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Lecture notes series, Institute For Mathematical Sciences

Synthetic Gauge Field and Spin-Orbit Coupling in Ultracold Atomic Condensate

Li Chen, Han Pu

Published Jan 30, 2023• 0 citations
Publisher
DOI
10.1142/9789811266058_0004

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A central aim of this research is to study the dynamics of ultracold atoms in synthetic gauge fields. In this work, we developed a method to optimize the evaporation of ultracold atoms to the Bose-Einstein condensate (BEC) phase. We implement a model of atomic evaporation in a trapping potential, and we find optimal parameters for the trap depth and stiffness during evaporation. Using this model, we achieve a high efficiency of optical evaporation (γ eff = 4.0). Using that BEC, we study the dynamics of the BEC in various light-induced synthetic gauge fields. In particular, we have studied the transition between adiabatic and diabatic transport in a spin-orbit (SO) coupled BEC, and found the behavior to be well understood by the Landau-Zener (LZ) theory. Various parameters of the SO coupled BEC were explored, and we demonstrated the ability to use such LZ transitions as the basis of an atomic transistor. Finally, we created a novel type of 3π spin-orbit coupling for ultracold atoms using modulated Raman coupling. Using the 3π SO coupling eigenlevel structure, we observed a Stueckelberg type interference of the BEC. We developed a model of Stueckelberg type interferometers, and we were able to quantitatively account for the observed interference fringes.

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Since the realization of Bose-Einstein condensation in 1995, experimentalists in ultracold atomic gas community have developed a set of entirely new methods to study quantum gases. In ultracold atomic gases, implementation of synthetic gauge fields, the spin-orbit coupling, optical lattices and Feshbach resonances, provides a clean and highly controllable platform to tune the parameters of the system, which are typically fixed for real materials. Motivated by the rapid developments of experimental progresses, I investigate the ultracold atomic gases with synthetic gauge fields. \n \nIn this thesis, a bosonic gas in optical lattices in the presence of an effective staggered magnetic flux will be studied, using a generalized Bose-Hubbard model. Phase transition from the Mott insulating phase to the superfluid phase will be discussed. Novel superfluid phases including the stripe phase and the plane wave phase will be discussed. Furthermore, the existence of a tricritical point in the phase diagram is predicted. \n \nTo study Fermi systems with synthetic gauge fields, a spin-1=2 Fermi gas with Rashba spin-orbit coupling is investigated by studying the structure of vortex line through the Bardeen-Cooper-Schrieffer to Bose-Einstein condensation (BCSBEC) crossover. Due to the spin-orbit coupling, the s-wave interacting Fermi gas behaves like an effective p-wave paired system. A discussion about the vortex line structure will be provided by calculating the spatial distribution of the gap function, the density, the particle current, and also the elementary excitations. It has been found that the most robust superfluid occurs around the unitary point, indicated by the smallest healing length and the largest critical current. \n \nFinally, motivated by the recent progress of p-wave resonantly Fermi gas in experiment, an extension of Nozières-Schmitt-Rink method to the p-wave case will be given. An investigation of the normal state properties will be given by calculating the equation of state and the p-wave contacts, which have been measured by the experiment. Furthermore, the superfluid transition temperature with realistic parameters appropriate for experiment is calculated and is found to be within experimental reach.

•Jan 1, 2016•0 citations
A central aim of this research is to study the dynamics of ultracold atoms in synthetic gauge fields. In this work, we developed a method to optimize the evaporation of ultracold atoms to the Bose-Einstein condensate (BEC) phase. We implement a model of atomic evaporation in a trapping potential, and we find optimal parameters for the trap depth and stiffness during evaporation. Using this model, we achieve a high efficiency of optical evaporation (γ eff = 4.0). Using that BEC, we study the dynamics of the BEC in various light-induced synthetic gauge fields. In particular, we have studied the transition between adiabatic and diabatic transport in a spin-orbit (SO) coupled BEC, and found the behavior to be well understood by the Landau-Zener (LZ) theory. Various parameters of the SO coupled BEC were explored, and we demonstrated the ability to use such LZ transitions as the basis of an atomic transistor. Finally, we created a novel type of 3π spin-orbit coupling for ultracold atoms using modulated Raman coupling. Using the 3π SO coupling eigenlevel structure, we observed a Stueckelberg type interference of the BEC. We developed a model of Stueckelberg type interferometers, and we were able to quantitatively account for the observed interference fringes.
Two-body scattering constitutes one of the most fundamental processes in various physical systems ranging from ultracold dilute quantum gases to energetic quark- gluon plasmas. In this dissertation, we study the low-energy atomic collision physics in the presence of synthetic gauge fields, which are generated by atom-light interaction. One category of synthetic gauge fields is the artificial spin-orbit coupling. We discuss three different aspects in scattering theory: ultracold collision, scattering resonance, and bound state formation from a few-body perspective when the atomic spin states are coupled with their center-of-mass motion. The understanding of the spin-orbit effects on the modification of the scattering processes not only builds the foundation of collision physics in the presence of non-abelian gauge fields but also paves the way towards unraveling the few-body correlations in many-body systems.
Since the realization of Bose-Einstein condensation in 1995, experimentalists in ultracold atomic gas community have developed a set of entirely new methods to study quantum gases. In ultracold atomic gases, implementation of synthetic gauge fields, the spin-orbit coupling, optical lattices and Feshbach resonances, provides a clean and highly controllable platform to tune the parameters of the system, which are typically fixed for real materials. Motivated by the rapid developments of experimental progresses, I investigate the ultracold atomic gases with synthetic gauge fields. \n \nIn this thesis, a bosonic gas in optical lattices in the presence of an effective staggered magnetic flux will be studied, using a generalized Bose-Hubbard model. Phase transition from the Mott insulating phase to the superfluid phase will be discussed. Novel superfluid phases including the stripe phase and the plane wave phase will be discussed. Furthermore, the existence of a tricritical point in the phase diagram is predicted. \n \nTo study Fermi systems with synthetic gauge fields, a spin-1=2 Fermi gas with Rashba spin-orbit coupling is investigated by studying the structure of vortex line through the Bardeen-Cooper-Schrieffer to Bose-Einstein condensation (BCSBEC) crossover. Due to the spin-orbit coupling, the s-wave interacting Fermi gas behaves like an effective p-wave paired system. A discussion about the vortex line structure will be provided by calculating the spatial distribution of the gap function, the density, the particle current, and also the elementary excitations. It has been found that the most robust superfluid occurs around the unitary point, indicated by the smallest healing length and the largest critical current. \n \nFinally, motivated by the recent progress of p-wave resonantly Fermi gas in experiment, an extension of Nozières-Schmitt-Rink method to the p-wave case will be given. An investigation of the normal state properties will be given by calculating the equation of state and the p-wave contacts, which have been measured by the experiment. Furthermore, the superfluid transition temperature with realistic parameters appropriate for experiment is calculated and is found to be within experimental reach.