# Étude du phénomène de compression de spin dans un condensat de Bose-Einstein piégé sur microcircuit

Abstract : In this manuscript, we present an experimental study of spin squeezing in a spinor Bose-Einstein condensate of $^{87}Rb$, arising from a non-linear interaction originating from collisions between the two internal states $|F=1, m_F=-1>$ and $|F=2, m_F=1>$ of the $5^2S_{1/2}$ manifold. The atoms are cooled down in a magneto-optical trap and magnetically trapped thanks to our atom-chip which acts as a top wall for our vacuum cell. The chip is also used to emit the radio-frequency field that perform the evaporative cooling leading to Bose-Einstein condensation, and the microwave field used to coherently transfer the atoms from one internal state to another.The atomic ensemble in a coherent superposition is well described by the so-called textit{one-axis-twisting} Hamiltonian that contains a term quadratic in the $z$-component of the spin vector $S_z$. the strength of this non-linear interaction, initially very weak, depends on the intra- and inter-state s-wave scattering lengths, and can be greatly enhanced by reducing the wave-function spatial overlap between the two states. We therefore place the system in a configuration (high atom number and cigar-shaped trap) for which the two states experience spontaneous relative spatial separation and recombination phases. The impact of this spatial dynamics on the mean field interaction and coherence of the system is experimentally analyzed through the study of the contrast and central frequency of a Ramsey interferometer.Theoretically, when the two states are separated, the spin noise distribution evolves from a uniform circular distribution defined by the quantum projection noise, to an elliptic one whose small axis is smaller than the standard quantum limit, under the action of the $S_z^2$ interaction. This is verified experimentally by performing the tomography of the atomic state, when the two internal modes recombine. A squeezing parameter $xi^2=-1.3 pm 0.4$ dB is reached for 5000 atoms and a 90% contrast. The study of the different instability sources highlights the atomic-density-dependent losses as the main limitation for both the noise reduction and the contrast of the interferometer.This work has been initiated in the context of quantum metrology and represents a step towards the production of spin squeezed states enabling the realization of atom interferometers working below the standard quantum limit. It also addresses the fundamental question of coherence of spinor Bose-Einstein condensates undergoing many elastic and inelastic collisions.
Keywords :

Cited literature [230 references]

https://tel.archives-ouvertes.fr/tel-01688752
Contributor : Abes Star :  Contact
Submitted on : Thursday, October 4, 2018 - 2:40:12 PM
Last modification on : Friday, April 3, 2020 - 11:12:07 AM
Document(s) archivé(s) le : Saturday, January 5, 2019 - 3:35:54 PM

### File

laudat_2017_archivage_82070.pd...
Version validated by the jury (STAR)

### Identifiers

• HAL Id : tel-01688752, version 2

### Citation

Théo Laudat. Étude du phénomène de compression de spin dans un condensat de Bose-Einstein piégé sur microcircuit. Astrophysique [astro-ph]. PSL Research University, 2017. Français. ⟨NNT : 2017PSLEO014⟩. ⟨tel-01688752v2⟩

Record views