Effective Nonlinear Schrödinger Equations for Cigar-Shaped and Disk-Shaped Fermi Superfluids at Unitarity
arXiv:0811.2758 · doi:10.1088/1367-2630/11/2/023011
Abstract
In the case of tight transverse confinement (cigar-shaped trap) the three-dimensional (3D) nonlinear Schrödinger equation, describing superfluid Fermi atoms at unitarity (infinite scattering length ), is reduced to an effective one-dimensional form by averaging over the transverse coordinates. The resultant effective equation is a 1D nonpolynomial Schrodinger equation, which produces results in good agreement with the original 3D one. In the limit of small and large fermion number the nonlinearity is of simple power-law type. A similar reduction of the 3D theory to a two-dimensional form is also performed for a tight axial confinement (disk-shaped trap). The resultant effective 2D nonpolynomial equation also produces results in agreement with the original 3D equation and has simple power-law nonlinearity for small and large . For both cigar- and disk-shaped superfluids our nonpolynomial Schrödinger equations are quite attractive for phenomenological application.
22 pages, 5 figures
References in corpus (65)
- Theory of ultracold Fermi gases
- Observation of resonance condensation of fermionic atom pairs
- Condensation of Pairs of Fermionic Atoms Near a Feshbach Resonance
- Observation of a Strongly-Interacting Degenerate Fermi Gas of Atoms
- Observation of the Pairing Gap in a Strongly Interacting Fermi Gas
- Creation of ultracold molecules from a Fermi gas of atoms
- Evidence for Superfluidity in a Resonantly Interacting Fermi Gas
- Effective wave-equations for the dynamics of cigar-shaped and disc-shaped Bose condensates
- Collective excitations of a degenerate gas at the BEC-BCS crossover
- Superfluid Fermi Gases with Large Scattering Length
- Conversion of an Atomic Fermi Gas to a Long-Lived Molecular Bose Gas
- Equation of state of a Fermi gas in the BEC-BCS crossover: a quantum Monte Carlo study
- General coordinate invariance and conformal invariance in nonrelativistic physics: Unitary Fermi gas
- Fermi systems with long scattering lengths
- Quantum Monte Carlo Studies of Superfluid Fermi Gases
- Resonance Superfluidity: Renormalization of Resonance Scattering Theory
- Bulk and Collective Properties of a Dilute Fermi Gas in the BCS-BEC Crossover
- Local Density Functional Theory for Superfluid Fermionic Systems: The Unitary Gas
- Time-Dependent Density-Functional Theory for Trapped Strongly-Interacting Fermionic Atoms
- Bose-Einstein condensation dynamics from the numerical solution of the Gross-Pitaevskii equation
- Quantitative comparison between theoretical predictions and experimental results for the BCS-BEC crossover
- Cold Bose gases with large scattering lengths
- Mechanical Stability of a Strongly-Interacting Fermi Gas of Atoms
- From the Bogoliubov-de Gennes equations for superfluid fermions to the Gross-Pitaevskii equation for condensed bosons
- Momentum distribution and condensate fraction of a Fermi gas in the BCS-BEC crossover
- Collective oscillations of a trapped Fermi gas near a Feshbach resonance
- Universal properties of a trapped two-component Fermi gas at unitarity
- Formation Time of a Fermion Pair Condensate
- Superfluid Bose-Fermi mixture from weak-coupling to unitarity
- Vector solitons in nearly-one-dimensional Bose-Einstein condensates
- Collective oscillations of a trapped Fermi gas near the unitary limit
- Effective action for Superconductors and BCS-Bose crossover
- Condensate Fraction of a Fermi Gas in the BCS-BEC Crossover
- Extended Thomas-Fermi Density Functional for the Unitary Fermi Gas
- Energetics and Structural Properties of Trapped Two-Component Fermi Gases
- Fermionic bright soliton in a boson-fermion mixture
- Unitary Fermi Gas in a Harmonic Trap
- Exact particle and kinetic energy densities for one-dimensional confined gases of non-interacting fermions
- Nonlinear Schrödinger equation for a superfluid Fermi gas from BCS to Bose crossover
- Oscillation Frequencies for a Bose Condensate in a Triaxial Magnetic Trap
- Ideal Quantum Gases in D-dimensional Space and Power-law Potentials
- BEC-BCS Crossover of a Trapped Two-Component Fermi Gas with Unequal Masses
- Mean-field description of dynamical collapse of a fermionic condensate in a trapped boson-fermion mixture
