arXiv:1209.2533 · Physical Review A

Phase diagram of spin-1 antiferromagnetic Bose-Einstein condensates

David Jacob, Lingxuan Shao, Vincent Le Corre, Tilman Zibold, L. De Sarlo, Emmanuel Mimoun, Jean Dalibard, Fabrice Gerbier

Published Dec 5, 2012• 80 citations

arXiv HTML PDF

Abstract

We study experimentally the equilibrium phase diagram of a spin-1 Bose-Einstein condensate with antiferromagnetic interactions, in a regime where spin and spatial degrees of freedom are decoupled. For a given total magnetization ${m}_{z}$, we observe for low magnetic fields an ``antiferromagnetic'' phase where atoms condense in the $m=\ifmmode\pm\else\textpm\fi{}1$ Zeeman states, and occupation of the $m=0$ state is suppressed. Conversely, for large enough magnetic fields, a phase transition to a ``broken-axisymmetry'' phase takes place: The $m=0$ component becomes populated and rises sharply above a critical field ${B}_{c}({m}_{z})$. This behavior results from the competition between antiferromagnetic spin-dependent interactions (dominant at low fields) and the quadratic Zeeman energy (dominant at large fields). We compare the measured ${B}_{c}$ as well as the global shape of the phase diagram with mean-field theory, and find good quantitative agreement.

DOI: 10.1103/physreva.86.061601

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arXiv:1209.2533 · Physical Review A

Phase diagram of spin-1 antiferromagnetic Bose-Einstein condensates

David Jacob, Lingxuan Shao, Vincent Le Corre, Tilman Zibold, L. De Sarlo, Emmanuel Mimoun, Jean Dalibard, Fabrice Gerbier

Published Dec 5, 2012• 80 citations

arXiv HTML PDF

Abstract

{m}_{z}

, we observe for low magnetic fields an

antiferromagnetic'' phase where atoms condense in the $m=\ifmmode\pm\else\textpm\fi{}1$ Zeeman states, and occupation of the $m=0$ state is suppressed. Conversely, for large enough magnetic fields, a phase transition to a

broken-axisymmetry'' phase takes place: The

m=0

component becomes populated and rises sharply above a critical field

{B}_{c}({m}_{z})

. This behavior results from the competition between antiferromagnetic spin-dependent interactions (dominant at low fields) and the quadratic Zeeman energy (dominant at large fields). We compare the measured

{B}_{c}

as well as the global shape of the phase diagram with mean-field theory, and find good quantitative agreement.

DOI: 10.1103/physreva.86.061601

Related papers

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Shao, Lingxuan

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{m}_{z}

, we observe for low magnetic fields an

antiferromagnetic'' phase where atoms condense in the $m=\ifmmode\pm\else\textpm\fi{}1$ Zeeman states, and occupation of the $m=0$ state is suppressed. Conversely, for large enough magnetic fields, a phase transition to a

broken-axisymmetry'' phase takes place: The

m=0

component becomes populated and rises sharply above a critical field

{B}_{c}({m}_{z})

{B}_{c}

as well as the global shape of the phase diagram with mean-field theory, and find good quantitative agreement.

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.