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

Physical Review A

Theory of domain formation in inhomogeneous ferromagnetic dipolar condensates within the truncated Wigner approximation

Jay Deep Sau, Sabrina R. Leslie, Dan Stamper-Kurn, Marvin L. Cohen

Published Aug 27, 2009• 35 citations
Publisher

Abstract

Recent experimental studies of $^{87}\text{R}\text{b}$ spinor Bose Einstein condensates have shown the existence of a magnetic field driven quantum phase transition accompanied by structure formation on the ferromagnetic side of the transition. In this theoretical study we examine the dynamics of the unstable modes following the transition within the framework of the semiclassical truncated Wigner approximation. In the process we present a systematic study of the effects of the trap, nonlinearities, finite temperature, and dipole-dipole interactions. Starting from an initial state which includes quantum fluctuations, we attempt to make quantitative comparisons with recent experimental data on this system by combining results presented here with those presented previously [S. Leslie, J. Guzman, M. Vengalattore, J. D. Sau, M. L. Cohen, and D. M. Stamper-Kurn, Phys. Rev. A 79, 043631 (2009)]. In the process we estimate the contribution of quantum zero-point fluctuations to the domain formation with quantitative accuracy and find discrepancies between the calculations and experiments at the quantitative level, despite the qualitative agreement between theory and experiment. We discuss the possible origins of these discrepancies. Finally, using the strong anisotropy of the trap, we propose ways to observe directly the effects of dipole-dipole interactions on the spinor condensate dynamics.

DOI
10.1103/physreva.80.023622

Related papers

Theory of domain formation in inhomogeneous ferromagnetic dipolar condensates

Jay Deep Sau, Sabrina R. Leslie, Dan Stamper-Kurn +1 more

Recent experimental studies of $^{87}$Rb spinor Bose Einstein condensates have shown the existence of a magnetic field driven quantum phase transition accompanied by structure formation on the ferromagnetic side of the transition. In this theoretical study we examine the dynamics of the unstable modes following the transition taking into account the effects of the trap, non-linearities, finite temperature and dipole-dipole interactions. Starting from an initial state which includes quantum fluctuations, we attempt to make quantitative comparisons with recent experimental data on this system and estimate the contribution of quantum zero-point fluctuations to the domain formation. Finally, using the strong anisotropy of the trap, we propose ways to observe directly the effects of dipole-dipole interactions on the spinor condensate dynamics.

arXiv:0904.1199•Apr 7, 2009•2 citations

Quantum noise, scaling, and domain formation in a spinor Bose-Einstein condensate

George I. Mias, Nigel R. Cooper, S. M. Girvin

In this paper we discuss Bose-Einstein spinor condensates for $F=1$ atoms in the context of $^{87}\text{R}\text{b}$, as studied experimentally by the Stamper-Kurn group [L. E. Sadler et al., Nature (London) 443, 312 (2006)]. The dynamical quantum fluctuations of a sample that starts as a condensate of $N$ atoms in a pure $F=1$, ${m}_{F}=0$ state are described in analogy to the two-mode squeezing of quantum optics in terms of an $\mathfrak{s}\mathfrak{u}(1,1)$ algebra. In this system the initial ${m}_{F}=0$ condensate acts as a source (pump) for the creation pairs of ${m}_{F}=1,\ensuremath{-}1$ atoms. We show that even though the system as a whole is described by a pure state with zero entropy, the reduced density matrix for the ${m}_{F}=+1$ degree of freedom, obtained by tracing out the ${m}_{F}=\ensuremath{-}1,0$ degrees of freedom, corresponds to a thermal state. Furthermore, these quantum fluctuations of the initial dynamics of the system provide the seeds for the formation of domains of ferromagnetically aligned spins.

arXiv:0710.3547•Physical Review A•Feb 14, 2008•44 citations

Dynamical Instability and Domain Formation in a Spin-1 Bose-Einstein Condensate

Wenxian Zhang, D. L. Zhou, M.-S. Chang +2 more

We interpret the recently observed spatial domain formation in spin-1 atomic condensates as a result of dynamical instability. Within the mean field theory, a homogeneous condensate is dynamically unstable (stable) for ferromagnetic (antiferromagnetic) atomic interactions. We find that this dynamical instability naturally leads to spontaneous domain formation as observed in several recent experiments for condensates with rather small numbers of atoms. For trapped condensates, our numerical simulations compare quantitatively to the experimental results, thus largely confirming the physical insight from our analysis of the homogeneous case.

