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:1101.5639 · Physical Review A

Pairing, ferromagnetism, and condensation of a normal spin-1 Bose gas

Stefan S. Natu, Erich J. Mueller

Published Nov 22, 2011• 22 citations
arXivHTMLPDF

Abstract

We find the conditions under which the normal state of a spin-1 Bose gas is unstable toward condensation, ferromagnetism, liquid crystalline-like nematicity, and Bardeen-Cooper-Schrieffer-like pairing. When the spin-dependent interactions are much weaker than the density-density interaction there is direct transition from a featureless normal state to a fully ordered Bose-Einstein condensate with either ferromagnetic or nematic order. When the spin-independent and spin-dependent interactions are of comparable magnitude, we find several different symmetry breaking transitions at intermediate temperatures above the Bose-condensation transition temperature. We make predictions for the ${T}_{c}$ for these transitions, and assess the role of magnetic field and finite system size.

DOI
10.1103/physreva.84.053625

Related papers

Superfluid transition of a ferromagnetic Bose gas

Pye Ton How, Sungkit Yip

The strongly ferromagnetic spin-1 Bose-Einstein condensate has recently been realized with atomic Li7 . It was predicted that a strong ferromagnetic interaction can drive the normal gas into a magnetized phase at a temperature above the superfluid transition, and Li7 likely satisfies the criterion. We reexamine this theoretical proposal employing the two-particle-irreducible effective potential, and conclude that there exists no stable normal magnetized phase for a dilute ferromagnetic Bose gas. For Li7 , we predict that the normal gas undergoes a joint first-order transition and jumps directly into a state with finite condensate density and magnetization. We estimate the size of the first-order jump and examine how a partial spin polarization in the initial sample affects the first-order transition. We propose a qualitative phase diagram at fixed temperature for the trapped gas. Published by the American Physical Society 2024

arXiv:2401.12541•Physical Review Research•May 3, 2024•2 citations

Pairing transitions in a Binary Bose Gas

Shen, Zesheng, Lan Yin

The stable Bardeen-Schrieffer-Cooper (BCS) pairing state of a bosonic system has long been sought theoretically and experimentally. Here we study the BCS state of a binary Bose gas with $s$-wave intra-species repulsions and an inter-species attraction in the mean-field-stable region. We find that above the Bose-Einstein-Condensation (BEC) transtion temperature, there is a phase transtion from the normal state to the BCS state due to inter-species pairing. When the temperature decreases, another phase transtion from the BCS state to the mixture state with both atomic BEC and inter-species pairs occurs. As the temperature is further lowered, the mixuture state is taken over by the BEC state. The phase diagram of this system is presented and experimental implications are discussed.

arXiv:2409.01565•Sep 3, 2024•0 citations

Stoner Ferromagnetism in a Thermal Pseudospin- 1/2 Bose Gas

Juraj Radić, Stefan S. Natu, Victor M. Galitski

We compute the finite-temperature phase diagram of a pseudospin-1/2 Bose gas with contact interactions, using two complementary methods: the random-phase approximation and self-consistent Hartree-Fock theory. We show that the spin-dependent interactions, which break the (pseudo-) spin-rotational symmetry of the Hamiltonian, generally lead to the appearance of a magnetically ordered phase at temperatures above the superfluid transition. In three dimensions, we predict a normal easy-axis (easy-plane) ferromagnet for sufficiently strong repulsive (attractive) interspecies interactions, respectively. The normal easy-axis ferromagnet is the bosonic analog of Stoner ferromagnetism known in electronic systems. For the case of interspecies attraction, we also discuss the possibility of a bosonic analog of the Cooper-paired phase. This state is shown to significantly lose in energy to the transverse ferromagnet in three dimensions, but is more energetically competitive in lower dimensions. Extending our calculations to a spin-orbit-coupled Bose gas with equal Rashba and Dresselhaus-type couplings (as recently realized in experiment), we investigate the possibility of stripe ordering in the normal phase. Within our approximations, however, we do not find an instability towards stripe formation, suggesting that the stripe order melts below the condensation temperature, which is consistent with the experimental observations of Ji et al. [Ji et al., Nat. Phys. 10, 314 (2014)].

