arXiv:cond-mat/9803199 · Physical Review A

Magnetic properties of a Bose-Einstein condensate

Mikhail V. Simkin, E. G. D. Cohen

Published Feb 1, 1999• 28 citations

Abstract

Three hyperfine states of Bose-condensed sodium atoms, recently optically trapped, can be described as a spin-1 Bose gas. We study the behavior of this system in a magnetic field, and construct the phase diagram, where the temperature of the Bose condensation ${T}_{\mathrm{BEC}}$ increases with magnetic field. In particular the system is ferromagnetic below ${T}_{\mathrm{BEC}}$ and the magnetization is proportional to the condensate fraction in a vanishing magnetic field. Second derivatives of the magnetization with regard to temperature or magnetic field are discontinuous along the phase boundary.

DOI: 10.1103/physreva.59.1528

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arXiv:cond-mat/9803199 · Physical Review A

Magnetic properties of a Bose-Einstein condensate

Mikhail V. Simkin, E. G. D. Cohen

Published Feb 1, 1999• 28 citations

arXiv HTML PDF

Abstract

{T}_{\mathrm{BEC}}

increases with magnetic field. In particular the system is ferromagnetic below

{T}_{\mathrm{BEC}}

and the magnetization is proportional to the condensate fraction in a vanishing magnetic field. Second derivatives of the magnetization with regard to temperature or magnetic field are discontinuous along the phase boundary.

DOI: 10.1103/physreva.59.1528

Related papers

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We have observed Bose-Einstein condensation of sodium atoms. The atoms were trapped in a novel trap that employed both magnetic and optical forces. Evaporative cooling increased the phase-space density by 6 orders of magnitude within seven seconds. Condensates contained up to 5\ifmmode\times\else\texttimes\fi{} ${10}^{5}$ atoms at densities exceeding ${10}^{14}$ ${\mathrm{cm}}^{\ensuremath{-}3}$. The striking signature of Bose condensation was the sudden appearance of a bimodal velocity distribution below the critical temperature of \ensuremath{\sim}2\ensuremath{\mu}K. The distribution consisted of an isotropic thermal distribution and an elliptical core attributed to the expansion of a dense condensate.We have observed Bose-Einstein condensation of sodium atoms. The atoms were trapped in a novel trap that employed both magnetic and optical forces. Evaporative cooling increased the phase-space density by 6 orders of magnitude within seven seconds. Condensates contained up to 5\ifmmode\times\else\texttimes\fi{}${10}^{5}$ atoms at densities exceeding ${10}^{14}$ ${\mathrm{cm}}^{\ensuremath{-}3}$. The striking signature of Bose condensation was the sudden appearance of a bimodal velocity distribution below the critical temperature of \ensuremath{\sim}2\ensuremath{\mu}K. The distribution consisted of an isotropic thermal distribution and an elliptical core attributed to the expansion of a dense condensate.

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{T}_{\mathrm{BEC}}

increases with magnetic field. In particular the system is ferromagnetic below

{T}_{\mathrm{BEC}}

B

. The predictions of the mean-field theory agree very well with most of our experimental results, including the values of the critical magnetic field

B_c

, asymptotic values of

n_0

(relative atom number in

m_F=0

state) at large

B

and the phase diagram of

n_0

. However, for small magnetization and small magnetic fields, we find abnormally large fluctuations (super-Poissonian) of

n_0

. In order to describe these large fluctuations, we develop a full quantum statistical description for the spinor condensate at finite temperature. To describe uncondensed thermal atoms (also present in the same trap), we use the ``semi-ideal" Hartree-Fock approximation to deal with the interactions between the condensate atoms and the thermal ones. The experimental results lead us to introduce two kinds of temperatures, the ``spin temperature"

T_s

and the ``kinetic temperature"

T_k

with

T_s\ll T_k

, characterizing respectively the fluctuaitons of the condensate spin and the thermal gas. We conclude that the system is reaching a quasi-equilibrium states, where different degrees of freedom reach equilibrium by separate mechanisms but where the mutual thermalization does not occur over the lifetime of the cloud.

{10}^{5}

atoms at densities exceeding

{10}^{14}

${\mathrm{cm}}^{\ensuremath{-}3}$. The striking signature of Bose condensation was the sudden appearance of a bimodal velocity distribution below the critical temperature of \ensuremath{\sim}2\ensuremath{\mu}K. The distribution consisted of an isotropic thermal distribution and an elliptical core attributed to the expansion of a dense condensate.