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:0911.0984 · Physical Review A

Trapped Two-Dimensional Fermi Gases with Population Imbalance

Bert Van Schaeybroeck, Achilleas Lazarides, Serghei N. Klimin, Jacques Tempere

Published Nov 5, 2009• 1 citation
arXivHTMLPDF

Abstract

We study population imbalanced Fermi mixtures under quasi-two-dimensional confinement at zero temperature. Using mean-field theory and the local-density approximation, we study the ground state configuration throughout the BEC-BCS crossover. We find the trapped system to be either fully normal or to consist of a superfluid core surrounded by a normal shell, which is itself either fully or partially polarized. Upon changing the trap imbalance, the trap configuration may undergo continuous transitions between the different ground states. Finally, we argue that thermal equilibration throughout the trap will be considerably slowed down at low temperatures when a superfluid phase is present.

DOI
10.48550/arxiv.0911.0984

Related papers

Phase diagram of a cold polarized Fermi gas in two dimensions

Lianyi He, Pengfei Zhuang

The superfluid phase diagrams of a two-dimensional cold polarized Fermi gas in the BCS-BEC crossover are systematically and analytically investigated. In the BCS-Leggett mean-field theory, the transition from unpolarized superfluid phase to normal phase is always of first order. For a homogeneous system, the two critical Zeeman fields and the critical population imbalance are analytically determined in the whole coupling parameter region, and the superfluid-normal mixed phase is shown to be the ground state between the two critical fields. The density profile in the presence of a harmonic trap calculated in the local-density approximation exhibits a shell structure, a superfluid core at the center, and a normal shell outside. For weak interaction, the normal shell contains a partially polarized cloud with constant density difference surrounded by a fully polarized state. For strong interaction, the normal shell is in a fully polarized state with a density profile depending only on the global population imbalance. The difermion bound states can survive in the whole highly imbalanced normal phase.

arXiv:0801.3127•Physical Review A•Sep 19, 2008•46 citations

Finite temperature effects in trapped Fermi gases with population imbalance

Chih-Chun Chien, Qijin Chen, Yan He +1 more

We study the finite temperature $T$ behavior of trapped Fermi gases as they undergo BCS--Bose-Einstein condensation (BEC) crossover, in the presence of a population imbalance. Our results, in qualitative agreement with recent experiments, show how the superfluid phase transition is directly reflected in the particle density profiles. We demonstrate that at $T\ensuremath{\ne}0$ and in the near-BEC and unitary regimes, the polarization is excluded from the superfluid core. Importantly, a substantial polarization fraction is carried by a normal region of the trap having strong pair correlations, which we associate with noncondensed pairs or the ``pseudogap phase.''

arXiv:cond-mat/0605684•Physical Review A•Aug 24, 2006•23 citations

Superfluidity at the BEC-BCS crossover in two-dimensional Fermi gases with population and mass imbalance

G. J. Conduit, P. H. Conlon, Benjamin D. Simons

We explore the zero-temperature phase behavior of a two-dimensional two-component atomic Fermi gas with population and mass imbalance in the regime of the BEC-BCS crossover. Working in the mean-field approximation, we show that the normal and homogeneous balanced superfluid phases are separated by an inhomogeneous superfluid phase of Fulde-Ferrel-Larkin-Ovchinnikov (FFLO) type. We obtain an analytical expression for the line of continuous transitions separating the normal and inhomogeneous FFLO phases. We further show that the transition from the FFLO phase to the homogeneous balanced superfluid is discontinuous leading to phase separation. If the species have different masses, the superfluid phase is favored when the lighter species is in excess. We explore the implications of these findings for the properties of the two-component Fermi gas in the atomic trap geometry. Finally, we compare and contrast our findings with the predicted phase behavior of the electron-hole bilayer system.