- Fermi Gases in Slowly Rotating Traps: Superfluid vs Collisional Hydrodynamics
- Transition from 3D to 1D in Bose Gases at Zero Temperature
- Macroscopic Periodic Tunneling of Fermi Atoms in the BCS-BEC Crossover
- Matter-wave vortices in cigar-shaped and toroidal waveguides
- Kirzhnits gradient expansion for a D-dimensional Fermi gas
- Expansion of a Fermi Cloud in the BCS-BEC Crossover
- Pulsed Macroscopic Quantum Tunneling of Falling Bose Condensates
- Bose-Einstein condensates under a spatially-modulated transverse confinement
- Cooper pair dispersion relation for weak to strong coupling
- Condensate Fraction of a Two-Dimensional Attractive Fermi Gas
- Collective Excitations of Strongly Interacting Fermi Gases of Atoms in a Harmonic Trap
- Quasi One-Dimensional Bosons in Three-dimensional Traps: From Strong Coupling to Weak Coupling Regime
- Gap solitons in superfluid boson-fermion mixtures
- Visualization of vortex bound states in polarized Fermi gases at unitarity
- Mixing-demixing in a trapped degenerate fermion-fermion mixture
- Miscibility in a degenerate fermionic mixture induced by linear coupling
- Destroying superfluidity by rotating a Fermi gas at unitarity
- Bosons and Fermions near Feshbach resonances
- Mixing-demixing transition and collapse of a vortex state in a quasi-two-dimensional boson-fermion mixture
- Hydrodynamic Modes in a Trapped Strongly Interacting Fermi Gases of Atoms
- Black soliton in a quasi-one-dimensional trapped fermion-fermion mixture
- Bright solitons and soliton trains in a fermion-fermion mixture
Cited by in corpus (34)
- Spontaneous symmetry breaking of Bose-Fermi mixtures in double-well potentials
- Self-trapping of a Fermi super-fluid in a double-well potential in the BEC-unitarity crossover
- Modulation of breathers in cigar-shaped Bose-Einstein condensates
- Bose-Einstein condensation: Twenty years after
- Modulation of localized solutions in quadratic-cubic nonlinear Schrödinger equation with inhomogeneous coefficients
- Shock waves in strongly interacting Fermi gas from time-dependent density functional calculations
- Structure and dynamics of a rotating superfluid Bose-Fermi mixture
- Bright solitons in ultracold atoms
- Validating Simple Dynamical Simulations of the Unitary Fermi Gas
- Universal scaling in a trapped Fermi super-fluid in the BCS-unitarity crossover
- Low-temperature thermodynamics of the unitary Fermi gas: superfluid fraction, first sound and second sound
- Unidimensional reduction of the 3D Gross-Pitaevskii equation with two- and three-body interactions
- Trapped unitary two-component Fermi gases with up to ten particles
- Self-consistent derivation of the modified Gross-Pitaevskii equation with Lee-Huang-Yang correction
- BCS-BEC crossover in a trapped Fermi super-fluid using a density-functional equation
- Surface Effects in the Unitary Fermi Gas
- Viscosity-entropy ratio of the unitary Fermi gas from zero-temperature elementary excitations
- Universal behavior of a trapped Fermi superfluid in the BCS-unitarity crossover
- Double-layer Bose-Einstein condensates: A quantum phase transition in the transverse direction, and reduction to two dimensions
- First and second sound of a unitary Fermi gas in highly oblate harmonic traps
- Quasi-one-dimensional approximation for Bose-Einstein condensates transversely trapped by a funnel potential
- Weak-coupling to unitarity crossover in Bose-Fermi mixtures: Mixing-demixing and spontaneous symmetry breaking in trapped systems
- Two-dimensional composite solitons in a spin-orbit-coupled Fermi gas in free space
- Dynamical properties of the unitary Fermi gas: collective modes and shock waves
- Collective modes in the anisotropic unitary Fermi gas and the inclusion of a backflow term
- Detecting Entrainment in Fermi-Bose Mixtures
- Nonequilibrium Kinetics of One-Dimensional Bose Gases
- Superfluid properties of bright solitons in a ring
- Dynamics of shock waves in a superfluid unitary Fermi gas
- Critical velocity for superfluidity in the one-dimensional mean-field regime: From matter to light quantum fluids
- Critical velocity, vortex shedding and drag in a unitary Fermi superfluid
- Crow instability in unitary Fermi gas
- Goldstone and Higgs Hydrodynamics in the BCS-BEC Crossover
- Dispersive effects in the unitary Fermi gas