Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:cond-mat/0610675

Exact treatment of trapped imbalanced fermions in the BEC limit

P. Pieri, Giancarlo Strinati Calvanese

Published Jan 1, 2007• 0 citations
arXivHTMLPDF

Abstract

In the present contribution we shall analyze the effects of imbalancing the populations of two-component trapped fermions in the BEC (strong-coupling) limit of the attractive interaction between fermions of different components. In particular, we shall derive a set of coupled equations which describe composite bosons and excess fermions in this limit,

DOI
10.3254/978-1-58603-846-5-621

Related papers

Trapped Fermions with Density Imbalance in the Bose-Einstein Condensate Limit

P. Pieri, Giancarlo Calvanese Strinati

We analyze the effects of imbalancing the populations of two-component trapped fermions, in the Bose-Einstein condensate limit of the attractive interaction between different fermions. Starting from the gap equation with two fermionic chemical potentials, we derive a set of coupled equations that describe composite bosons and excess fermions. We include in these equations the processes leading to the correct dimer-dimer and dimer-fermion scattering lengths. The coupled equations are then solved in the Thomas-Fermi approximation to obtain the density profiles for composite bosons and excess fermions, which are relevant to the recent experiments with trapped fermionic atoms.

arXiv:cond-mat/0512354•Physical Review Letters•Apr 21, 2006•104 citations

Trap-imbalanced fermion mixtures

M. Iskin, Carl J. Williams

We analyze the ground-state phases of two-component $(\ensuremath{\sigma}\ensuremath{\equiv}{\ensuremath{\uparrow},\ensuremath{\downarrow}})$ population- and mass-balanced (${N}_{\ensuremath{\uparrow}}={N}_{\ensuremath{\downarrow}}$ and ${m}_{\ensuremath{\uparrow}}={m}_{\ensuremath{\downarrow}}$) but trap-imbalanced $({\ensuremath{\omega}}_{\ensuremath{\uparrow}}\ensuremath{\ne}{\ensuremath{\omega}}_{\ensuremath{\downarrow}})$ fermion mixtures as a function of interaction strength from the weak attraction Bardeen-Cooper-Schrieffer (BCS) to the strong attraction Bose-Einstein condensation (BEC) limit. In the BCS limit, we find that the unpolarized superfluid (UPS) fermions exist away from the central core of the trapping potentials, and are surrounded by partially $\ensuremath{\sigma}$-polarized normal $(\mathrm{P}\ensuremath{\sigma}\mathrm{PN})$ fermions. As the interactions increase towards unitarity, we find that the central $\mathrm{P}\ensuremath{\sigma}\mathrm{PN}$ core first transitions to a UPS, and then expands towards the edges until the entire mixture becomes a UPS in the BEC limit.

arXiv:0710.0353•Physical Review A•Jan 7, 2008•12 citations

Fermi-Fermi mixtures in the strong-attraction limit

M. Iskin, C. A. R. Sá de Melo

The phase diagrams of low density Fermi-Fermi mixtures with equal or unequal masses and equal or unequal populations are described at zero and finite temperatures in the strong attraction limit. In this limit, the Fermi-Fermi mixture can be described by a weakly interacting Bose-Fermi mixture, where the bosons correspond to Feshbach molecules and the fermions correspond to excess atoms. First, we discuss the three and four fermion scattering processes, and use the exact boson-fermion and boson-boson scattering lengths to generate the phase diagrams in terms of the underlying fermion-fermion scattering length. In three dimensions, in addition to the normal and uniform superfluid phases, we find two stable nonuniform states corresponding to (i) phase separation between pure unpaired (excess) and pure paired fermions (molecular bosons); and (ii) phase separation between pure excess fermions and a mixture of excess fermions and molecular bosons. Lastly, we also discuss the effects of the trapping potential in the density profiles of condensed and noncondensed molecular bosons, and excess fermions at zero and finite temperatures, and discuss possible implications of our findings to experiments involving mixtures of ultracold fermions.