arXiv:0805.2726•Physical Review A•May 29, 2008•62 citations

Superfluidity in two-dimensional imbalanced Fermi gases

Heron Caldas, A L Mota, R L S Farias +1 more

We study the zero temperature ground state of a two-dimensional atomic Fermi gas with chemical potential and population imbalance in the mean-field approximation. All calculations are performed in terms of the two-body binding energy B , whose variation allows one to investigate the evolution from the BEC to the BCS regimes. By means of analytical and exact expressions we show that, similarly to what is found in three dimensions, at fixed chemical potentials, BCS is the ground state until the critical imbalance h c , after which there is a first-order phase transition to the normal state. We find that h c , the Chandrasekhar–Clogston limit of superfluidity, has the same value as in three-dimensional systems. We show that for a fixed ratio B / F , where F is the two-dimensional Fermi energy, as the density imbalance m is increased from zero, the ground state evolves from BCS to phase separation to the normal state. At the critical imbalance m c , phase separation is not supported and the normal phase is energetically preferable. The BCS–BEC crossover is discussed in balanced and imbalanced configurations. Possible pictures of what may be found experimentally in these systems are also shown. We also investigate the necessary conditions for the existence of bound states in the balanced and imbalanced normal phase.

arXiv:1108.5407•Journal of Statistical Mechanics Theory and Experiment•Oct 23, 2012•14 citations

Profiles of near-resonant population-imbalanced trapped Fermi gases

Theja N. De Silva, Erich J. Mueller

We investigate the density profiles of a partially polarized trapped Fermi gas in the BCS-BEC crossover region using mean field theory within the local density approximation. Within this approximation the gas is phase separated into concentric shells. We describe how the structure of these shells depends upon the polarization and the interaction strength. A comparison with experiments yields insight into the possibility of a polarized superfluid phase.

arXiv:cond-mat/0601314•Physical Review A•May 19, 2006•109 citations

Imbalanced Superfluid Phase of a Trapped Fermi Gas in the BCS–BEC Crossover Regime

Takeshi Mizushima, Masanori Ichioka, Kazushige Machida

We theoretically investigate the ground state of trapped neutral fermions with population imbalance in the BCS-BEC crossover regime. On the basis of the single-channel Hamiltonian, we perform full numerical calculations of the Bogoliubov-de Gennes equation coupled with the regularized gap and number equations. The zero-temperature phase diagram in the crossover regime is presented, where the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) pairing state governs the weak-coupling BCS region of a resonance. It is found that the FFLO oscillation vanishes in the BEC side, in which the system under population imbalance turns into a phase separation (PS) between locally binding superfluid and fully polarized spin domains. We also demonstrate numerical calculations with a large particle number O(10^5), comparable to that observed in recent experiments. The resulting density profile on a resonance yields the PS, which is in good agreement with the recent experiments, while the FFLO modulation exists in the pairing field. It is also proposed that the most favorable location for the detection of the FFLO oscillation is in the vicinity of the critical population imbalance in the weak coupling BCS regime, where the oscillation periodicity becomes much larger than the interparticle spacing. Finally, we analyze the radio-frequency (RF) spectroscopy in the imbalanced system. The clear difference in the RF spectroscopy between BCS and BEC sides reveals the structure of the pairing field and local ``magnetization''.

