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Chinese Physics B

Suppression of moving-potential effect in an optical Raman lattice scheme for spin–orbit-coupled alkaline-earth fermions

Rui Wu, Han Zhang, Tao Deng, Wen-Wei Wang, Xibo Zhang

Published Mar 3, 2026• 0 citations
Publisher

Abstract

Abstract Optical Raman lattices in ultra-cold alkali-metal and alkaline-earth atoms provide a powerful method to synthesize spin–orbit (SO) coupling. While the ground-state energy splittings (divided by Planck’s constant) can reach the range of tens of megahertz in alkali-metal atoms, the typical ground-state energy splittings are on the order of tens of kilohertz or smaller in alkaline-earth atoms (AEAs) such as 87 Sr. For AEAs, because such limited ground-state energy splittings are rather close to the kilohertz-scale recoil energy that is relevant for optical lattice physics, a standard implementation of a two-dimensional (2D) optical Raman lattice can lead to parasitic periodic moving potentials that heat up the atoms and severely limit the atomic lifetime. Recently, an improved optical Raman lattice scheme was proposed and experimentally realized in ultra-cold strontium fermions, which significantly enhanced the lifetime of 2D-SO-coupled fermions. However, a concrete electro-optical setup has yet to be demonstrated, and its control precision needs to be quantified. Here we demonstrate the electro-optical setup of an improved optical Raman lattice scheme that suppresses the effect of moving lattice potentials for alkaline-earth fermions by introducing a sufficiently large frequency separation between two sets of laser polarization components, where each set yields an independent Raman coupling. To quantify the precision of this setup, we feedback-control the relative phase between the two sets of Raman couplings, which is an important parameter characterizing the 1D–2D crossover of SO couplings, and measure the stability of this phase over hour-long periods. We also investigate the optimum range for the applied frequency separation. Our approach provides a useful tool that helps achieve long-lived SO-coupled systems using AEAs.

