connection with Luttinger liquid theory [9,10]. Recati et al. [10] investigate the properties of a two-component Fermi gas with repulsive interspecies interactions confined in highly-elongated harmonic traps. In the limit of weak and strong coupling these authors relate the parameters of the Luttinger Hamiltonian, which describe the low-energy properties of the gas, to the microscopic parameters of the system. The Luttinger model is used to analyze the manifestations of the uncoupled dynamics of spin and density waves (spin-charge separation).This Letter investigates the properties of inhomogeneous quasi-1d two-component Fermi gases under harmonic confinement with attractive and repulsive interspecies interactions. The present study is based on the exact equation of state of a homogeneous 1d system of fermions with zero-range attractive [11,12] and repulsive [13] interactions treated within the local density approximation (LDA). We calculate the energy per particle, the size of the cloud, and the frequency of the lowest compressional mode as a function of the effective 1d coupling constant, including infinitely strong attractive and repulsive interactions. Moreover, for attractive interactions we discuss the cross-over from the weak-to the strongcoupling regime and point out the possibility of forming a mechanically stable molecular Tonks-Girardeau gas.Quasi-1d two-component Fermi gases with effectively attractive and repulsive 1d interspecies interactions can be realized in highly-elongated traps. The behavior of atomic gases tightly-confined in two directions can, if the confinement is chosen properly, be characterized to a very good approximation by an effective 1d coupling constant, g 1d , which encapsulates the atom-atom interaction strength. This coupling constant can be tuned to essentially any value, including zero and ±∞, by varying the 3d s-wave scattering length a 3d through application of an external magnetic field in the proximity of a Feshbach resona...
Spectroscopic experiments on molecules embedded in free clusters of liquid helium reveal a number of unusual features deriving from the unique quantum behavior of this nanoscale matrix environment. The apparent free rotation of small molecules in bosonic He4 clusters is one of the experimentally most well documented of these features. In this Focus article, we set this phenomenon in the context of experimental and theoretical advances in this field over the last ten years, and describe the microscopic insight which it has provided into the nature and dynamic consequences of quantum solvation in a superfluid. We provide a comprehensive theoretical analysis which is based on a unification of conclusions drawn from diffusion and path integral Monte Carlo calculations. These microscopic quantum calculations elucidate the origin of the empirical free rotor spectrum, and its relation to the boson character and superfluid nature of the quantum nanosolvent. The free rotor behavior of the molecular rotation is preserved because of inefficient angular momentum coupling between the dopant and its quantum liquid surroundings. This is consistent with the superfluid character of the droplet, and has significant implications for the hydrodynamic response of the local quantum fluid environment of the embedded molecule. The molecule–helium interaction appears to induce a local nonsuperfluid density component in the first quantum solvation shell. This can adiabatically follow the molecular rotation, resulting in a reduction of the rotational constant. The dynamic nature of this adiabatically following density, its relation to the magnitude of the gas-phase molecular rotational constant and to the anisotropy of the interaction potential, are characterized with several examples. The role of the local superfluid density is analyzed within a continuum hydrodynamic model which is subject to microscopic quantum constraints. The result is a consistent theoretical framework which unites a zero temperature description based on analysis of cluster rotational energy levels, with a quantum two-fluid description based on finite temperature analysis of local quantum solvation structure in the superfluid.
We treat the trapped two-component Fermi system, in which unlike fermions interact through a two-body short-range potential having no bound state but an infinite scattering length. By accurately solving the Schrödinger equation for up to N=6 fermions, we show that no many-body bound states exist other than those bound by the trapping potential, and we demonstrate unique universal properties of the system: Certain excitation frequencies are separated by 2variant Planck's over 2piomega, the wave functions agree with analytical predictions and a virial theorem is fulfilled. Further calculations up to N=30 determine the excitation gap, an experimentally accessible universal quantity, and it agrees with recent predictions based on a density functional approach.
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