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Synthetic gauge field with highly magnetic lanthanide atoms

Xiaoling Cui, Biao Lian, Tin-Lun Ho, Benjamin L. Lev, and Hui Zhai
Phys. Rev. A 88, 011601(R) – Published 23 July 2013
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Abstract

We present a scheme for generating a synthetic magnetic field and spin-orbit coupling via Raman coupling in highly magnetic lanthanide atoms such as dysprosium. Employing these atoms offers several advantages for realizing strongly correlated states and exotic spinor phases. The large spin and narrow optical transitions of these atoms allow the generation of synthetic magnetic fields that are an order of magnitude larger than those in the alkali metals, but with considerable reduction of the heating rate for equal Raman coupling. The effective Hamiltonian of these systems differs from that of the alkali metals' by an additional nematic coupling term, which leads to a phase transition in the dressed states as detuning varies. For high-spin condensates, spin-orbit coupling leads to a spatially periodic structure, which is described in a Majorana representation by a set of points moving periodically on a unit sphere. We name this a “Majorana spinor helix,” in analogy to the persistent spin-12 helix observed in electronic systems.

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  • Received 26 March 2013

DOI:https://doi.org/10.1103/PhysRevA.88.011601

©2013 American Physical Society

Authors & Affiliations

Xiaoling Cui1, Biao Lian1,2, Tin-Lun Ho1,3, Benjamin L. Lev2,4,5, and Hui Zhai1

  • 1Institute for Advanced Study, Tsinghua University, Beijing, 100084, People's Republic of China
  • 2Department of Physics, Stanford University, Stanford, California 94305, USA
  • 3Department of Physics, The Ohio State University, Columbus, Ohio 43210, USA
  • 4Department of Applied Physics, Stanford University, Stanford, California 94305, USA
  • 5E. L. Ginzton Laboratory, Stanford University, Stanford, California 94305, USA

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Vol. 88, Iss. 1 — July 2013

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  • Figure 1
    Figure 1
    (a) Raman laser and quantization B-field configuration; (b) Raman coupling scheme for an alkali-metal atom such as Rb (left) and for Dy (right); (c) Raman transition energy-level diagram for magnetic sublevels of the F=8 ground state of bosonic Dy.Reuse & Permissions
  • Figure 2
    Figure 2
    (a) The dispersion of the lowest branch for the Dy case with different δ [indicated by the arrows in (b)]. (b) kmin as a function of δ for Dy. The dashed line in (b) excludes the tensor term. (c) Majorana spinor representation for two ground-state spinor wave functions at different δ [marked by (1) and (2)] in (b). (d) dkmin/dδ (which is proportional to Beff) for Dy (black solid line; black dashed line excludes the tensor term contribution) and for Rb (orange solid line). In all cases, Ω is fixed at 4EL, and for the Rb case the strength of the quadratic Zeeman term ωqFz2 is taken as ωq=1.9EL, as used in Ref. [1]. In all plots, [kmin,Ek,δ] are in units of [2kL,EL,EL].Reuse & Permissions
  • Figure 3
    Figure 3
    (a) Single-particle spectrum for δ=0 and Ω=0.083EL. k, Ek are in units of 2kL and EL, respectively. (b) A one-parameter phase diagram in terms of Ω/EL. δ is fixed at zero. For the purpose of illustration, we choose a set of parameters {g0,⋯,g16}={6,7,7,7,7,2,0,7,7} as an example (other interaction parameters will result in spinors of differing symmetry—see Ref. [26]; these parameters remain unmeasured for Dy). With this set of interaction parameters, the system is in an octahedron Oh phase at zero Ω, and C3v(α), C3v(β), and C∞v phases for 0<Ω/EL<0.101, 0.101<Ω/EL<0.133, and Ω/EL>0.133, respectively. The phases are labeled by symmetry in the dressed-state basis. (c) Schematic of a “Majorana spinor helix” in the C3v(β) phase of (b). The gray lines are the trajectory of each Majorana point on the sphere vs ŷ translation.Reuse & Permissions
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