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:1209.5509 · Physical Review A

Hydrodynamic description of spin-1 Bose-Einstein condensates

Emi Yukawa, Masahito Ueda

Published Dec 13, 2012• 52 citations
arXivHTMLPDF

Abstract

We establish a complete set of hydrodynamic equations for a spin-1 Bose-Einstein condensate, which are equivalent to the multicomponent Gross-Pitaevskii equations and expressed in terms of only observable physical quantities: the spin and the nematic (or quadrupolar) tensor in addition to the density of particles and the mass current that appear in the hydrodynamic description of a scalar condensate. The obtained hydrodynamic equations involve a generalized Mermin-Ho relation that is valid regardless of the spatiotemporal dependence of the spin polarization. Low-lying collective modes for phonons and magnons are reproduced by linearizing the hydrodynamic equations. We also apply the single-mode approximation to the hydrodynamic equations and find a complete set of analytic solutions.

DOI
10.1103/physreva.86.063614

Related papers

Nematic tensor evolution in the partially-polarized spin-1 Bose–Einstein condensates

Mariya Iv. Trukhanova

We develop the complete hydrodynamical description of the spin-1 partially polarized Bose–Einstein condensate (BEC), based on the many-particle quantum hydrodynamic formalism. We derive the continuity equation, momentum balance equation, spin evolution and nematicity evolution equations considering the spin–spin dipole long-range interactions and short-range interactions between partially spin-polarized atoms of condensate. The nematic or quadrupolar tensor plays an important role in the experiments of spin-nematic squeezing. We predict the influence of the spin–spin dipole interactions and spin torque force on the dynamics of nematic tensor. The collective modes for phonons and magnons are predicted for the ferromagnetic phase of spinor condensate, where the spin–spin and short-range interactions modify the dispersion equation.

Modern Physics Letters B•Apr 9, 2021•0 citations

Quantum hydrodynamics of the spinor Bose–Einstein condensate at non-zero temperatures

Pavel A. Andreev, Ilia Mosaki, Mariya Iv. Trukhanova

A finite temperature hydrodynamic model is derived for the spin-1 ultracold bosons by the many-particle quantum hydrodynamic method. It is presented as the two fluid model of the Bose–Einstein condensate (BEC) and normal fluid. The continuity, Euler, spin evolution, and nematic tensor evolution equations are derived for each fluid. The linear and quadratic Zeeman effects are included. Scalar and spin–spin like short-range interactions are considered in the first order by the interaction radius. Obtained hydrodynamic equations are also represented as the set of two nonlinear Pauli equations. The spectrum of the bulk collective excitations is considered for the ferromagnetic phase in the small temperature limit. The spin wave is not affected by the presence of the small temperature in the described minimal coupling model, where the thermal part of the spin-current of the normal fluid is neglected. The two sound waves are affected by the spin evolution in the same way as the change of spectrum of the single sound wave in BEC, where speed of sound is proportional to g1+g2 with gi as the interaction constants.

arXiv:2102.12538•Physics of Fluids•Jun 1, 2021•24 citations

Self-consistent spin waves in magnetized BEC

Pavel A. Andreev

We obtain equations of quantum hydrodynamic (QHD) for magnetized spin-1 neutral Bose-Einstein condensate (BEC). System of QHD equations contains the equation of magnetic moment evolution (an analog of the Bloch equation). We account spin-spin interaction along with the short range interaction. We consider self-consistent field approximation of QHD equations. Starting from QHD equation we derive the Gross-Pitaevskii equation for magnetized BEC. We show that Gross-Pitaevskii equation exists under condition that the magnetic moment direction is not change. Using obtained QHD equations we study the dispersion of collective excitation. As in electrically polarized BEC [P. A. Andreev, L. S. Kuz'menkov, arXiv: 1201.2440], in the magnetically polarized BEC there is second wave mode (polarization mode or spin wave), in addition to the Bogoliubov's mode. Second wave solution appears due to the magnetic moment evolution. The influence of magnetization on dispersion of Bogoliubov's mode is found. We found strong difference of dispersion properties of waves in magnetized BEC from electrically polarized BEC.

arXiv:1202.3398•Feb 15, 2012•0 citations

Geometrical approach to hydrodynamics and low-energy excitations of spinor condensates

