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Fulde-Ferrell-Larkin-Ovchinnikov states in one-dimensional spin-polarized ultracold atomic Fermi gases
Statistical Mechanics · Submitted 27 Jul 2007
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim We find that a spatially inhomogeneous Fulde-Ferrell-Larkin-Ovchinnikov phase, which lies between the fully paired BCS state and the fully polarized normal state, dominates most of the phase diagram of a uniform gas.
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We present a systematic study of quantum phases in a one-dimensional spin-polarized Fermi gas. Three comparative theoretical methods are used to explore the phase diagram at zero temperature: the mean-field theory with either an order parameter in a single-plane-wave form or a self-consistently determined order parameter using the Bogoliubov-de Gennes equations, as well as the exact soluble Bethe ansatz method. We find that a spatially inhomogeneous Fulde-Ferrell-Larkin-Ovchinnikov phase, which lies between the fully paired BCS state and the fully polarized normal state, dominates most of the phase diagram of a uniform gas. The phase transition from the BCS state to the Fulde-Ferrell-Larkin-Ovchinnikov phase is of second order, and therefore there are no phase separation states in one-dimensional homogeneous polarized gases. This is in sharp contrast to the three-dimensional situation, where a phase separation regime is predicted to occupy a very large space in the phase diagram. We conjecture that the prediction of the dominance of the phase separation phases in three dimension could be an artifact of the non-self-consistent mean-field approximation, which is heavily used in the study of three-dimensional polarized Fermi gases. We consider also the effect of a harmonic trapping potential on the phase diagram, and find that in this case the trap generally leads to phase separation, in accord with the experimental observations for a trapped gas in three dimension. We finally investigate the local fermionic density of states of the Fulde-Ferrell-Larkin-Ovchinnikov ansatz. A two-energy-gap structure is shown up, which could be used as an experimental probe of the Fulde-Ferrell-Larkin-Ovchinnikov states.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We present a systematic study of quantum phases in a one-dimensional spin-polarized Fermi gas. | contribution 0.99 | 0.93 | 0.03 | asserted 0.76 |
| s1 | Three comparative theoretical methods are used to explore the phase diagram at zero temperature: the mean-field theory with either an order parameter in a single-plane-wave form or a self-consistently determined order parameter using the Bogoliubov-de Gennes equations, as well as the exact soluble Bethe ansatz method. | method 1.00 | 0.87 | 0.03 | asserted 0.94 |
| s2 | We find that a spatially inhomogeneous Fulde-Ferrell-Larkin-Ovchinnikov phase, which lies between the fully paired BCS state and the fully polarized normal state, dominates most of the phase diagram of a uniform gas. | result 1.00 | 0.96 | 0.76 | asserted 1.00 |
| s3 | The phase transition from the BCS state to the Fulde-Ferrell-Larkin-Ovchinnikov phase is of second order, and therefore there are no phase separation states in one-dimensional homogeneous polarized gases. | result 0.81 | 0.93 | 0.28 | asserted 1.00 |
| s4 | This is in sharp contrast to the three-dimensional situation, where a phase separation regime is predicted to occupy a very large space in the phase diagram. | interpretation 0.56 | 0.09 | 0.09 | asserted 0.85 |
| s5 | We conjecture that the prediction of the dominance of the phase separation phases in three dimension could be an artifact of the non-self-consistent mean-field approximation, which is heavily used in the study of three-dimensional polarized Fermi gases. | interpretation 1.00 | 0.13 | 0.09 | speculative 0.94 |
| s6 | We consider also the effect of a harmonic trapping potential on the phase diagram, and find that in this case the trap generally leads to phase separation, in accord with the experimental observations for a trapped gas in three dimension. | result 0.98 | 0.95 | 0.06 | asserted 0.95 |
| s7 | We finally investigate the local fermionic density of states of the Fulde-Ferrell-Larkin-Ovchinnikov ansatz. | contribution 0.97 | 0.92 | 0.02 | unclear 0.53 |
| s8 | A two-energy-gap structure is shown up, which could be used as an experimental probe of the Fulde-Ferrell-Larkin-Ovchinnikov states. | result 0.76 | 0.91 | 0.05 | hedged possibility 0.66 |
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Original abstract
We present a systematic study of quantum phases in a one-dimensional spin-polarized Fermi gas. Three comparative theoretical methods are used to explore the phase diagram at zero temperature: the mean-field theory with either an order parameter in a single-plane-wave form or a self-consistently determined order parameter using the Bogoliubov-de Gennes equations, as well as the exact soluble Bethe ansatz method. We find that a spatially inhomogeneous Fulde-Ferrell-Larkin-Ovchinnikov phase, which lies between the fully paired BCS state and the fully polarized normal state, dominates most of the phase diagram of a uniform gas. The phase transition from the BCS state to the Fulde-Ferrell-Larkin-Ovchinnikov phase is of second order, and therefore there are no phase separation states in one-dimensional homogeneous polarized gases. This is in sharp contrast to the three-dimensional situation, where a phase separation regime is predicted to occupy a very large space in the phase diagram. We conjecture that the prediction of the dominance of the phase separation phases in three dimension could be an artifact of the non-self-consistent mean-field approximation, which is heavily used in the study of three-dimensional polarized Fermi gases. We consider also the effect of a harmonic trapping potential on the phase diagram, and find that in this case the trap generally leads to phase separation, in accord with the experimental observations for a trapped gas in three dimension. We finally investigate the local fermionic density of states of the Fulde-Ferrell-Larkin-Ovchinnikov ansatz. A two-energy-gap structure is shown up, which could be used as an experimental probe of the Fulde-Ferrell-Larkin-Ovchinnikov states.
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Cites as background 6 papers
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A number of theoretical papers have sought to explain these experiments on polarized atomic Fermi gases [ref] . >From these analyses, the issues that require timely clarification may be summarized as follows:
Quantum Liquid Crystal Phases in Fermionic Superfluids with Pairing between Fermion Species of Unequal Densities · Introduction · 0.86
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A number of theoretical papers have sought to explain these experiments on polarized atomic Fermi gases [ref] . >From these analyses, the issues that require timely clarification may be summarized as follows:
Surface Energy in Cold Asymmetrical Fermion Superfluids · Introduction · 0.86
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A number of theoretical papers have sought to explain these experiments on polarized atomic Fermi gases [ref] . >From these analyses, the issues that require timely clarification may be summarized as follows:
Fermion pairing with population imbalance: energy landscape and phase separation in a constrained Hilbert subspace · Introduction · 0.86
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