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arXiv:cond-mat/0308306 · Physical Review Letters

Achieving a BCS Transition in an Atomic Fermi Gas

Lincoln D. Carr, Gora V. Shlyapnikov, Yvan Castin

Published Apr 15, 2004• 112 citations
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Abstract

We consider a gas of cold fermionic atoms having two spin components with interactions characterized by their s-wave scattering length a. At positive scattering length the atoms form weakly bound bosonic molecules which can be evaporatively cooled to undergo Bose-Einstein condensation, whereas at negative scattering length BCS pairing can take place. It is shown that, by adiabatically tuning the scattering length a from positive to negative values, one may transform the molecular Bose-Einstein condensate into a highly degenerate atomic Fermi gas, with the ratio of temperature to Fermi temperature T/T(F) approximately 10(-2). The corresponding critical final value of k(F)/a/, which leads to the BCS transition, is found to be about one-half, where k(F) is the Fermi momentum.

DOI
10.1103/physrevlett.92.150404

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We consider a gas of cold fermionic atoms having two spin components with interactions characterized by their s-wave scattering length a. At positive scattering length the atoms form weakly bound bosonic molecules which can be evaporatively cooled to undergo Bose-Einstein condensation, whereas at negative scattering length BCS pairing can take place. It is shown that, by adiabatically tuning the scattering length a from positive to negative values, one may transform the molecular Bose-Einstein condensate into a highly degenerate atomic Fermi gas, with the ratio of temperature to Fermi temperature T/T(F) approximately 10(-2). The corresponding critical final value of k(F)/a/, which leads to the BCS transition, is found to be about one-half, where k(F) is the Fermi momentum.
The physics of quantum degenerate atomic 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 that 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 sss-wave scattering length, whose value can be tuned using an external magnetic field near a broad 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, on 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 nonperturbative methods based on quantum Monte Carlo techniques. A major goal of the review is to compare theoretical predictions with available experimental results.
Preparation of molecular quantum gas promises novel applications including quantum control of chemical reactions, precision measurements, quantum simulation and quantum information processing. Experimental preparation of colder and denser molecular samples, however, is frequently hindered by fast inelastic collisions that heat and deplete the population. Here we report the formation of two-dimensional Bose-Einstein condensates (BECs) of spinning g−g-g−wave molecules by inducing pairing interactions in an atomic condensate. The trap geometry and the low temperature of the molecules help reducing inelastic loss to ensure thermal equilibrium. We determine the molecular scattering length to be +220(30)+220(30)+220(30)~Bohr and investigate the unpairing dynamics in the strong coupling regime. Our work confirms the long-sought transition between atomic and molecular condensates, the bosonic analog of the BEC-BCS (Bardeen-Cooper-Schieffer superfluid) crossover in a Fermi gas.
We study a two-component Bose gas with a symmetric spin-orbit coupling, and find that two atoms can form a bound state with any intra- or inter-species scattering length. Consequently, in the dilute limit, the BCS-pairing state of bosons can be formed with weakly attractive interspecies and repulsive intraspecies interactions. The quasiparticle excitation energies are anisotropic due to spin-orbit coupling. This BCS-pairing state is energetically favored over Bose-Einstein condensation (BEC) of atoms at low densities. As the density increases, there is a first-order transition from the BCS to BEC states.
This study presents a simple idea and a conceptual understandingof the crossover from the Bardeen Cooper (BCS) state of weakly-correlatedpairs of fermions to the Bose{Einstein condensation (BEC) of diatomicmolecules in the atomic Fermi gas. In the context of ultra cold Fermi gases,a BCS-BEC crossover means that by tuning the interaction strength, onegoes from a BCS state to a BEC state without encountering a phase transition.BEC state is a Bose-Einstein condensate of two-atom molecules (boundfermions), while the BCS state is made up of pair of atoms. The differencebetween the pairs and the molecules is that the molecules are localized inthe real space, whereas the BCS pairs are made of two particles with oppositemomenta in the momentum space.
We study a gas of fermions undergoing a wide resonance sss-wave BCS--Bose-Einstein-condensate (BEC) crossover, in the BEC regime at zero temperature. We calculate the chemical potential and the speed of sound of this Bose-Einstein-condensed gas, as well as the condensate depletion, in the low-density approximation. We discuss how higher-order terms in the low-density expansion can be constructed. We demonstrate that the standard BCS-BEC gap equation is invalid in the BEC regime and is inconsistent with the results obtained here. The low-density approximation we employ breaks down in the intermediate BCS-BEC crossover region. Hence our theory is unable to predict how the chemical potential and the speed of sound evolve once the interactions are tuned towards the BCS regime. As a part of our theory, we derive the well-known result for the bosonic scattering length diagrammatically and check that there are no bound states of two bosons.