arXiv:0709.4424•Physical Review A•Jan 31, 2008•41 citations

Popov approximation for composite bosons in the BCS-BEC crossover

P. Pieri, Giancarlo Calvanese Strinati

Theoretical treatments of the BCS-BEC crossover need to provide as accurate as possible descriptions of the two regimes where the diluteness condition applies, either in terms of the constituent fermions (BCS limit) or of the composite bosons which form as bound-fermion pairs (BEC limit). This has to occur via a single fermionic theory that bridges across these two limiting representations. In this paper, we set up successive improvements of the fermionic theory, that result into composite bosons described at the level of either the Bogoliubov or the Popov approximations for pointlike bosons. This work bears on the recent experimental advances on the BCS-BEC crossover with trapped Fermi atoms, which show the need for accurate theoretical descriptions of the BEC side of the crossover.

arXiv:cond-mat/0407728•Physical Review B•Mar 31, 2005•29 citations

Quantum kinetic description of attractive two-component fermions from the weak-coupling Fermi liquid to the strong-coupling Bose liquid regime

Mehrtash Babadi, Eugene Demler

Bulletin of the American Physical Society•Mar 6, 2014•0 citations

Two-component few-fermion mixtures in a one-dimensional trap: Numerical versus analytical approach

Ioannis Brouzos, Peter Schmelcher

We explore a few-fermion mixture consisting of two components that are repulsively interacting and confined in a one-dimensional harmonic trap. Different scenarios of population imbalance ranging from the completely imbalanced case where the physics of a single impurity in the Fermi sea is discussed to the partially imbalanced and equal population configurations are investigated. For the numerical calculations the multiconfigurational time-dependent Hartree method is employed, extending its application to few-fermion systems. Apart from numerical calculations we generalize our ansatz for a correlated pair wave function proposed recently [I. Brouzos and P. Schmelcher, Phys. Rev. Lett. 108, 045301 (2012)] for bosons to mixtures of fermions. From weak to strong coupling between the components the energies, the densities and the correlation properties of one-dimensional systems change vastly with an upper limit set by fermionization where for infinite repulsion all fermions can be mapped to identical ones. The numerical and analytical treatments are in good agreement with respect to the description of this crossover. We show that for equal populations each pair of different component atoms splits into two single peaks in the density while for partial imbalance additional peaks and plateaus arise for very strong interaction strengths. The case of a single-impurity atom shows rich behavior of the energy and density as we approach fermionization and is directly connected to recent experiments [G. Z\"urn et al., Phys. Rev. Lett. 108, 075303 (2012)].

