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      Transdimensional equivalence of universal constants for Fermi gases at unitarity

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          Abstract

          I present lattice Monte Carlo calculations for a universal four-component Fermi gas confined to a finite box and to a harmonic trap in one spatial dimension. I obtain the values xi_1d = 0.370(4) and xi_1d = 0.372(1), respectively, for the Bertsch parameter, a nonperturbative universal constant defined as the (square of the) energy of the untrapped (trapped) system measured in units of the free gas energy. The Bertsch parameter for the one-dimensional system is consistent to within ~1% uncertainties with the most recent numerical and experimental estimates of the analogous Bertsch parameter for a three-dimensional spin-1/2 Fermi gas at unitarity. The finding suggests the intriguing possibility that there exists a universality between two conformal theories in different dimensions. To lend support to this study, I also compute continuum extrapolated ground state energies for four and five fermions confined to a harmonic trap and demonstrate the restoration of a Virial theorem in the continuum limit. The continuum few-body energies obtained are consistent with exact analytical calculations to within ~1.0% and ~0.25% statistical uncertainties, respectively.

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          Theory of ultracold Fermi gases

          The physics of quantum degenerate Fermi gases in uniform as well as in harmonically trapped configurations is reviewed from a theoretical perspective. Emphasis is given to the effect of interactions which play a crucial role, bringing the gas into a superfluid phase at low temperature. In these dilute systems interactions are characterized by a single parameter, the s-wave scattering length, whose value can be tuned using an external magnetic field near a Feshbach resonance. The BCS limit of ordinary Fermi superfluidity, the Bose-Einstein condensation (BEC) of dimers and the unitary limit of large scattering length are important regimes exhibited by interacting Fermi gases. In particular the BEC and the unitary regimes are characterized by a high value of the superfluid critical temperature, of the order of the Fermi temperature. Different physical properties are discussed, including the density profiles and the energy of the ground-state configurations, the momentum distribution, the fraction of condensed pairs, collective oscillations and pair breaking effects, the expansion of the gas, the main thermodynamic properties, the behavior in the presence of optical lattices and the signatures of superfluidity, such as the existence of quantized vortices, the quenching of the moment of inertia and the consequences of spin polarization. Various theoretical approaches are considered, ranging from the mean-field description of the BCS-BEC crossover to non-perturbative methods based on quantum Monte Carlo techniques. A major goal of the review is to compare the theoretical predictions with the available experimental results.
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            Continuum limit and improved action in lattice theories

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              Creation of ultracold molecules from a Fermi gas of atoms

              Since the realization of Bose-Einstein condensates (BEC) in atomic gases an experimental challenge has been the production of molecular gases in the quantum regime. A promising approach is to create the molecular gas directly from an ultracold atomic gas; for example, atoms in a BEC have been coupled to electronic ground-state molecules through photoassociation as well as through a magnetic-field Feshbach resonance. The availability of atomic Fermi gases provides the exciting prospect of coupling fermionic atoms to bosonic molecules, and thus altering the quantum statistics of the system. This Fermi-Bose coupling is closely related to the pairing mechanism for a novel fermionic superfluid proposed to occur near a Feshbach resonance. Here we report the creation and quantitative characterization of exotic, ultracold \(^{40}\)K\(_2\) molecules. Starting with a quantum degenerate Fermi gas of atoms at T < 150 nanoKelvin we scan over a Feshbach resonance to adiabatically create over a quarter million trapped molecules, which we can convert back to atoms by reversing the scan. The small binding energy of the molecules is controlled by detuning from the Feshbach resonance and can be varied over a wide range. We directly detect these weakly bound molecules through rf photodissociation spectra that probe the molecular wavefunction and yield binding energies that are consistent with theory.
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                Author and article information

                Journal
                10 October 2012
                2012-12-23
                Article
                10.1103/PhysRevLett.109.250403
                1210.3104
                fc8128cf-1407-47de-b7b5-10495fe96c94

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

                History
                Custom metadata
                RIKEN-QHP-49
                Phys. Rev. Lett. 109, 250403 (2012)
                4 pages, 3 figures, 1 Table; minor revisions to the title, abstract and main text
                hep-lat cond-mat.quant-gas hep-th

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