arXiv:0705.3361•Journal of the Physical Society of Japan•Oct 10, 2007•34 citations
We study population imbalanced Fermi mixtures under quasi-two-dimensional confinement at zero temperature. Using mean-field theory and the local-density approximation, we study the ground state configuration throughout the BEC-BCS crossover. We find the trapped system to be either fully normal or to consist of a superfluid core surrounded by a normal shell, which is itself either fully or partially polarized. Upon changing the trap imbalance, the trap configuration may undergo continuous transitions between the different ground states. Finally, we argue that thermal equilibration throughout the trap will be considerably slowed down at low temperatures when a superfluid phase is present.
The superfluid phase diagrams of a two-dimensional cold polarized Fermi gas in the BCS-BEC crossover are systematically and analytically investigated. In the BCS-Leggett mean-field theory, the transition from unpolarized superfluid phase to normal phase is always of first order. For a homogeneous system, the two critical Zeeman fields and the critical population imbalance are analytically determined in the whole coupling parameter region, and the superfluid-normal mixed phase is shown to be the ground state between the two critical fields. The density profile in the presence of a harmonic trap calculated in the local-density approximation exhibits a shell structure, a superfluid core at the center, and a normal shell outside. For weak interaction, the normal shell contains a partially polarized cloud with constant density difference surrounded by a fully polarized state. For strong interaction, the normal shell is in a fully polarized state with a density profile depending only on the global population imbalance. The difermion bound states can survive in the whole highly imbalanced normal phase.
We study the finite temperature TTT behavior of trapped Fermi gases as they undergo BCS--Bose-Einstein condensation (BEC) crossover, in the presence of a population imbalance. Our results, in qualitative agreement with recent experiments, show how the superfluid phase transition is directly reflected in the particle density profiles. We demonstrate that at $T\ensuremath{\ne}0$ and in the near-BEC and unitary regimes, the polarization is excluded from the superfluid core. Importantly, a substantial polarization fraction is carried by a normal region of the trap having strong pair correlations, which we associate with noncondensed pairs or the ``pseudogap phase.''
We explore the zero-temperature phase behavior of a two-dimensional two-component atomic Fermi gas with population and mass imbalance in the regime of the BEC-BCS crossover. Working in the mean-field approximation, we show that the normal and homogeneous balanced superfluid phases are separated by an inhomogeneous superfluid phase of Fulde-Ferrel-Larkin-Ovchinnikov (FFLO) type. We obtain an analytical expression for the line of continuous transitions separating the normal and inhomogeneous FFLO phases. We further show that the transition from the FFLO phase to the homogeneous balanced superfluid is discontinuous leading to phase separation. If the species have different masses, the superfluid phase is favored when the lighter species is in excess. We explore the implications of these findings for the properties of the two-component Fermi gas in the atomic trap geometry. Finally, we compare and contrast our findings with the predicted phase behavior of the electron-hole bilayer system.
We study the zero temperature ground state of a two-dimensional atomic Fermi gas with chemical potential and population imbalance in the mean-field approximation. All calculations are performed in terms of the two-body binding energy B , whose variation allows one to investigate the evolution from the BEC to the BCS regimes. By means of analytical and exact expressions we show that, similarly to what is found in three dimensions, at fixed chemical potentials, BCS is the ground state until the critical imbalance h c , after which there is a first-order phase transition to the normal state. We find that h c , the Chandrasekhar–Clogston limit of superfluidity, has the same value as in three-dimensional systems. We show that for a fixed ratio B / F , where F is the two-dimensional Fermi energy, as the density imbalance m is increased from zero, the ground state evolves from BCS to phase separation to the normal state. At the critical imbalance m c , phase separation is not supported and the normal phase is energetically preferable. The BCS–BEC crossover is discussed in balanced and imbalanced configurations. Possible pictures of what may be found experimentally in these systems are also shown. We also investigate the necessary conditions for the existence of bound states in the balanced and imbalanced normal phase.
We theoretically investigate the ground state of trapped neutral fermions with population imbalance in the BCS-BEC crossover regime. On the basis of the single-channel Hamiltonian, we perform full numerical calculations of the Bogoliubov-de Gennes equation coupled with the regularized gap and number equations. The zero-temperature phase diagram in the crossover regime is presented, where the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) pairing state governs the weak-coupling BCS region of a resonance. It is found that the FFLO oscillation vanishes in the BEC side, in which the system under population imbalance turns into a phase separation (PS) between locally binding superfluid and fully polarized spin domains. We also demonstrate numerical calculations with a large particle number O(10^5), comparable to that observed in recent experiments. The resulting density profile on a resonance yields the PS, which is in good agreement with the recent experiments, while the FFLO modulation exists in the pairing field. It is also proposed that the most favorable location for the detection of the FFLO oscillation is in the vicinity of the critical population imbalance in the weak coupling BCS regime, where the oscillation periodicity becomes much larger than the interparticle spacing. Finally, we analyze the radio-frequency (RF) spectroscopy in the imbalanced system. The clear difference in the RF spectroscopy between BCS and BEC sides reveals the structure of the pairing field and local ``magnetization''.