arXiv:1409.1242•Physical Review Letters•Oct 31, 2014•11 citations

Metastable spin-phase diagrams in antiferromagnetic Bose-Einstein condensates

Eduardo Serrano-Ensástiga, Francisco Mireles

Spinor Bose-Einstein condensates under external magnetic fields exhibit well-characterized spin domains of its ground state due to spin-dependent interactions. At low temperatures, collision-induced spin-mixing instabilities may promote the condensate to dwell into metastable states occurring near the phase boundaries. In this paper, we study theoretically the metastable spin-phase diagram of a spin-1 antiferromagnetic Bose-Einstein condensate at zero and finite temperatures. The approach makes use of Hartree-Fock theory and exploits the symmetry of the Hamiltonian and of the order parameters yielding a closed system of transcendental equations for the free energy, fully avoiding the use of self-consistency methods. Our results are consistent with recent experiments and allow us to explain qualitatively the different types of observed quench dynamics. In addition, we found that similar phenomena should occur in antiferromagnetic spinor condensates with a sudden change in the temperature. It is shown also that the increase in temperature induces a traceable shift of the ferromagnetic-polar transition boundary, behavior previously not noted by self-consistent mean-field calculations.

arXiv:2109.01986•Physical Review A•Dec 13, 2021•4 citations

Striped ferronematic ground states in a spin-orbit-coupled S=1 Bose gas

Stefan S. Natu, Xiaopeng Li, William S. Cole

We theoretically establish the mean-field phase diagram of a homogeneous spin-1, spin-orbit-coupled Bose gas as a function of the spin-dependent interaction parameter, the Raman coupling strength, and the quadratic Zeeman shift. We find that the interplay between spin-orbit coupling and spin-dependent interactions leads to the occurrence of ferromagnetic or ferronematic phases which also break translational symmetry. For weak Raman coupling, increasing attractive spin-dependent interactions (as in $^{87}\mathrm{Rb}$ or $^{7}\mathrm{Li}$) induces a transition from a uniform to a stripe $XY$ ferromagnet (with no nematic order). For repulsive spin-dependent interactions (as in $^{23}\mathrm{Na}$), however, we find a transition from an $XY$ spin spiral phase ($\ensuremath{\langle}{S}_{z}\ensuremath{\rangle}=0$ and uniform total density) with uniaxial nematic order to a biaxial ferronematic, where the total density, spin vector, and nematic director oscillate in real space. We investigate the stability of these phases against the quadratic Zeeman effect, which generally tends to favor uniform phases with either ferromagnetic or nematic order but not both. We discuss the relevance of our results to ongoing experiments on spin-orbit-coupled, spinor Bose gases.

arXiv:1411.2990•Physical Review A•Feb 9, 2015•44 citations

Pairing transitions in a binary Bose gas

Zesheng 泽盛 Shen 沈, Lan Yin

Abstract The stable Bardeen–Schrieffer–Cooper (BCS) pairing state of a bosonic system has long been sought theoretically and experimentally. Here we propose that a stable BCS state of bosons can be realized in a binary Bose gas with s-wave intra-species repulsion and an inter-species attraction in the mean-field-stable region. We find that above the Bose–Einstein condensation (BEC) transition temperature, there is a phase transition from the normal state to a BCS state driven by inter-species pairing. When the temperature decreases, another phase transition from the BCS state to a mixed state featuring both atomic BEC and inter-species pairing occurs. As the temperature is further lowered, the mixed state is eventually taken over by the pure BEC state. We present the phase diagram of this system and discuss its experimental implications.