Ryan Barnett, Daniel K. Podolsky, Gil Refael

In this work, we derive the equations of motion governing the dynamics of spin-$F$ spinor condensates. We pursue a description based on standard physical variables (total density and superfluid velocity), alongside $2F$ ``spin nodes:'' unit vectors that describe the spin-$F$ state and also exhibit the point-group symmetry of a spinor condensate's mean-field ground state. In the first part of our analysis, we derive the hydrodynamic equations of motion, which consist of a mass continuity equation, $2F$ Landau-Lifshitz equations for the spin nodes, and a modified Euler equation. In particular, we provide a generalization of the Mermin-Ho relation to spin one and find an analytic solution for the skyrmion texture in the incompressible regime of a spin-half condensate. In the second part, we study the linearized dynamics of spinor condensates. We provide a general method to linearize the equations of motion based on the symmetry of the mean-field ground state using the local stereographic projection of the spin nodes. We also provide a simple construction to extract the collective modes from symmetry considerations alone akin to the analysis of vibrational excitations of polyatomic molecules. Finally, we present a mapping between the spin-wave modes, and the wave functions of electrons in atoms, where the spherical symmetry is degraded by a crystal field. These results demonstrate the beautiful geometrical structure that underlies the dynamics of spinor condensates.

arXiv:0812.3403•Physical Review B•Jul 21, 2009•57 citations

Three-fluid hydrodynamics of spin-1 Bose-Einstein condensates

Gergely Szirmai, P. Szépfalusy

We study excitations of the spin-1 Bose gas at finite temperatures and in the presence of a not-so-strong magnetic field or, equivalently, when the gas sample is partially polarized. Motivated by the success of two-fluid hydrodynamics of scalar superfluids we develop a three-fluid hydrodynamic description to treat the low-frequency and long-wavelength excitations of the spin-1 Bose gas. We derive coupled linear hydrodynamic equations of the three sounds and evaluate them numerically in a self-consistent mean-field approximation valid for dilute gas in the intermediate and critical temperature regions. In this latter region we identify the critical mode.

arXiv:1112.3220•Physical Review A•May 4, 2012•11 citations

Hydrodynamics of the atomic Bose–Einstein condensate beyond the mean-field approximation

Pavel A Andreev

Abstract Several hydrodynamic models of the atomic Bose–Einstein condensate (BEC) obtained beyond the mean-field approximation are discussed together from a single point of view. All these models are derived from the microscopic quantum description. The derivation is made within the many-particle quantum hydrodynamics method suggested by L Kuz’menkov. The derivation is demonstrated and discussed for the mean-field regime revealing the Gross–Pitaevskii equation as the simplest illustration. It appears in the first order by the interaction radius. Generalization of the hydrodynamic Euler equation obtained in the third order by the interaction radius is discussed. It includes the contribution of the isotropic short-range interaction (SRI) presented by the third space derivative of the square of concentration. The Euler equation also includes the contribution of the anisotropic part of the SRI proportional to the second order spherical function. A systematic account of the quantum fluctuations in terms of the many-particle quantum hydrodynamics method requires the extension of the set of hydrodynamic equations from the couple continuity and Euler equations to the set of four equations which also includes the pressure evolution equation and the evolution equation for the third rank tensor of the pressure flux. The pressure evolution equation contains no interaction contribution in the first order by the interaction radius. The source of the quantum fluctuations is in the interaction caused term existing in the third rank tensor evolution equation which is obtained in the first order by the interaction radius. The presented models are considered for the single-component BECs.