arXiv:1209.2891•Physical Review A•Feb 6, 2013•43 citations
In the present contribution we shall analyze the effects of imbalancing the populations of two-component trapped fermions in the BEC (strong-coupling) limit of the attractive interaction between fermions of different components. In particular, we shall derive a set of coupled equations which describe composite bosons and excess fermions in this limit,
We analyze the effects of imbalancing the populations of two-component trapped fermions, in the Bose-Einstein condensate limit of the attractive interaction between different fermions. Starting from the gap equation with two fermionic chemical potentials, we derive a set of coupled equations that describe composite bosons and excess fermions. We include in these equations the processes leading to the correct dimer-dimer and dimer-fermion scattering lengths. The coupled equations are then solved in the Thomas-Fermi approximation to obtain the density profiles for composite bosons and excess fermions, which are relevant to the recent experiments with trapped fermionic atoms.
We analyze the ground-state phases of two-component $(\ensuremath{\sigma}\ensuremath{\equiv}{\ensuremath{\uparrow},\ensuremath{\downarrow}})$ population- and mass-balanced (${N}_{\ensuremath{\uparrow}}={N}_{\ensuremath{\downarrow}}$ and ${m}_{\ensuremath{\uparrow}}={m}_{\ensuremath{\downarrow}}$) but trap-imbalanced $({\ensuremath{\omega}}_{\ensuremath{\uparrow}}\ensuremath{\ne}{\ensuremath{\omega}}_{\ensuremath{\downarrow}})$ fermion mixtures as a function of interaction strength from the weak attraction Bardeen-Cooper-Schrieffer (BCS) to the strong attraction Bose-Einstein condensation (BEC) limit. In the BCS limit, we find that the unpolarized superfluid (UPS) fermions exist away from the central core of the trapping potentials, and are surrounded by partially $\ensuremath{\sigma}$-polarized normal $(\mathrm{P}\ensuremath{\sigma}\mathrm{PN})$ fermions. As the interactions increase towards unitarity, we find that the central $\mathrm{P}\ensuremath{\sigma}\mathrm{PN}$ core first transitions to a UPS, and then expands towards the edges until the entire mixture becomes a UPS in the BEC limit.
The phase diagrams of low density Fermi-Fermi mixtures with equal or unequal masses and equal or unequal populations are described at zero and finite temperatures in the strong attraction limit. In this limit, the Fermi-Fermi mixture can be described by a weakly interacting Bose-Fermi mixture, where the bosons correspond to Feshbach molecules and the fermions correspond to excess atoms. First, we discuss the three and four fermion scattering processes, and use the exact boson-fermion and boson-boson scattering lengths to generate the phase diagrams in terms of the underlying fermion-fermion scattering length. In three dimensions, in addition to the normal and uniform superfluid phases, we find two stable nonuniform states corresponding to (i) phase separation between pure unpaired (excess) and pure paired fermions (molecular bosons); and (ii) phase separation between pure excess fermions and a mixture of excess fermions and molecular bosons. Lastly, we also discuss the effects of the trapping potential in the density profiles of condensed and noncondensed molecular bosons, and excess fermions at zero and finite temperatures, and discuss possible implications of our findings to experiments involving mixtures of ultracold fermions.
Theoretical treatments of the BCS-BEC crossover need to provide as accurate as possible descriptions of the two regimes where the diluteness condition applies, either in terms of the constituent fermions (BCS limit) or of the composite bosons which form as bound-fermion pairs (BEC limit). This has to occur via a single fermionic theory that bridges across these two limiting representations. In this paper, we set up successive improvements of the fermionic theory, that result into composite bosons described at the level of either the Bogoliubov or the Popov approximations for pointlike bosons. This work bears on the recent experimental advances on the BCS-BEC crossover with trapped Fermi atoms, which show the need for accurate theoretical descriptions of the BEC side of the crossover.
We explore a few-fermion mixture consisting of two components that are repulsively interacting and confined in a one-dimensional harmonic trap. Different scenarios of population imbalance ranging from the completely imbalanced case where the physics of a single impurity in the Fermi sea is discussed to the partially imbalanced and equal population configurations are investigated. For the numerical calculations the multiconfigurational time-dependent Hartree method is employed, extending its application to few-fermion systems. Apart from numerical calculations we generalize our ansatz for a correlated pair wave function proposed recently [I. Brouzos and P. Schmelcher, Phys. Rev. Lett. 108, 045301 (2012)] for bosons to mixtures of fermions. From weak to strong coupling between the components the energies, the densities and the correlation properties of one-dimensional systems change vastly with an upper limit set by fermionization where for infinite repulsion all fermions can be mapped to identical ones. The numerical and analytical treatments are in good agreement with respect to the description of this crossover. We show that for equal populations each pair of different component atoms splits into two single peaks in the density while for partial imbalance additional peaks and plateaus arise for very strong interaction strengths. The case of a single-impurity atom shows rich behavior of the energy and density as we approach fermionization and is directly connected to recent experiments [G. Z\"urn et al., Phys. Rev. Lett. 108, 075303 (2012)].