From the Bogoliubov-de Gennes equations for superfluid fermions to the Gross-Pitaevskii equation for condensed bosons

Abstract

We derive the time-independent Gross-Pitaevskii equation at zero temperature for condensed bosons, which form as bound-fermion pairs when the mutual fermionic attractive interaction is sufficiently strong, from the strong-coupling limit of the Bogoliubov-de Gennes equations that describe superfluid fermions in the presence of an external potential. Three-body corrections to the Gross-Pitaevskii equation are also obtained by our approach. Our results are relevant to the recent advances with ultracold fermionic atoms in a trap.

4 pages

References in corpus (2)

• Creation of ultracold molecules from a Fermi gas of atoms
• Three body problem in a dilute Bose-Einstein condensate

Cited by in corpus (71)

• The BCS-BEC crossover: From ultra-cold Fermi gases to nuclear systems
• From Bloch Oscillations to Many Body Localization in Clean Interacting Systems
• Trapped fermions with density imbalance in the BEC limit
• BCS-BEC crossover of neutron pairs in symmetric and asymmetric nuclear matter
• Condensate Fraction of a Fermi Gas in the BCS-BEC Crossover
• Extended Thomas-Fermi Density Functional for the Unitary Fermi Gas
• Dark solitons in a superfluid Fermi gas
• Nonlinear Schrödinger equation for a superfluid Fermi gas from BCS to Bose crossover
• The Josephson effect throughout the BCS-BEC crossover
• Temperature and coupling dependence of the universal contact intensity for an ultracold Fermi gas
• DC Josephson Effect with Fermi gases in the Bose-Einstein regime
• Traveling Dark Solitons in Superfluid Fermi Gases
• Snake instability of dark solitons in fermionic superfluids
• Universality in Phase Transitions for Ultracold Fermionic Atoms
• Effective Nonlinear Schrödinger Equations for Cigar-Shaped and Disk-Shaped Fermi Superfluids at Unitarity
• Momentum distribution of a trapped Fermi gas with large scattering length
• Thermodynamics and superfluid density in BCS-BEC crossover with and without population imbalance
• Comparison of Different Pairing Fluctuation Approaches to BCS-BEC Crossover
• Atypical BCS-BEC crossover induced by quantum-size effects
• Functional Integral for Ultracold Fermionic Atoms
• Grey solitons in a strongly interacting superfluid Fermi Gas
• Gap equation with pairing correlations beyond mean field and its equivalence to a Hugenholtz-Pines condition for fermion pairs
• Imbalanced Superfluid Phase of a Trapped Fermi Gas in the BCS-BEC Crossover Regime
• Ground State Description of a Single Vortex in an Atomic Fermi gas: From BCS to Bose-Einstein Condensation
• Structure and dynamics of a rotating superfluid Bose-Fermi mixture
• Rotating quantum turbulence in the unitary Fermi gas
• Popov approximation for composite bosons in the BCS-BEC crossover
• Temperature dependence of a vortex in a superfluid Fermi gas
• Equation for the superfluid gap obtained by coarse graining the Bogoliubov-de Gennes equations throughout the BCS-BEC crossover
• Superfluid equation of state of dilute composite bosons
• Integrable model for density-modulated quantum condensates: solitons passing through a soliton lattice
• Dark Solitons in Holographic Superfluids
• Berezinskii-Kosterlitz-Thouless transition and BCS-Bose crossover in the two-dimensional attractive Hubbard model
• Generation of vortices and stabilization of vortex lattices in holographic superfluids
• Unidimensional reduction of the 3D Gross-Pitaevskii equation with two- and three-body interactions
• Superconducting nanofilms: molecule-like pairing induced by quantum confinement
• Finite temperature effects in trapped Fermi gases with population imbalance
• Josephson oscillations and self-trapping of superfluid fermions in a double-well potential
• Swallowtail Band Structure of the Superfluid Fermi Gas in an Optical Lattice
• Dark solitons dynamics and snake instability in superfluid Fermi gases trapped by an anisotropic harmonic potential
• Proper phase imprinting method for a dark soliton excitation in a superfluid Fermi mixture
• Quantum dark solitons in ultracold one-dimensional Bose and Fermi gases
• Pair Wave Functions in Atomic Fermi Condensates
• Persistent currents in ultracold gases
• Crossover dynamics of dispersive shocks in Bose-Einstein condensates characterized by two and three-body interactions
• Josephson effect at finite temperature along the BCS-BEC crossover
• Derivation of hydrodynamics for the gapless mode in the BEC-BCS crossover from the exact one-loop effective action
• Ginzburg-Landau theory of a trapped Fermi gas with a BEC-BCS crossover
• Vortex structure and spectrum of atomic Fermi superfluid in a spherical bubble trap
• Role of the effective range in the density-induced BEC-BCS crossover
• Incompatibility of time-dependent Bogoliubov--de-Gennes and Ginzburg--Landau equations
• Exactly solvable Gross-Pitaevskii type equations
• Correlated Pair Approach to Composite Boson Scattering Lengths
• Superfluid equation of state of cold fermionic gases in the Bose-Einstein regime
• Collective Modes and Stability of Bose-Fermi Mixtures with a BCS-BEC Crossover
• Weak-coupling to unitarity crossover in Bose-Fermi mixtures: Mixing-demixing and spontaneous symmetry breaking in trapped systems
• Bogolubov-Hartree-Fock theory for strongly interacting fermions in the low density limit
• Effective action for superfluid Fermi systems in the strong-coupling limit
• Emergence of dark soliton signatures in a one-dimensional unpolarized attractive Fermi gas on a ring
• Non-local equation for the superconducting gap parameter
• Time-dependent Gross-Pitaevskii equation for composite bosons as the strong-coupling limit of the fermionic BCS-RPA approximation
• Aspects of Superfluid Cold Atomic Gases in Optical Lattices
• Bound states in a superfluid vortex: A detailed study along the BCS-BEC crossover
• Observation of Breathers in an Attractive Bose Gas
• Extension of the Ginzburg - Landau approach for ultracold Fermi gases below a critical temperature
• Tuning Dissipation and Excitations in Superfluid Fermi Gases with a Moving Impurity
• Dynamical mean-field equations for strongly interacting fermionic atoms in a potential trap
• Integral equation for inhomogeneous condensed bosons generalizing the Gross-Pitaevskii differential equation
• Bose-representation for a strongly coupled nonequilibrim fermionic superfluid in a time-dependent trap
• When are two fermions a simple boson? New Gross-Pitaevskii actions for cold Fermi condensates
• Equilibrium and Non-equilibrium Gross-Pitaevskii Lattice Dynamics: Interactions, Disorder, and Thermalization