Trapped and cooled gases of alkali atoms can be manipulated to exhibit a variety of interesting phenomena.For example, dilute gases of fermionic atoms, in 2 hyperfine states, can be cooled to temperatures where they become superfluid.An external field can be applied to tune the scattering length a.When |a| exceeds the interparticle spacing, nonperturbative tools are needed to study the system theoretically.The unitary limit, |a| → ∞, is particularly interesting due to its universality and symmetry.Lattice field theory and effective field theory can be used to systematically calculate properties of this system.Results are presented for the finite temperature phase transition and for behavior near zero temperature.Trapped and cooled gases of alkali atoms can be manipulated to exhibit a variety of interesting phenomena.For example, dilute gases of fermionic atoms, in 2 hyperfine states, can be cooled to temperatures where they become superfluid.An external field can be applied to tune the scattering length a.When |a| exceeds the interparticle spacing, nonperturbative tools are needed to study the system theoretically.The unitary limit, |a| → ∞, is particularly interesting due to its universality and symmetry.Lattice field theory and effective field theory can be used to systematically calculate properties of this system.Results are presented for the finite temperature phase transition and for behavior near zero temperature.

International Symposium on Lattice Field Theory (LATTICE)Dec 18, 20061 citation

Theory of ultracold atomic Fermi gases

S. Giorgini, Лев П. Питаевский, S. Stringari

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 $s$ -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.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 $s$-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.

arXiv:0706.3360Reviews of Modern PhysicsOct 2, 20081,997 citations

Optically-trapped Fermi gas

Michael E. Gehm, S. R. Granade, M.-S. Chang +2 more

Summary form only given. Cold, dense gases of fermions offer exciting new opportunities for fundamental studies of quantum degeneracy, collective behavior, and superfluidity. Fermionic /sup 6/Li has been the subject of numerous theoretical treatments. This is due in part to its anomalously large and negative triplet scattering length, a/sub T/=-2160 a/sub O/, which arises from a near zero energy resonance. The large scattering length leads to two-state mixtures which are predicted to undergo a transition to a superfluid state at a relatively high temperature. To increase our well depth, we retroreflect the CO/sub 2/ beam which forms our optical trap, nearly doubling the intensity of the trapping field and thus the well depth. We will discuss this technique and its effect on evaporative cooling, and report our progress towards producing a degenerate gas of /sup 6/Li.Summary form only given. Cold, dense gases of fermions offer exciting new opportunities for fundamental studies of quantum degeneracy, collective behavior, and superfluidity. Fermionic /sup 6/Li has been the subject of numerous theoretical treatments. This is due in part to its anomalously large and negative triplet scattering length, a/sub T/=-2160 a/sub O/, which arises from a near zero energy resonance. The large scattering length leads to two-state mixtures which are predicted to undergo a transition to a superfluid state at a relatively high temperature. To increase our well depth, we retroreflect the CO/sub 2/ beam which forms our optical trap, nearly doubling the intensity of the trapping field and thus the well depth. We will discuss this technique and its effect on evaporative cooling, and report our progress towards producing a degenerate gas of /sup 6/Li.

Quantum Electronics and Laser Science ConferenceNov 13, 20022 citations

Cold dilute neutron matter on the lattice. I. Lattice virial coefficients and large scattering lengths

Dean Lee, Thomas Schäfer

We study cold dilute neutron matter on the lattice using an effective field theory. We work in the unitary limit in which the scattering length is much larger than the interparticle spacing. In this article we focus on the equation of state at temperatures above the Fermi temperature and compare lattice simulations to the virial expansion on the lattice and in the continuum. We find that in the unitary limit lattice discretization errors in the second virial coefficient are significantly enhanced. As a consequence the equation of state does not show the universal scaling behavior expected in the unitary limit. We suggest that scaling can be improved by tuning the second virial coefficient rather than the scattering length.We study cold dilute neutron matter on the lattice using an effective field theory. We work in the unitary limit in which the scattering length is much larger than the interparticle spacing. In this article we focus on the equation of state at temperatures above the Fermi temperature and compare lattice simulations to the virial expansion on the lattice and in the continuum. We find that in the unitary limit lattice discretization errors in the second virial coefficient are significantly enhanced. As a consequence the equation of state does not show the universal scaling behavior expected in the unitary limit. We suggest that scaling can be improved by tuning the second virial coefficient rather than the scattering length.

