Realization of Qi-Wu-Zhang model in spin-orbit-coupled ultracold fermions

Abstract

Based on the optical Raman lattice technique, we experimentally realize the Qi-Wu-Zhang model for quantum anomalous Hall phase in ultracold fermions with two-dimensional (2D) spin-orbit (SO) coupling. We develop a novel protocol of pump-probe quench measurement to probe, with minimal heating, the resonant spin flipping on particular quasi-momentum subspace called band-inversion surfaces. With this protocol we demonstrate a continuous crossover between 1D and 2D SO couplings by tuning the relative phase between two coherent Raman couplings, and detect the non-trivial topological band structures by varying the twophoton detuning. The non-trivial band topology is also observed by slowly loading the atoms into optical Raman lattices and measuring the spin textures. Our results show solid evidence for the realization of the minimal SO-coupled quantum anomalous Hall model, which can provide a feasible platform to investigate novel topological physics including the correlation effects with SO-coupled ultracold fermions.

Topological chiral currents in the Gross-Neveu model extension

“…This scheme avoids the use of state-dependent optical lattices or Floquet-assisted tunnelings in interacting Fermi gases, minimising in this way the effective heating due to residual photon scattering from the auxiliary excited states. In light of the recent experimental progress with Raman optical lattices [150][151][152][153], we believe that the current scheme opens a new direction in the realisation of strongly-coupled QFTs that incorporate Lorentz-violating terms of the SME, such as the GNME studiend in this work. Additionally, the particular lattice regularization explored in this work would allow to explore the interplay of these relativistic models with current-carrying topological phases.…”

“…In these schemes, one combines periodic ac-Stark shifts from a standing wave with Raman potentials that stem from the interference of lasers in standing-and traveling-wave configurations. As discussed in more detail below, when the beatnote of the standing-and traveling-wave laser beams is tuned close to the spin-flip transition frequency, the Raman cross terms do not drive local spin flips [202][203][204][205][206], but instead assist a spin-flipping tunneling that can be used to simulate spin-orbit coupling [150][151][152][153]. Although these Raman schemes may also be limited by residual photon scattering from the off-resonant excited state, the associated heating is not as severe as that of fermions trapped in state-dependent lattices since, if the available laser intensity is not the limiting factor, this heating can be minimised by working with larger Raman detunings ∆ with respect to the excited state (see inset of Fig.…”

Unconventional Floquet topological phases from quantum engineering of band inversion surfaces

“…( 1) with H s (k) = h(k) • σ and V(t)σ z = 2V 0 cos ωtσ z (σ x,y,z are the Pauli matrices). Here h(k) = (2t so sin k x , 2t so sin k y , m z − 2t 0 cos k x − 2t 0 cos k y ) describes a quantum anomalous Hall model [61], which has been realized in cold atoms, with t 0 (t so ) being the spin-conserved (-flipped) hopping in a square optical Raman lattice [62][63][64]. The periodic drive V(t) can be achieved by modulating the Zeeman energy.…”

Large-$N$ Chern insulators: lattice field theory and quantum simulation approaches to correlation effects in the quantum anomalous Hall effect

“…In this section, we focus on QSs based on ultracold atoms in optical lattices [92]. We present a detailed scheme for the QS of the four-Fermi-Wilson model using the so-called Raman optical lattices [121][122][123][124][125][126]. These quantum simulators can be considered as Fermi gases with a specific synthetic spin-orbit coupling [118][119][120], mimicking the coupling of the intrinsic angular momentum of the electron with its own motion [233] in the solid state [234,235].…”

“…In a recent manuscript [117], we have explored a different route to explore correlated QAH insulators and their connection to strongly-coupled four-Fermi QFTs. This alternative route considers Fermi gases with synthetic spin-orbit coupling [118][119][120] induced by a so-called Raman optical lattice [121,122], which has been recently demonstrated in experiments [123][124][125][126]. Although residual photon scattering from the Raman beams can also induce some heating, it should not be as severe as in the shaken optical lattice if sufficient laser power is available, allowing one to work at sufficiently large Raman detunings.…”