arXiv:cond-mat/0509549•Physical Review Letters•Oct 27, 2005•119 citations

Dynamics of F=1 Rb87 condensates at finite temperatures

Jordi Mur-Petit, M. Guilleumas, A. Polls +4 more

We investigate the dynamics of a $F=1$ spinor Bose-Einstein condensate of $^{87}\mathrm{Rb}$ atoms confined in a quasi-one-dimensional trap both at zero and at finite temperature. At zero temperature, we observe coherent oscillations between populations of the various spin components and the formation of multiple domains in the condensate. We study also finite temperature effects in the spin dynamics taking into account the phase fluctuations in the Bogoliubov-de Gennes framework. At finite $T$, despite complex multidomain formation in the condensate, population equipartition occurs. The length scale of these spin domains seems to be determined intrinsically by nonlinear interactions.

arXiv:cond-mat/0507521•Physical Review A•Jan 31, 2006•58 citations

Spontaneous magnetic ordering in a ferromagnetic spinor dipolar Bose-Einstein condensate

Yuki Kawaguchi, Hiroki Saito, Kazue Kudo +1 more

We study the spin dynamics of a spin-1 ferromagnetic Bose-Einstein condensate with magnetic dipole-dipole interaction (MDDI) based on the Gross-Pitaevskii and Bogoliubov theories. We find that various magnetic structures such as checkerboards and stripes emerge in the course of the dynamics due to the combined effects of spin-exchange interaction, MDDI, quadratic Zeeman and finite-size effects, and nonstationary initial conditions. However, the short-range magnetic order observed by the Berkeley group [Phys. Rev. Lett. 100, 170403 (2008)] is not fully reproduced in our calculations; the periodicity of the order differs by a factor of 3 and the checkerboard pattern eventually dissolves in the course of time. Possible reasons for the discrepancy are discussed.

arXiv:0909.0565•Physical Review A•Oct 27, 2010•37 citations

Topological defect formation in a quenched ferromagnetic Bose-Einstein condensates

Hiroki Saito, Yuki Kawaguchi, Masahito Ueda

We study the dynamics of the quantum phase transition of a ferromagnetic spin-1 Bose-Einstein condensate (BEC) from the polar phase to the broken-axisymmetry phase by changing magnetic field, and find the spontaneous formation of spinor domain walls followed by the creation of polar-core spin vortices. We also find that the spin textures depend very sensitively on the initial noise distribution, and that an anisotropic and colored initial noise is needed to reproduce the Berkeley experiment [Sadler et al., Nature (London) 443, 312 (2006)]. The dynamics of vortex nucleation and the number of created vortices depend also on the manner in which the magnetic field is changed. We point out an analogy between the formation of spin vortices from domain walls in a spinor BEC and that of vortex-antivortex pairs from dark solitons in a scalar BEC.