DOI
10.1088/1674-1056/ae4c71

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Abstract Optical Raman lattices in ultra-cold alkali-metal and alkaline-earth atoms provide a powerful method to synthesize spin–orbit (SO) coupling. While the ground-state energy splittings (divided by Planck’s constant) can reach the range of tens of megahertz in alkali-metal atoms, the typical ground-state energy splittings are on the order of tens of kilohertz or smaller in alkaline-earth atoms (AEAs) such as 87 Sr. For AEAs, because such limited ground-state energy splittings are rather close to the kilohertz-scale recoil energy that is relevant for optical lattice physics, a standard implementation of a two-dimensional (2D) optical Raman lattice can lead to parasitic periodic moving potentials that heat up the atoms and severely limit the atomic lifetime. Recently, an improved optical Raman lattice scheme was proposed and experimentally realized in ultra-cold strontium fermions, which significantly enhanced the lifetime of 2D-SO-coupled fermions. However, a concrete electro-optical setup has yet to be demonstrated, and its control precision needs to be quantified. Here we demonstrate the electro-optical setup of an improved optical Raman lattice scheme that suppresses the effect of moving lattice potentials for alkaline-earth fermions by introducing a sufficiently large frequency separation between two sets of laser polarization components, where each set yields an independent Raman coupling. To quantify the precision of this setup, we feedback-control the relative phase between the two sets of Raman couplings, which is an important parameter characterizing the 1D–2D crossover of SO couplings, and measure the stability of this phase over hour-long periods. We also investigate the optimum range for the applied frequency separation. Our approach provides a useful tool that helps achieve long-lived SO-coupled systems using AEAs.
We propose a hierarchy set of minimal optical Raman lattice schemes to pave the way for experimental realization of high-dimensional spin-orbit (SO) couplings for ultracold atoms, including two-dimensional (2D) Dirac type, 2D Rashba type, and three-dimensional (3D) Weyl type. The proposed Dirac-type SO coupling exhibits precisely controllable high symmetry, for which a large topological phase region is predicted. The generation of 2D Rashba and 3D Weyl types requires that two sources of laser beams have distinct frequencies of factor 2 difference. Surprisingly, we find that 133Cs^{133}\mathrm{Cs}133Cs atoms provide an ideal candidate for the realization. A common and essential feature is of high controllability and absent of any fine-tuning in the realization, and the resulting SO coupled ultracold atoms have a long lifetime. In particular, a long-lived topological Bose gas of 2D Dirac SO coupling has been proved in the follow-up experiment. These schemes essentially improve over the current experimental accessibility and controllability, and open a realistic way to explore novel high-dimensional SO physics, particularly quantum many-body physics and quantum far-from-equilibrium dynamics with novel topology for ultracold atoms.
Recently, alkaline-earth (-like) atoms and alkaline earth metals (AEL) gained experimental and theoretical interest principally related to the possibility offered in metrological field by the excitation of visible and UV clock transitions. AEL atoms, in their neutral \nform and in the ground state, have a null total electronic momentum, resulting nearly insensitive to external magnetic fields. While the absence of magnetic coupling does not allow the simply interactions tuning by exploiting Feshbach resonances as it occurs \nin alkaline atoms, these atoms are characterized by highly symmetric ground states allowing the simulation of SU(N) systems. This characteristic, that can be attributed in AEL atoms to the decoupling between electronic and nuclear atomic momenta, can be \nexploited to perform quantum simulation of a wealth of novel systems and constitutes a fundamental property of isotopes that have a nonzero nuclear spin, as it occurs for all the fermionic species and in particular for 173Yb and 87Sr. This feature also ensures the \nabsence of spin-changing collisions in ground state sublevels, implying that nuclear-spin mixtures are observationally stable. This attribute is fundamental for the study of transitions between different nuclear-spin states, for example by exploiting the two-photon \nRaman coupling. The degeneracy related to the SU(N) symmetry can be controllably removed by applying a two-photon Raman coupling, allowing for the simulation of systems with broken symmetries. \nBesides the possibility to induce couplings within the nuclear-spin degree of freedom, AEL atoms also offer the possibility to access a second, electronic degree of freedom; the possibility to address visible doubly-forbidden transitions between long-lived electronic \nclock states comprises a fantastic tool that allowed the building of optical lattice clocks improving metrological measurements and offering a richer platform for simulating complex systems. \nThe main difference between the two internal degrees of freedom offered by AEL atoms is that the possibility to address ultranarrow optical clock transitions exists also for AEL bosonic isotopes in which the nuclear-spin degree of freedom is not present because the \ntotal atomic momentum is absent. \nThe possibilities related to the excitation of long-lived metastable triplet levels, that, referring only to the lowest lying atomic levels are 3P(0;2) (in Russell-Saunders approximation they result doubly forbidden with respect to the electric dipole operator), are \nmultiple. If bosonic atoms are considered, the metrological applications based on the clock transition at the state of the art have performances comparable to optical lattice clocks realized with fermionic isotopes. Bosonic isotopes, requiring external fields in order \nto excite transitions from the ground state to long-lived states, have been proposed as good candidates in order to build a reliable and fast system in which controllable qu-bits could be realized. Most of these applications, and in particular the possibility to create \nquantum computers with