Synthetic Dimensions and Spin-Orbit Coupling with an Optical Clock Transition

Abstract

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. DOI: 10.1103/PhysRevLett.117.220401 Ultracold atoms are emerging as a very versatile platform for the investigation of topological states of matter [1], thanks to the possibility of using laser light to synthesize artificial gauge fields [2,3] and to engineer lattices with topological band structures [4][5][6][7][8]. A prime element for the emergence of nontrivial topological properties is the presence of spin-orbit coupling (SOC) [9,10], locking the spin of the particles to their motion. This interaction was first synthesized in cold atomic gases by using twophoton Raman transitions [11] coupling two hyperfine spin states with a transfer of momentum. The coupling between spin states also enables a new powerful tool for engineering topological states of matter, which relies on the "synthetic dimension" (SD) concept [12,13]. According to this approach, the internal states of an atom are treated as effective sites along a synthetic lattice dimension, and coherent coupling between them is interpreted in terms of an effective tunneling. This idea has recently been realized in Refs. [14,15], where synthetic flux ladders have been implemented by using the spin degree of freedom, and has allowed the first observation of chiral edge states in ultracold atomic systems. Its extension has inspired several proposals, opening the way, e.g., to the observation of new quantum states [16,17], to the detection of fractional charge pumping [18,19], or to the observation of the four-dimensional quantum Hall effect [20].In this Letter, we demonstrate that SOC and SDs can be efficiently implemented by exploiting different degrees of freedom, specifically, the long-lived electronic state of alkaline-earth(-like) atoms. By using the technology developed in the context of optical atomic clocks, we induce a coherent coupling between the ground state g ¼ 1 S 0 and the metastable state e ¼ 3 P 0 (lifetime ∼20 s) of ultracold 173 Yb atoms. Since the two states are separated by an optical energy, it is possible to have a sizable transfer of momentum with a single-photon transition, as pointed out An ultranarrow clock laser with wavelength λ C drives the singlephoton transition between the ground state g ¼ 1 S 0 and the long...

Synthetic dimensions for cold atoms from shaking a harmonic trap

“…(27) for two relevant cases. Firstly, in Section III A, we consider the simplest experimental setup where the second dimension consists of only two discrete lattice sites, labelled by m = {−1/2, +1/2}.…”

“…In terms of the effective Hamiltonian [Eq. (27)], a system with only two sites along the second dimension simulates a two-leg ladder pierced by a magnetic flux, as shown in Fig. 5(b).…”

“…An exciting development in this direction has been the introduction of the "synthetic dimension" concept into ultracold atomic gases [8,9,[22][23][24][25][26][27][28] and photonics [29][30][31][32]. In this approach, discrete internal degrees of freedom are reinterpreted as labelling lattice sites along an additional synthetic dimension; by externally-coupling together these degrees of freedom, particles can be understood to "hop" between lattice sites and so move along this extra dimension.…”

Tunable spin-orbit coupling for ultracold atoms in two-dimensional optical lattices

“…Although SOC with equal Rashba and Dresselhaus magnitudes have been proposed [28][29][30] and realized [31,32], to access more general forms of SOC, most proposals [33][34][35][36][37] and recent experimental work [38] focus on generating non-Abelian gauge fields, which can be considered as TR-breaking forms of SOC. There exist only a few proposals for specific forms of (TR-invariant) SOC [39,40] and, thus far, no experimental realization.…”

Tuning Feshbach resonances in cold atomic gases with interchannel coupling

“…1(b)(c), the interchannel coupling can be implemented either by imposing Raman lasers coupling the nuclear-spin states in the same manifold (the Raman scheme), or by directly driving the clock transition 1 S 0 -3 P 0 (the Rabi scheme). While coupling the clock states typically require ultra-stable and high-power lasers, which can give rise to additional heating due to the photon recoil, these difficulties should be manageable with existing techniques, particularly in light of the recent experimental realization of synthetic spinorbit coupling in alkaline-earth-like atoms [18][19][20][21]. Note that while the inter-channel couplings also realizes synthetic SOC within the clock-state manifolds, as has recently been experimentally realized, the dressing of the FR and the modification of the resonance properties are related to the shifting of the continuum thresholds of the scattering channels, rather than the momentum transfer of the SOC.…”