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Physical Review A

Synthesizing quantum Hall systems with multiple optical clock transition couplings

Changyue Sun, Xinye Xu

Published Oct 16, 2024• 0 citations
Publisher

Abstract

The recent experimental realization of clock-laser-induced synthetic gauge fields and one-dimensional spin-orbit coupling in ultracold alkaline-earth(-like) atoms provides a new way to explore topological quantum states with suppressed heating effects. Here, we propose a scheme for realizing a synthetic quantum Hall tube and ribbon in an optical lattice clock system with multiple optical clock transition couplings. The legs of the synthetic Hall system are composed of the atomic ground and metastable orbital states, and the couplings between the legs are generated by clock lasers, resulting in a synthetic gauge flux. We investigate the band structure and topological phase diagram under various conditions and demonstrate the phase transition. The momentum-resolved quench dynamics of the synthetic Hall system is analyzed to demonstrate the presence of gauge flux on plaquettes and reveal the critical point of the phase transition. The hyperfine spin can serve as an additional synthetic dimension, allowing a two-component Hall system to be realized in synthetic dimensions. A size-enlarged Hall system could be realized by coupling the magnetic sublevels and orbital states simultaneously. Our scheme is within reach of existing optical lattice clocks and thus provides a realistic method to achieve topological quantum Hall systems with ultracold alkaline-earth(-like) atoms. This study paves the way for realizing quantum spin Hall states with hyperfine spins and has the potential to explore more interesting topological phases.

DOI
10.1103/physreva.110.043109

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The recent experimental realization of clock-laser-induced synthetic gauge fields and one-dimensional spin-orbit coupling in ultracold alkaline-earth(-like) atoms provides a new way to explore topological quantum states with suppressed heating effects. Here, we propose a scheme for realizing a synthetic quantum Hall tube and ribbon in an optical lattice clock system with multiple optical clock transition couplings. The legs of the synthetic Hall system are composed of the atomic ground and metastable orbital states, and the couplings between the legs are generated by clock lasers, resulting in a synthetic gauge flux. We investigate the band structure and topological phase diagram under various conditions and demonstrate the phase transition. The momentum-resolved quench dynamics of the synthetic Hall system is analyzed to demonstrate the presence of gauge flux on plaquettes and reveal the critical point of the phase transition. The hyperfine spin can serve as an additional synthetic dimension, allowing a two-component Hall system to be realized in synthetic dimensions. A size-enlarged Hall system could be realized by coupling the magnetic sublevels and orbital states simultaneously. Our scheme is within reach of existing optical lattice clocks and thus provides a realistic method to achieve topological quantum Hall systems with ultracold alkaline-earth(-like) atoms. This study paves the way for realizing quantum spin Hall states with hyperfine spins and has the potential to explore more interesting topological phases.
We report the experimental realization of a synthetic three-leg Hall tube with ultracold fermionic atoms in a one-dimensional optical lattice. The legs of the synthetic tube are composed of three hyperfine spin states of the atoms, and the cyclic interleg links are generated by two-photon Raman transitions between the spin states, resulting in a uniform gauge flux ϕ penetrating each side plaquette of the tube. Using quench dynamics, we investigate the band structure of the Hall tube system for a commensurate flux ϕ=2π/3. Momentum-resolved analysis of the quench dynamics reveals a critical point of band gap closing as one of the interleg coupling strengths is varied, which is consistent with a topological phase transition predicted for the Hall tube system.
Realizing the topological bands of helical states poses a challenge in studying ultracold atomic gases. Motivated by the recent experimental success in realizing chiral optical ladders, here we present a scheme for synthesizing topological quantum matter, especially the quantum spin Hall phase, in the chiral optical ladders. More precisely, we first establish the synthetic pseudo-spin-orbit coupling and Zeeman splitting in the chiral ladders. After analyzing the band structure of the ladders exposed to the bichromatic optical potentials, we report the existence of quantum spin Hall phase. We further identify a rich phase diagram of the bichromatic chiral ladders, illustrating that our proposal features a large space of system parameters exhibiting quantum phase transitions. Our scheme is within reach of the existing ladder optical lattices and hence provides a new method to engineer the elaborate topological bands for cold atomic gases.
We propose to simulate and detect quantum anomalous Hall phase with ultracold atoms in a one-dimensional optical lattice, with the other synthetic dimension being realized by modulating spin-orbit coupling. We show that the system manifests a topologically nontrivial phase with two chiral edge states which can be readily detected in this synthetic two-dimensional system. Moreover, it is interesting that at the phase transition point there is a flat energy band and this system can also be in a topologically nontrivial phase with two Fermi zero modes existing at the boundaries by considering the synthetic dimension as a modulated parameter. We also show how to measure these topological phases experimentally in ultracold atoms. Another model with a random Rashba and Dresselhaus spin-orbit coupling strength is also found to exhibit topological nontrivial phase, and the impact of the disorder to the system is revealed.
We demonstrate a novel way of synthesizing spin-orbit interactions in ultracold quantum gases, based on a single-photon optical clock transition coupling two long-lived electronic states of two-electron ^{173}Yb atoms. By mapping the electronic states onto effective sites along a synthetic "electronic" dimension, we have engineered fermionic ladders with synthetic magnetic flux in an experimental configuration that has allowed us to achieve uniform fluxes on a lattice with minimal requirements and unprecedented tunability. We have detected the spin-orbit coupling with fiber-link-enhanced clock spectroscopy and directly measured the emergence of chiral edge currents, probing them as a function of the flux. These results open new directions for the investigation of topological states of matter with ultracold atomic gases.
We describe a synthetic three-leg Hall ladder system with a tunable magnetic flux for neutral 173Yb^{173}\mathrm{Yb}173Yb atoms in a one-dimensional optical lattice. The ladder legs are formed by three hyperfine ground spin states of the atoms, and the complex interleg links are generated through Raman couplings between the spin states using multiple laser beams. The effective magnetic flux through a ladder plaquette $\ensuremath{\phi}$ is controlled by the angles of the Raman laser beams with the lattice axis. We investigate the quench dynamics of the Hall ladder system for $\ensuremath{\phi}\ensuremath{\approx}\frac{\ensuremath{\pi}}{3},\frac{\ensuremath{\pi}}{2},$ and $\frac{2\ensuremath{\pi}}{3}$ after a sudden application of the Raman coupling in various interleg link configurations. The semiclassical trajectory of the atoms in the plane of the spin composition and lattice position exhibits the characteristic motion of the effective magnetic field. In a tube configuration with the three legs cyclically linked, the quench evolution was observed to be substantially damped, which is attributed to the random flux threading the Hall tube.
Recent experimental realization of one-dimensional spin-orbit coupling (SOC) for ultracold alkaline-earth(-like) atoms in optical lattice clocks opens a new avenue for exploring exotic quantum matter because of the strongly suppressed heating of atoms from lasers comparing with alkaline-earth atoms. Here we propose a scheme to realize two-dimensional (2D) Rashba and three-dimensional (3D) Weyl types of SOC in a 3D optical lattice clock and explore their topological phases. With 3D Weyl SOC, the system can support topological phases with various numbers as well as types (I or II) of Weyl points. The spin distributions of such topological bands for 2D Rashba and 3D Weyl SOCs can be detected using suitably designed spectroscopic sequences. Our proposal may pave the way for the experimental realization of robust topological quantum matters and their exotic quasiparticle excitations in ultracold atomic gases.