neutral atoms, crucially rely on the control of the scattering properties of atoms in different electronic states. \nRegarding fermionic isotopes, the clock transitions recently allowed for the demonstration of spin-orbit coupling and quantum simulation via the synthetic dimension approach. As recently discovered, the clock transitions from the ground to the 3P(0;2) states give rise to rich interactions possibilities between atoms in the fundamental and in the metastable states. The spin-exchange interaction that has been observed between ground and metastable states, supports also a new kind of Feshbach resonance, called Orbital Feshbach Resonance (OrbFR). As occurs in magnetic Feshbach resonances for alkali atoms, also the OrbFR, that occurs in AEL atoms, supports the existence of extremely shallow homonuclear molecules. After considering the (s-wave) scattering parameters of all the AEL atoms that have been characterized experimentally, 173Yb is the only isotope in which the production and manipulation of Orbital Feshbach molecules (produced e.g. with photoassociation) is experimentally viable. Molecules generated by employing this atom, may lead to the investigation of fermionic superfluidity in still-unexplored regimes. In this thesis we report the characterization of interactions in bosonic 174Yb isotope by probing the clock transition between the singlet 1S0 ground state and the triplet 3P0 \nmetastable excited state. Interactions and inelastic losses between ground-state and excited metastable-state atoms have been experimentally determined with high accuracy, resulting consistent with an indipendent evaluation realized in the same period by Yb \nBEC group at LKB. \nThe obtained values for the interactions among ground and metastable atoms for the specified isotope constitute a first step in order to design an experimental system in which quantum information can be realized by means of exploiting the clock transition of bosonic Yb atoms. \nThis work, by exploiting the internal degrees of freedom of 173Yb atoms, reports a study on Orbital Feshbach molecules, showing experimentally the possibility to employ the nuclear degree of freedom in 173Yb atoms to manipulate and precisely detect homo-nuclear photoassociated molecules. \nThis first result regarding this new kind of shallow-bound molecules allowed the characterization of interactions between ground-state and metastable-state of 173Yb atoms. \nThis first intensive study of orbital Feshbach molecules is a fundamental step for future studies on the possibilities offered by these homo-nuclear molecules. \nFinally, we exploited the ground state SU(N) symmetry and its controlled breaking via Raman coupling (in 173Yb N = 1...6) to simulate the physical processes that are supposed to be driven by the hybridation of d-orbitals of iron atoms in iron based-superconductors, \nin which orbital-selective Mott insulating phases have been experimentally observed and are suspected to be the fundamental ingredient to achieve high-temperature superconductivity in these compounds.
Cold atoms with laser-induced spin-orbit (SO) interactions provide a platform to explore quantum physics beyond natural conditions of solids. Here we propose and experimentally realize two-dimensional (2D) SO coupling and topological bands for a rubidium-87 degenerate gas through an optical Raman lattice, without phase-locking or fine-tuning of optical potentials. A controllable crossover between 2D and 1D SO couplings is studied, and the SO effects and nontrivial band topology are observed by measuring the atomic cloud distribution and spin texture in momentum space. Our realization of 2D SO coupling with advantages of small heating and topological stability opens a broad avenue in cold atoms to study exotic quantum phases, including topological superfluids.
We demonstrate all-optical implementation of spin-orbit coupling (SOC) in a two-electron Fermi gas of 173Yb^{173}\mathrm{Yb}173Yb atoms by coupling two hyperfine ground states with a narrow optical transition. Due to the SU(N)\mathrm{SU}(N)SU(N) symmetry of the 1S0^{1}S_{0}1S0​ ground-state manifold which is insensitive to external magnetic fields, an optical ac Stark effect is applied to split the ground spin states, which exhibits a high stability compared with experiments on alkali-metal and lanthanide atoms, and separate out an effective spin-12\frac{1}{2}21​ subspace from other hyperfine levels for the realization of SOC. The dephasing spin dynamics when a momentum-dependent spin-orbit gap is suddenly opened and the asymmetric momentum distribution of the spin-orbit-coupled Fermi gas are observed as a hallmark of SOC. The realization of all-optical SOC for ytterbium fermions should offer a route to a long-lived spin-orbit-coupled Fermi gas and greatly expand our capability of studying spin-orbit physics with alkaline-earth-metal-like atoms.
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.
We introduce a method for quantum simulation of U(1) lattice gauge theories coupled to matter, utilizing alkaline-earth(-like) atoms in state-dependent optical lattices.The proposal enables the study of both gauge and fermionic matter fields without integrating out one of them in one and two dimensions.We focus on a realistic and robust implementation that utilizes the long-lived metastable clock state available in alkaline-earth(-like) atomic species.Starting from an ab initio modeling of the experimental setting, we systematically carry out a derivation of the target U(1) gauge theory.This approach allows us to identify and address conceptual and practical challenges for the implementation of lattice gauge theories that-while pivotal for a successful implementation-have never been rigorously addressed in the literature: those include the specific engineering of lattice potentials to achieve the desired structure of Wannier functions and the subtleties involved in realizing the proper separation of energy scales to enable gauge-invariant dynamics.We discuss realistic experiments that can be carried out within such a platform using the fermionic isotope 173 Yb, addressing via simulations all key sources of imperfections, and provide concrete parameter estimates for relevant energy scales in both one-and two-dimensional settings.