arXiv:nucl-th/0509017Physical Review CJan 13, 200651 citations

Pair condensation in a finite trapped Fermi gas

C. N. Gilbreth, Y. Alhassid

Superfluidity in the cold atomic two-species Fermi gas system in the unitary limit of infinite scattering length remains incompletely understood. In particular, a pseudogap phase has been proposed to exist above the superfluid critical temperature. Here we apply the auxiliary-field quantum Monte Carlo method to perform ab initio calculations of the temperature dependence of three quantities---the energy-staggering pairing gap, the condensate fraction, and the heat capacity---in a trapped finite-size cold atom system in the unitary limit of infinite scattering length. As the calculations of the energy-staggering pairing gap require the use of the canonical ensemble, we employ an efficient algorithm for the stabilization of particle-number projection that is essential for reaching convergence in the size of the model space. We observe clear signatures of the superfluid phase transition in all three quantities, including a signature of the recently measured $\ensuremath{\lambda}$ peak in the heat capacity. We also find that the energy-staggering gap does not lead the condensate fraction as the temperature decreases.Superfluidity in the cold atomic two-species Fermi gas system in the unitary limit of infinite scattering length remains incompletely understood. In particular, a pseudogap phase has been proposed to exist above the superfluid critical temperature. Here we apply the auxiliary-field quantum Monte Carlo method to perform ab initio calculations of the temperature dependence of three quantities---the energy-staggering pairing gap, the condensate fraction, and the heat capacity---in a trapped finite-size cold atom system in the unitary limit of infinite scattering length. As the calculations of the energy-staggering pairing gap require the use of the canonical ensemble, we employ an efficient algorithm for the stabilization of particle-number projection that is essential for reaching convergence in the size of the model space. We observe clear signatures of the superfluid phase transition in all three quantities, including a signature of the recently measured $\ensuremath{\lambda}$ peak in the heat capacity. We also find that the energy-staggering gap does not lead the condensate fraction as the temperature decreases.

arXiv:1210.4131Physical Review ADec 27, 201317 citations

Signatures of superfluidity in atomic Fermi gases

Mirta Rodríquez Pinilla

After the experimental realization of Bose-Einstein condensation in dilute gases of alkali atoms, experimentalists started to trap the fermionic isotopes. The degenerate state for fermions was reported in 1999. The main objective of these experiments is to obtain superfluidity of fermionic gases. When there are attractive interactions between the fermions, the Fermi sea becomes unstable with respect to the formation of atomic Cooper pairs and the system becomes a superfluid. It turns out that the existing experimental cooling techniques allow minimum temperatures for fermions of the order of the Fermi temperature. Using Feshbach resonances induced by magnetic fields enhances the effective interactions between the atoms leading to superfluid transition temperatures of the order of the Fermi energy. This is a completely new regime of fermionic superfluidity far from the BCS superconductors, He and even high- superconductors. The achievement of superfluidity on gasesAfter the experimental realization of Bose-Einstein condensation in dilute gases of alkali atoms, experimentalists started to trap the fermionic isotopes. The degenerate state for fermions was reported in 1999. The main objective of these experiments is to obtain superfluidity of fermionic gases. When there are attractive interactions between the fermions, the Fermi sea becomes unstable with respect to the formation of atomic Cooper pairs and the system becomes a superfluid. It turns out that the existing experimental cooling techniques allow minimum temperatures for fermions of the order of the Fermi temperature. Using Feshbach resonances induced by magnetic fields enhances the effective interactions between the atoms leading to superfluid transition temperatures of the order of the Fermi energy. This is a completely new regime of fermionic superfluidity far from the BCS superconductors, He and even high- superconductors. The achievement of superfluidity on gases

Nov 14, 20032 citations

s

-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.