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Spinor Bose Gases in 1D: Equilibrium properties, Dynamics, and Spin-orbit coupling

Periodic Reporting for period 1 - Spin1D (Spinor Bose Gases in 1D: Equilibrium properties, Dynamics, and Spin-orbit coupling)

Reporting period: 2016-04-01 to 2018-03-31

"Ultracold atomic gases are quantum systems with an extraordinary degree of experimental control. They allow us to unveil fundamental aspects of many body physics in the realm of quantum mechanics with unprecedented precision.

We worked with ultracold spinor Bose gases —atomic quantum systems with spin degree of freedom— to investigate the origins of magnetism in materials. A general understanding the nature of magnetic quantum phases of matter requires the study of magnetic systems —beyond electronic spin-1/2 systems— where more magnetic phases are possible. Therefore, we studied a sample of optically trapped ultracold sodium atoms, a physical realization of a gas of spin 1 particles with antiferromagnetic interactions.

The scientific objectives of the action are (i.) understand quantum phase transitions in a 1D spin-1 system with and without a lattice; (ii.) investigate out-of-equilibrium systems across a quantum phase transition; and (iii.) investigate spin-orbit coupling (SOC) in 1D spinor gases.

We studied magnetic phases in a spin-1 system where the atoms can populate any quantum superposition of the three components mF=+1,0,-1, in a reduced dimensionality (1D). We measured the magnetic phase diagram as a function of an external magnetic field B, and observed the formation of magnetic domains within the sample. At low B, the system forms a mF = ±1 mixture favored by antiferromagnetic interactions. At high B, the system evolves into a mF = 0,+1 phase separated state, energetically favored due to the quadratic Zeeman effect. In contrast to earlier work, we took special care to cancel external magnetic forces that would have influenced the formation and spatial arrangement of the domains.

We also investigated the linear response of phase separated magnetic domains to an external magnetic force. We found that the response of an antiferromagnetic spin-1 BEC was significantly larger than that for single atoms. This ""enhanced Zeeman effect"" arises from the interplay between atomic interactions and bosonic statistics.
Finally, we studied the out-of-equilibrium response of magnetic domains to an external magnetic force.

CONCLUSION
This MSCA fellowship, part of the Career Restart panel, allowed Karina Jiménez García to reincorporate to research after a maternity leave period. She successfully integrated in the existing group and resumed her research.

The Spin1D project realized at Laboratoire Kastler Brossel (LKB) in Paris aimed at addressing fundamental aspects of quantum magnetism, by performing experiments based on sample of ultracold spin-1 atoms with antiferromagnetic interactions in a 1D geometry.

The most relevant achievements are: 1) the implementation of a 1D optical trap for cold atoms; 2) the observation of a quantum phase transition in a spin-1 ultracold atom system; 3) the observation and characterization of spin domains in 1D; 4) the study out-of-equilibrium dynamics; and 5) the characterization of the enhanced response to a magnetic force.

The host laboratory obtained a great amount of knowledge from the work led by Karina during the fellowship. The laboratory will continue to pursue state-of-the-art experiments using this spinor system.

Karina’s performance during the development of the fellowship granted her a research position at Centro de Investigación y de Estudios Avanzados del IPN - Unidad Querétaro, Querétaro, in México, her home country."
From 01 April 2016 to 31 March 2018, Karina Jiménez García worked as a postdoctoral researcher at LKB in the Bose-Einstein condensates team, under the supervision of Fabrice Gerbier. Karina joined the team and was responsible to adapt it to investigate spin-1 systems in reduced dimensions. The main research and dissemination activities are described below:

1) A 1D optical trap for cold atoms.
Karina configured the existing experimental apparatus to perform 1D experiments. A significant difficulty was to transfer the ultracold gas from its initial 3D configuration to the 1D trap. Karina successfully solved the problem by implementing a careful two-step protocol ensuring this is done with minimal heating. A second difficulty of the project was to cancel external magnetic forces at the location of the atoms. Karina devised and implemented a protocol to achieve this goal, suppressing these forces at a level substantially below the one typically required in similar experiments.

2) Quantum phase transition in a spin-1 ultracold atom system in 1D
We measured the magnetic phase diagram as a function of an external magnetic field, and observed the formation of magnetic domains.

3) Observation and characterization of spin domains in a 1D geometry
We prepared a partially magnetized sample of ultracold spin-1 atoms in 1D, in the presence of a uniform magnetic field of several hundred mG. Using resonant absorption imaging, in combination with a separating magnetic field gradient, we were able to resolve the spatial distribution of the spin components inside the trap.

4) Out-of-equilibrium dynamics of spin domains
We studied out-of-equilibrium dynamics of phase separated spin domains in mF = 0, and +1 at high field, after the sudden removal of an external magnetic force. These experiments shed light on the relaxation mechanism, pointing to a thermally-assisted spin-changing process —instead of a tunneling mechanism— to decay to the equilibrium state.

5) Enhanced response of phase separated spin-1 systems in equilibrium.
As part of our characterization of spin-domains in equilibrium, we discovered an extraordinary large response of spin domains to external magnetic field gradients.

The results obtained during the fellowship have been presented in the following conferences:
ICAP 2016. July 2016. Seoul, Korea
UQUAM 2016. Octubre 2016. Berlin, Germany
ICOLS 2017. July 2017. Arcachon, Francia
BEC 2017. September 2017. Saint Feliu de Guixols, Spain
UQUAM 2017. Octubre 2017. Venice, Italy
ICQSSIM 2017. Novembre 2017. Paris, Francia
QuantumOptics 2018. February 2018. Obergurgl, Austria

The results of the research will be reported in two independent publications. The articles will be submitted shortly to top international peer-review journals and will also be available on the arXiv server.
The fellowship focused on the study of ultracold spin-1 systems in 1D, aiming to unveil fundamental aspects of quantum magnetism. We were able to observe the formation of spin domains in the absence of external forces and to quantify a phase transition arising from the competition of spin interactions and the quadratic Zeeman shift (introduced by an external magnetic field). To the best of our knowledge, our work constitutes the first demonstration of equilibrium spin domain formation in the absence of external forces.

Our study of out-of-equilibrium spin domains allowed us to understand the relaxation mechanism toward the equilibrium configuration. We learned that a thermally-assisted spin-changing process —instead of a macroscopic quantum tunneling mechanism— drives the decay to the equilibrium state.

The study of out of equilibrium dynamics in combination with the understanding of the spatial configuration of the spin domains in the trap helped us to better understand spin-exchange interactions in spin-1 Bose gases in 1D.
Fluorescence of nearly 20 million Na atoms used to produce 1D systems for the Spin1D project