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# Theoretical and experimental study of spin-1 antiferromagnetic Bose-Einstein Condensates

Abstract : In this thesis, we study theoretically and in experimentally the properties of spin-1 Bose-Einstein condensates with antiferromagnetic interactions realized in the ultra-cold sodium gases confined in optical dipole traps. We present in detail how to realize, diagnose and control the spinor Bose-Einstein condensates in our experiment. In order to describe the condensate, a mean-field theory is first adopted. This theory predicts a phase transition when changing the magnetic field $B$. 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.
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https://tel.archives-ouvertes.fr/tel-01104387
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Submitted on : Friday, January 16, 2015 - 4:05:36 PM
Last modification on : Thursday, March 17, 2022 - 10:08:07 AM
Long-term archiving on: : Friday, September 11, 2015 - 6:59:14 AM

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• HAL Id : tel-01104387, version 1

### Citation

Lingxuan Shao. Theoretical and experimental study of spin-1 antiferromagnetic Bose-Einstein Condensates. Quantum Gases [cond-mat.quant-gas]. Ecole Normale Supérieure, 2014. English. ⟨tel-01104387⟩

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