Abstract
The experimental and theoretical research of spin–orbit-coupled ultracold atomic gases has advanced and expanded rapidly in recent years. Here, we review some of the progress that either was pioneered by our own work, has helped to lay the foundation, or has developed new and relevant techniques. After examining the experimental accessibility of all relevant spin–orbit coupling parameters, we discuss the fundamental properties and general applications of spin–orbit-coupled Bose–Einstein condensates (BECs) over a wide range of physical situations. For the harmonically trapped case, we show that the ground state phase transition is a Dicke-type process and that spin–orbit-coupled BECs provide a unique platform to simulate and study the Dicke model and Dicke phase transitions. For a homogeneous BEC, we discuss the collective excitations, which have been observed experimentally using Bragg spectroscopy. They feature a roton-like minimum, the softening of which provides a potential mechanism to understand the ground state phase transition. On the other hand, if the collective dynamics are excited by a sudden quenching of the spin–orbit coupling parameters, we show that the resulting collective dynamics can be related to the famous Zitterbewegung in the relativistic realm. Finally, we discuss the case of a BEC loaded into a periodic optical potential. Here, the spin–orbit coupling generates isolated flat bands within the lowest Bloch bands whereas the nonlinearity of the system leads to dynamical instabilities of these Bloch waves. The experimental verification of this instability illustrates the lack of Galilean invariance in the system.
Highlights
Ultracold atoms are charge neutral, the intrinsic physics relevant to the charge degree of freedom of particles is absent in these systems
We have reviewed the theoretical work showing that the ground state physics of a spin–orbit coupling (SOC) Bose–Einstein condensates (BECs) can be related to the Dicke model and that the phase transition between the plane wave phase and the conventional BEC phase is a Dicke-type phase transition [103]
The transition between the plane wave phase and the conventional BEC phase is of Dicke-type type, which means that the system can be mapped to a Dicke model
Summary
Ultracold atoms are charge neutral, the intrinsic physics relevant to the charge degree of freedom of particles is absent in these systems. The study of SOC ultracold atomic systems can be divided into two stages, separated by the benchmark experiment of Ian Spielman’s group at the National Institute of Standards and Technology (NIST) in 2011 [9] Before this experiment, most research efforts focused on theoretical proposals regarding the implementation of SOC in ultracold atoms and the physical effects on the single particle level. The Washington State University (WSU) group investigated the physics of the ZB effect in 87Rb [21], realized the Dicke model and the Dicke phase transition [22], measured the collective excitation spectrum (indicating the existence of roton-like structures) [23], and demonstrated the lack of Galilean invariance in SOC systems by measuring dynamical instabilities of a BEC in a moving optical lattice [24]. We will first briefly describe the experimental approaches to generate SOC [9, 16,17,18,19,20,21,22,23,24,25,26,27,28,29, 31,32,33,34,35]
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