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arXiv:2406.14042 · Physical Review A

Synthetic spin-orbit coupling for the multispin models in optical lattices

Zhen Zheng, Yan-Qing Zhu, Shanchao Zhang, Shi-Liang Zhu, Z. D. Wang

Published Sep 23, 2024• 4 citations
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Abstract

The essential role of synthetic spin-orbit coupling in discovering new topological matter phases with cold atoms is widely acknowledged. However, the engineering of spin-orbit coupling remains unclear for arbitrary-spin models due to the complexity of spin matrices. In this paper, we develop a more general but relatively straightforward method to achieve spin-orbit coupling for multispin models. Our approach hinges on controlling the coupling between distinct pseudospins through two intermediary states, resulting in tunneling with spin flips that have direction-dependent strength. The engineered spin-orbit coupling can facilitate topological phase transitions with Chern numbers over 1, a unique characteristic of multispin models compared to spin-1/2 models. By utilizing existing cold atom techniques, our proposed method provides an ideal platform for investigating topological properties related to large Chern numbers.

DOI
10.1103/physreva.110.033327

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The essential role of synthetic spin-orbit coupling in discovering new topological matter phases with cold atoms is widely acknowledged. However, the engineering of spin-orbit coupling remains unclear for arbitrary-spin models due to the complexity of spin matrices. In this paper, we develop a more general but relatively straightforward method to achieve spin-orbit coupling for multispin models. Our approach hinges on controlling the coupling between distinct pseudospins through two intermediary states, resulting in tunneling with spin flips that have direction-dependent strength. The engineered spin-orbit coupling can facilitate topological phase transitions with Chern numbers over 1, a unique characteristic of multispin models compared to spin-1/2 models. By utilizing existing cold atom techniques, our proposed method provides an ideal platform for investigating topological properties related to large Chern numbers.
Topological phases with a widely tunable number of edge modes have been extensively studied as a typical class of exotic states of matter with potentially important applications. Although several models have been shown to support such phases, they are not easy to realize in solid-state systems due to the complexity of various intervening factors. Inspired by the realization of synthetic spin-orbit coupling in a cold-atom system [Z. Wu et al., Science 354, 83 (2016)], we propose a periodic quenching scheme to realize large-topological-number phases with multiple edge modes in optical lattices. Via introducing the periodic quenching to the Raman lattice, it is found that a large number of edge modes can be induced in a controllable manner from the static topologically trivial system. Our result provides an experimentally accessible method to artificially synthesize and manipulate exotic topological phases with large topological numbers and multiple edge modes.
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Spin and orbital are two basic degrees of freedom that play significant roles in exploring exotic quantum phases in optical lattices with synthetic spin-orbit coupling (SOC) and high orbital bands, respectively. Here, we combine these two crucial ingredients for the first time by proposing a completely new orbital optical Raman lattice scheme to explore exotic high-orbital Bose condensates with Raman-induced SOC in a square lattice. We find that both the SOC and p-orbital interactions influence the condensed state of bosons. Their interplay results in two novel high-orbital many-body quantum phases: the uniform angular momentum superfluid phase, which exhibits a global topological chiral orbital current characterized by a uniform Chern number, and the two-dimensional topological spin-orbital supersolid phase, which is characterized by the spin and orbital angular momentum density wave patterns and topological excitations with opposite Chern numbers, respectively protecting the chiral and antichiral edge modes in the neighboring supersolid clusters. Our scheme may open a new avenue for exploring exotic SOC and high-orbital physics in optical lattices, and is expected to advance the experimental realization of novel supersolids in higher dimensions.
In cold atom, the coupling between "spin" (atomic internal hyperfine states) and "orbit" (atomic center-of-mass motion) can be induced by Raman transition, where different hyperfine states are coupled by a pair of Raman lasers. In recent years, this synthetic spin-orbit coupling has received tremendous attention, as it leads to a variety of novel quantum phenomena in precisely controllable cold atom systems. In this thesis, we first present a comprehensive analysis of one-, two- and many- particle physics of harmonically trapped atoms with spin-orbit coupling, followed by the study of "novel spin-orbit coupling" in two different systems: (1) cold atom spinor mixtures and (2) cold atoms in an optical cavity. In the first system, we consider a spinor mixture consisting of two species of cold atoms, where the spin-orbit coupling can be transmitted from one species to the other, and we discuss novel topological properties and the supersolid stripe phase in this mixture. In the second system, we consider the coupling among three parts: the cavity photon field, the atomic internal hyperfine states, and the atomic external center-of-mass motion, and we discuss how this coupling affects familiar quantum optical phenomena, such as Rabi oscillation and Dicke superradiance phase transition. Our novel systems contribute new and practical platforms for the research field of synthetic spin-orbit coupling in cold atoms.
Achieving full control of a Bose-Einstein condensate can have valuable applications in metrology, quantum information processing, and quantum condensed matter physics. We propose protocols to simultaneously control the internal (related to its pseudospin-1/2) and motional (position-related) states of a spin-orbit-coupled Bose-Einstein condensate confined in a Morse potential. In the presence of synthetic spin-orbit coupling, the state transition of a noninteracting condensate can be implemented by Raman coupling and detuning terms designed by invariant-based inverse engineering. The state transfer may also be driven by tuning the direction of the spin-orbit-coupling field and modulating the magnitude of the effective synthetic magnetic field. The results can be generalized for interacting condensates by changing the time-dependent detuning to compensate for the interaction. We find that a two-level algorithm for the inverse engineering remains numerically accurate even if the entire set of possible states is considered. The proposed approach is robust against the laser-field noise and systematic device-dependent errors.