arXiv:2007.15045•Laser Physics Letters•Apr 19, 2021•5 citations
We establish a complete set of hydrodynamic equations for a spin-1 Bose-Einstein condensate, which are equivalent to the multicomponent Gross-Pitaevskii equations and expressed in terms of only observable physical quantities: the spin and the nematic (or quadrupolar) tensor in addition to the density of particles and the mass current that appear in the hydrodynamic description of a scalar condensate. The obtained hydrodynamic equations involve a generalized Mermin-Ho relation that is valid regardless of the spatiotemporal dependence of the spin polarization. Low-lying collective modes for phonons and magnons are reproduced by linearizing the hydrodynamic equations. We also apply the single-mode approximation to the hydrodynamic equations and find a complete set of analytic solutions.
We develop the complete hydrodynamical description of the spin-1 partially polarized Bose–Einstein condensate (BEC), based on the many-particle quantum hydrodynamic formalism. We derive the continuity equation, momentum balance equation, spin evolution and nematicity evolution equations considering the spin–spin dipole long-range interactions and short-range interactions between partially spin-polarized atoms of condensate. The nematic or quadrupolar tensor plays an important role in the experiments of spin-nematic squeezing. We predict the influence of the spin–spin dipole interactions and spin torque force on the dynamics of nematic tensor. The collective modes for phonons and magnons are predicted for the ferromagnetic phase of spinor condensate, where the spin–spin and short-range interactions modify the dispersion equation.
A finite temperature hydrodynamic model is derived for the spin-1 ultracold bosons by the many-particle quantum hydrodynamic method. It is presented as the two fluid model of the Bose–Einstein condensate (BEC) and normal fluid. The continuity, Euler, spin evolution, and nematic tensor evolution equations are derived for each fluid. The linear and quadratic Zeeman effects are included. Scalar and spin–spin like short-range interactions are considered in the first order by the interaction radius. Obtained hydrodynamic equations are also represented as the set of two nonlinear Pauli equations. The spectrum of the bulk collective excitations is considered for the ferromagnetic phase in the small temperature limit. The spin wave is not affected by the presence of the small temperature in the described minimal coupling model, where the thermal part of the spin-current of the normal fluid is neglected. The two sound waves are affected by the spin evolution in the same way as the change of spectrum of the single sound wave in BEC, where speed of sound is proportional to g1+g2 with gi as the interaction constants.
We obtain equations of quantum hydrodynamic (QHD) for magnetized spin-1 neutral Bose-Einstein condensate (BEC). System of QHD equations contains the equation of magnetic moment evolution (an analog of the Bloch equation). We account spin-spin interaction along with the short range interaction. We consider self-consistent field approximation of QHD equations. Starting from QHD equation we derive the Gross-Pitaevskii equation for magnetized BEC. We show that Gross-Pitaevskii equation exists under condition that the magnetic moment direction is not change. Using obtained QHD equations we study the dispersion of collective excitation. As in electrically polarized BEC [P. A. Andreev, L. S. Kuz'menkov, arXiv: 1201.2440], in the magnetically polarized BEC there is second wave mode (polarization mode or spin wave), in addition to the Bogoliubov's mode. Second wave solution appears due to the magnetic moment evolution. The influence of magnetization on dispersion of Bogoliubov's mode is found. We found strong difference of dispersion properties of waves in magnetized BEC from electrically polarized BEC.
In this work, we derive the equations of motion governing the dynamics of spin-FFF spinor condensates. We pursue a description based on standard physical variables (total density and superfluid velocity), alongside 2F2F2F ``spin nodes:'' unit vectors that describe the spin-FFF state and also exhibit the point-group symmetry of a spinor condensate's mean-field ground state. In the first part of our analysis, we derive the hydrodynamic equations of motion, which consist of a mass continuity equation, 2F2F2F Landau-Lifshitz equations for the spin nodes, and a modified Euler equation. In particular, we provide a generalization of the Mermin-Ho relation to spin one and find an analytic solution for the skyrmion texture in the incompressible regime of a spin-half condensate. In the second part, we study the linearized dynamics of spinor condensates. We provide a general method to linearize the equations of motion based on the symmetry of the mean-field ground state using the local stereographic projection of the spin nodes. We also provide a simple construction to extract the collective modes from symmetry considerations alone akin to the analysis of vibrational excitations of polyatomic molecules. Finally, we present a mapping between the spin-wave modes, and the wave functions of electrons in atoms, where the spherical symmetry is degraded by a crystal field. These results demonstrate the beautiful geometrical structure that underlies the dynamics of spinor condensates.
We study excitations of the spin-1 Bose gas at finite temperatures and in the presence of a not-so-strong magnetic field or, equivalently, when the gas sample is partially polarized. Motivated by the success of two-fluid hydrodynamics of scalar superfluids we develop a three-fluid hydrodynamic description to treat the low-frequency and long-wavelength excitations of the spin-1 Bose gas. We derive coupled linear hydrodynamic equations of the three sounds and evaluate them numerically in a self-consistent mean-field approximation valid for dilute gas in the intermediate and critical temperature regions. In this latter region we identify the critical mode.
Abstract Several hydrodynamic models of the atomic Bose–Einstein condensate (BEC) obtained beyond the mean-field approximation are discussed together from a single point of view. All these models are derived from the microscopic quantum description. The derivation is made within the many-particle quantum hydrodynamics method suggested by L Kuz’menkov. The derivation is demonstrated and discussed for the mean-field regime revealing the Gross–Pitaevskii equation as the simplest illustration. It appears in the first order by the interaction radius. Generalization of the hydrodynamic Euler equation obtained in the third order by the interaction radius is discussed. It includes the contribution of the isotropic short-range interaction (SRI) presented by the third space derivative of the square of concentration. The Euler equation also includes the contribution of the anisotropic part of the SRI proportional to the second order spherical function. A systematic account of the quantum fluctuations in terms of the many-particle quantum hydrodynamics method requires the extension of the set of hydrodynamic equations from the couple continuity and Euler equations to the set of four equations which also includes the pressure evolution equation and the evolution equation for the third rank tensor of the pressure flux. The pressure evolution equation contains no interaction contribution in the first order by the interaction radius. The source of the quantum fluctuations is in the interaction caused term existing in the third rank tensor evolution equation which is obtained in the first order by the interaction radius. The presented models are considered for the single-component BECs.