Chinese Physics B•Jun 4, 2025•3 citations
We find the conditions under which the normal state of a spin-1 Bose gas is unstable toward condensation, ferromagnetism, liquid crystalline-like nematicity, and Bardeen-Cooper-Schrieffer-like pairing. When the spin-dependent interactions are much weaker than the density-density interaction there is direct transition from a featureless normal state to a fully ordered Bose-Einstein condensate with either ferromagnetic or nematic order. When the spin-independent and spin-dependent interactions are of comparable magnitude, we find several different symmetry breaking transitions at intermediate temperatures above the Bose-condensation transition temperature. We make predictions for the Tc{T}_{c}Tc​ for these transitions, and assess the role of magnetic field and finite system size.
The strongly ferromagnetic spin-1 Bose-Einstein condensate has recently been realized with atomic Li7 . It was predicted that a strong ferromagnetic interaction can drive the normal gas into a magnetized phase at a temperature above the superfluid transition, and Li7 likely satisfies the criterion. We reexamine this theoretical proposal employing the two-particle-irreducible effective potential, and conclude that there exists no stable normal magnetized phase for a dilute ferromagnetic Bose gas. For Li7 , we predict that the normal gas undergoes a joint first-order transition and jumps directly into a state with finite condensate density and magnetization. We estimate the size of the first-order jump and examine how a partial spin polarization in the initial sample affects the first-order transition. We propose a qualitative phase diagram at fixed temperature for the trapped gas. Published by the American Physical Society 2024
The stable Bardeen-Schrieffer-Cooper (BCS) pairing state of a bosonic system has long been sought theoretically and experimentally. Here we study the BCS state of a binary Bose gas with sss-wave intra-species repulsions and an inter-species attraction in the mean-field-stable region. We find that above the Bose-Einstein-Condensation (BEC) transtion temperature, there is a phase transtion from the normal state to the BCS state due to inter-species pairing. When the temperature decreases, another phase transtion from the BCS state to the mixture state with both atomic BEC and inter-species pairs occurs. As the temperature is further lowered, the mixuture state is taken over by the BEC state. The phase diagram of this system is presented and experimental implications are discussed.
We compute the finite-temperature phase diagram of a pseudospin-1/2 Bose gas with contact interactions, using two complementary methods: the random-phase approximation and self-consistent Hartree-Fock theory. We show that the spin-dependent interactions, which break the (pseudo-) spin-rotational symmetry of the Hamiltonian, generally lead to the appearance of a magnetically ordered phase at temperatures above the superfluid transition. In three dimensions, we predict a normal easy-axis (easy-plane) ferromagnet for sufficiently strong repulsive (attractive) interspecies interactions, respectively. The normal easy-axis ferromagnet is the bosonic analog of Stoner ferromagnetism known in electronic systems. For the case of interspecies attraction, we also discuss the possibility of a bosonic analog of the Cooper-paired phase. This state is shown to significantly lose in energy to the transverse ferromagnet in three dimensions, but is more energetically competitive in lower dimensions. Extending our calculations to a spin-orbit-coupled Bose gas with equal Rashba and Dresselhaus-type couplings (as recently realized in experiment), we investigate the possibility of stripe ordering in the normal phase. Within our approximations, however, we do not find an instability towards stripe formation, suggesting that the stripe order melts below the condensation temperature, which is consistent with the experimental observations of Ji et al. [Ji et al., Nat. Phys. 10, 314 (2014)].
Spinor Bose-Einstein condensates under external magnetic fields exhibit well-characterized spin domains of its ground state due to spin-dependent interactions. At low temperatures, collision-induced spin-mixing instabilities may promote the condensate to dwell into metastable states occurring near the phase boundaries. In this paper, we study theoretically the metastable spin-phase diagram of a spin-1 antiferromagnetic Bose-Einstein condensate at zero and finite temperatures. The approach makes use of Hartree-Fock theory and exploits the symmetry of the Hamiltonian and of the order parameters yielding a closed system of transcendental equations for the free energy, fully avoiding the use of self-consistency methods. Our results are consistent with recent experiments and allow us to explain qualitatively the different types of observed quench dynamics. In addition, we found that similar phenomena should occur in antiferromagnetic spinor condensates with a sudden change in the temperature. It is shown also that the increase in temperature induces a traceable shift of the ferromagnetic-polar transition boundary, behavior previously not noted by self-consistent mean-field calculations.
We theoretically establish the mean-field phase diagram of a homogeneous spin-1, spin-orbit-coupled Bose gas as a function of the spin-dependent interaction parameter, the Raman coupling strength, and the quadratic Zeeman shift. We find that the interplay between spin-orbit coupling and spin-dependent interactions leads to the occurrence of ferromagnetic or ferronematic phases which also break translational symmetry. For weak Raman coupling, increasing attractive spin-dependent interactions (as in 87Rb^{87}\mathrm{Rb}87Rb or 7Li^{7}\mathrm{Li}7Li) induces a transition from a uniform to a stripe XYXYXY ferromagnet (with no nematic order). For repulsive spin-dependent interactions (as in 23Na^{23}\mathrm{Na}23Na), however, we find a transition from an XYXYXY spin spiral phase ($\ensuremath{\langle}{S}_{z}\ensuremath{\rangle}=0$ and uniform total density) with uniaxial nematic order to a biaxial ferronematic, where the total density, spin vector, and nematic director oscillate in real space. We investigate the stability of these phases against the quadratic Zeeman effect, which generally tends to favor uniform phases with either ferromagnetic or nematic order but not both. We discuss the relevance of our results to ongoing experiments on spin-orbit-coupled, spinor Bose gases.
Abstract The stable Bardeen–Schrieffer–Cooper (BCS) pairing state of a bosonic system has long been sought theoretically and experimentally. Here we propose that a stable BCS state of bosons can be realized in a binary Bose gas with s-wave intra-species repulsion and an inter-species attraction in the mean-field-stable region. We find that above the Bose–Einstein condensation (BEC) transition temperature, there is a phase transition from the normal state to a BCS state driven by inter-species pairing. When the temperature decreases, another phase transition from the BCS state to a mixed state featuring both atomic BEC and inter-species pairing occurs. As the temperature is further lowered, the mixed state is eventually taken over by the pure BEC state. We present the phase diagram of this system and discuss its experimental implications.