arXiv:cond-mat/0610862•Physical Review A•Jan 23, 2007•85 citations
Recent experimental studies of 87Rb^{87}\text{R}\text{b}87Rb spinor Bose Einstein condensates have shown the existence of a magnetic field driven quantum phase transition accompanied by structure formation on the ferromagnetic side of the transition. In this theoretical study we examine the dynamics of the unstable modes following the transition within the framework of the semiclassical truncated Wigner approximation. In the process we present a systematic study of the effects of the trap, nonlinearities, finite temperature, and dipole-dipole interactions. Starting from an initial state which includes quantum fluctuations, we attempt to make quantitative comparisons with recent experimental data on this system by combining results presented here with those presented previously [S. Leslie, J. Guzman, M. Vengalattore, J. D. Sau, M. L. Cohen, and D. M. Stamper-Kurn, Phys. Rev. A 79, 043631 (2009)]. In the process we estimate the contribution of quantum zero-point fluctuations to the domain formation with quantitative accuracy and find discrepancies between the calculations and experiments at the quantitative level, despite the qualitative agreement between theory and experiment. We discuss the possible origins of these discrepancies. Finally, using the strong anisotropy of the trap, we propose ways to observe directly the effects of dipole-dipole interactions on the spinor condensate dynamics.
Recent experimental studies of 87^{87}87Rb spinor Bose Einstein condensates have shown the existence of a magnetic field driven quantum phase transition accompanied by structure formation on the ferromagnetic side of the transition. In this theoretical study we examine the dynamics of the unstable modes following the transition taking into account the effects of the trap, non-linearities, finite temperature and dipole-dipole interactions. Starting from an initial state which includes quantum fluctuations, we attempt to make quantitative comparisons with recent experimental data on this system and estimate the contribution of quantum zero-point fluctuations to the domain formation. Finally, using the strong anisotropy of the trap, we propose ways to observe directly the effects of dipole-dipole interactions on the spinor condensate dynamics.
In this paper we discuss Bose-Einstein spinor condensates for F=1F=1F=1 atoms in the context of 87Rb^{87}\text{R}\text{b}87Rb, as studied experimentally by the Stamper-Kurn group [L. E. Sadler et al., Nature (London) 443, 312 (2006)]. The dynamical quantum fluctuations of a sample that starts as a condensate of NNN atoms in a pure F=1F=1F=1, mF=0{m}_{F}=0mF​=0 state are described in analogy to the two-mode squeezing of quantum optics in terms of an su(1,1)\mathfrak{s}\mathfrak{u}(1,1)su(1,1) algebra. In this system the initial mF=0{m}_{F}=0mF​=0 condensate acts as a source (pump) for the creation pairs of ${m}_{F}=1,\ensuremath{-}1$ atoms. We show that even though the system as a whole is described by a pure state with zero entropy, the reduced density matrix for the mF=+1{m}_{F}=+1mF​=+1 degree of freedom, obtained by tracing out the ${m}_{F}=\ensuremath{-}1,0$ degrees of freedom, corresponds to a thermal state. Furthermore, these quantum fluctuations of the initial dynamics of the system provide the seeds for the formation of domains of ferromagnetically aligned spins.
We interpret the recently observed spatial domain formation in spin-1 atomic condensates as a result of dynamical instability. Within the mean field theory, a homogeneous condensate is dynamically unstable (stable) for ferromagnetic (antiferromagnetic) atomic interactions. We find that this dynamical instability naturally leads to spontaneous domain formation as observed in several recent experiments for condensates with rather small numbers of atoms. For trapped condensates, our numerical simulations compare quantitatively to the experimental results, thus largely confirming the physical insight from our analysis of the homogeneous case.
We investigate the dynamics of a F=1F=1F=1 spinor Bose-Einstein condensate of 87Rb^{87}\mathrm{Rb}87Rb atoms confined in a quasi-one-dimensional trap both at zero and at finite temperature. At zero temperature, we observe coherent oscillations between populations of the various spin components and the formation of multiple domains in the condensate. We study also finite temperature effects in the spin dynamics taking into account the phase fluctuations in the Bogoliubov-de Gennes framework. At finite TTT, despite complex multidomain formation in the condensate, population equipartition occurs. The length scale of these spin domains seems to be determined intrinsically by nonlinear interactions.
We study the spin dynamics of a spin-1 ferromagnetic Bose-Einstein condensate with magnetic dipole-dipole interaction (MDDI) based on the Gross-Pitaevskii and Bogoliubov theories. We find that various magnetic structures such as checkerboards and stripes emerge in the course of the dynamics due to the combined effects of spin-exchange interaction, MDDI, quadratic Zeeman and finite-size effects, and nonstationary initial conditions. However, the short-range magnetic order observed by the Berkeley group [Phys. Rev. Lett. 100, 170403 (2008)] is not fully reproduced in our calculations; the periodicity of the order differs by a factor of 3 and the checkerboard pattern eventually dissolves in the course of time. Possible reasons for the discrepancy are discussed.
We study the dynamics of the quantum phase transition of a ferromagnetic spin-1 Bose-Einstein condensate (BEC) from the polar phase to the broken-axisymmetry phase by changing magnetic field, and find the spontaneous formation of spinor domain walls followed by the creation of polar-core spin vortices. We also find that the spin textures depend very sensitively on the initial noise distribution, and that an anisotropic and colored initial noise is needed to reproduce the Berkeley experiment [Sadler et al., Nature (London) 443, 312 (2006)]. The dynamics of vortex nucleation and the number of created vortices depend also on the manner in which the magnetic field is changed. We point out an analogy between the formation of spin vortices from domain walls in a spinor BEC and that of vortex-antivortex pairs from dark solitons in a scalar BEC.