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arXiv:2412.04009 · Physical Review A

Orbital optical Raman lattice

Zhihao Huang, Kou-Han Ma, Bao‐Zong Wang, W. Vincent Liu, Xiong-Jun Liu

Published Dec 23, 2025• 0 citations
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Abstract

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.

DOI
10.1103/zdrw-kcpf

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The experimental realization of emergent spin-orbit coupling through laser-induced Raman transitions in ultracold atoms paves the way for exploring novel superfluid physics and simulating exotic many-body phenomena. A recent proposal with the use of Laguerre-Gaussian lasers enables another fundamental type of coupling between spin and orbital angular momentum (SOAM) in ultracold atoms. We hereby study quantum phases of a realistic Bose-Einstein condensate (BEC) with this synthetic SOAM coupling in a disk-shaped geometry, respecting radial inhomogeneity of the Raman coupling. We find that the experimental system naturally resides in a strongly interacting regime in which the phase diagram significantly deviates from the single-particle picture. The interplay between SOAM coupling and interaction leads to rich structures in spin-resolved position and momentum distributions, including a stripe phase and various types of immiscible states. Our results would provide a guide for an experimental investigation of SOAM-coupled BECs.
Recent experimental advances to create tunable synthetic spin-orbit coupling (SOC) in ultracold gases provide new possibilities to access fruitful spin-orbit coupled quantum many-body physics. In this paper, we demonstrate that the combined effect of two-dimensional (2D) SOC and one-dimensional (1D) optical lattice in interacting bosons can provide an alternative scheme in ultracold gases to achieve the crossover of the commensurate-incommensurate supersolid ground state ``with respect to the background optical lattice.'' Interestingly, it is shown that the anharmonicity arising from the lattice potential leads to the ``pin'' effect and make the ground-state break the continuous translational symmetry along the direction perpendicular to the 1D lattice, whereas the competition between the lattice period and the SOC length results in the crossover of commensurate-incommensurate ground state along the direction of 1D lattice with discrete translational symmetry breaking. Such a combined effect of SOC and optical lattice, thus, induces a new 2D periodic pattern in the ground state, accompanying with nonzero 2D superfluid density characterizing the supersolid nature in 2D of the ground state. Furthermore, a skyrmion-anti-skyrmion lattice is found associated with the appearance of such supersolid ground state, indicating its topological nontrivial properties. Experimental signature of our proposed supersolid ground state is also predicted by means of the time-of-flight measurement.
Recent advanced experimental implementations of optical lattices with highly tunable geometry open up new regimes for exploring quantum many-body states of matter that had not been accessible previously. Here we report that a topological fermionic superfluid with higher Chern number emerges spontaneously from sss-wave spin-singlet pairing in an orbital optical lattice when its geometry is tuned to explicitly break reflection symmetry. Qualitatively distinct from the conventional scheme that relies on higher partial-wave pairing, the crucial ingredient of our model is topology originating from mixing higher Wannier orbitals. It leads to unexpected changes in the topological band structure at the single-particle level, i.e., the bands are transformed from possessing two flux-$\ensuremath{\pi}$ Dirac points into a single quadratic touching point with flux $2\ensuremath{\pi}$. Based on such engineered single-particle bands, spin-singlet pairing of ultracold fermions arising from standard sss-wave attractive interaction is found to induce higher Chern number (Chern number of 2) and topologically protected chiral edge modes, all occurring at a higher critical temperatures in relative scales, potentially circumventing one of the major obstacle for its realization in ultracold gases.