Realization of Two-Dimensional Spin-orbit Coupling for Bose-Einstein Condensates (1511.08170v1)

Abstract: Cold atoms with laser-induced spin-orbit (SO) interactions provide intriguing new platforms to explore novel quantum physics beyond natural conditions of solids. Recent experiments demonstrated the one-dimensional (1D) SO coupling for boson and fermion gases. However, realization of 2D SO interaction, a much more important task, remains very challenging. Here we propose and experimentally realize, for the first time, 2D SO coupling and topological band with $^{87}$Rb degenerate gas through a minimal optical Raman lattice scheme, without relying on phase locking or fine tuning of optical potentials. A controllable crossover between 2D and 1D SO couplings is studied, and the SO effects and nontrivial band topology are observed by measuring the atomic cloud distribution and spin texture in the momentum space. Our realization of 2D SO coupling with advantages of small heating and topological stability opens a broad avenue in cold atoms to study exotic quantum phases, including the highly-sought-after topological superfluid phases.

• The paper demonstrates a novel minimal Raman lattice scheme that achieves 2D spin-orbit coupling in BECs and enables a crossover from 1D to 2D regimes.
• Experimental measurements of momentum distribution and spin texture reveal distinct topological band structures and state transitions.
• The study opens pathways for exploring exotic quantum phases, including topological superconductors and the potential observation of Majorana quasiparticles.

Overview of Two-Dimensional Spin-Orbit Coupling in Bose-Einstein Condensates

This paper presents a novel experimental realization of two-dimensional (2D) spin-orbit (SO) coupling in Bose-Einstein condensates (BECs) using a minimal optical Raman lattice scheme. Unlike previous endeavors that achieved one-dimensional (1D) SO coupling, this work breaks new ground by demonstrating 2D SO coupling without necessitating phase locking or precise tuning of the optical potentials, which has been a significant challenge in experimental setups.

Spin-orbit coupling is pivotal in understanding various quantum phenomena, especially in the field of condensed matter physics, where it plays a crucial role in the emergence of topological insulators and superconductors. These states are essential due to their exotic properties, such as the presence of Majorana fermions. The synthetic realization of SO coupling within cold atom systems provides a clean and controllable platform for exploring these phenomena further.

Experimental Methods and Findings

The authors innovatively employ a minimal optical Raman lattice scheme in a $^{87}$Rb degenerate gas. By utilizing a setup where laser beams form a square lattice, they are able to generate 2D SO coupling. The experiment involves BEC loaded into optical lattices, where Raman beams introduce the SO interaction. A significant aspect of this experiment is the modulation of the relative phase between lattice beams, which enables control over the transition between 1D and 2D SO coupling.

Key results are observed in the momentum distribution and spin texture of the atomic cloud. By varying the experimental parameters such as the detuning and optical path length, the paper demonstrates the crossover from 1D to 2D SO couplings, as evidenced by the altered momentum space distributions and spin textures. The paper further identifies topological band structures by measuring spin polarization across different symmetry points in the momentum space.

Implications and Future Developments

The realization of 2D SO coupling opens up a multitude of opportunities in the paper of quantum systems. The primary advantage lies in the system's robustness against fluctuations and its high level of control, making it ideal for investigating exotic phases of matter, such as topological superconductors and insulators. Moreover, the scheme presented herein has the potential to be applied to fermionic systems, paving the way for explorations into quantum anomalous Hall effects and the advancement toward realizing topological superfluids.

The findings could significantly impact the understanding of SO effects in various quantum phases, potentially leading to the experimental observation of Majorana quasiparticles. By extending this setup to three-dimensional optical lattices, researchers may explore even more complex topological states, such as Weyl semimetals, thereby expanding the horizon of quantum simulation in cold atom systems.

In conclusion, this paper not only demonstrates a successful realization of 2D SO coupling in BECs but also sets a strong foundation for future research in synthetic quantum systems, offering a promising avenue for the exploration of advanced quantum states and their technological implications.