# Thermodynamics and magnetism of antiferromagnetic spinor Bose-Einstein condensates

Abstract : In this manuscript, we present an experimental study of a Spin 1 Bose gas with antiferromagnetic interactions with ultracold sodium atoms in the F=1 manifold. The three Zeeman components are trapped simultaneously in optical dipole traps. By performing evaporative cooling, we obtain quasi-pure spinor Bose-Einstein condensates of which we study the magnetic properties. There are two types of interactions between the constituents of the system: Contact interactions that do not change the Zeeman populations and spin-exchange contact interactions that do. A competition between Zeeman energy and the spin-exchange energy sets the magnetic ordering in the system. We first study the magnetic phases of spinor Bose-Einstein condensates near zero temperature. The ground state present two phases that are observed by varying the magnetic field (hence the quadratic Zeeman energy) and the magnetization of the sample. In the antiferromagnetic phase, the spin of the sample is purely along the direction of the magnetic field. In the broken-axisymmetry phase, a transverse component appears in order to minimize the Zeeman energy. For zero magnetization, the spinor condensate forms a spin nematic. This state, named in analogy with the liquid crystal nematic phase, is characterized by spin fluctuations orthogonal to a particular axis, with no preferred direction along that axis. In both phases, spin nematic order manifests as a minimization of the transverse spin length that is realized by enforcing a particular value ($\pi$) of the relative phase of the Zeeman components $\theta = \phi_{+1} + \phi_{-1} - 2 \phi_0$. We measure the transverse spin length by analyzing spin noise after a spin rotation. Second, we study the thermodynamics of an antiferromagnetic spin 1 Bose gas next to the critical temperature for Bose-Einstein condensation. We measure several sequential condensation scenarii depending on the magnetization and the magnetic field. The measured critical temperatures reveal a large effect of interactions when one of the Zeeman component condenses in presence of a condensate in another component. We use a simplified Hartree-Fock theory, neglecting the spin exchange interactions and note a good agreement with our data. However, for low magnetic fields, the thermodynamic phase diagram is strongly modified which raises new open questions about the role of spin exchange interactions at finite temperatures.
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Cited literature [217 references]

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Submitted on : Wednesday, April 26, 2017 - 11:13:06 PM
Last modification on : Thursday, March 17, 2022 - 10:09:00 AM
Long-term archiving on: : Thursday, July 27, 2017 - 3:01:01 PM

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• HAL Id : tel-01515042, version 1

### Citation

Camille Frapolli. Thermodynamics and magnetism of antiferromagnetic spinor Bose-Einstein condensates. Quantum Gases [cond-mat.quant-gas]. École normale supérieure de Paris, 2017. English. ⟨tel-01515042v1⟩

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