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...
The advent of novel measurement instrumentation can lead to paradigm shifts in scientific research. Optical atomic clocks, due to their unprecedented stability 1,2,3 and uncertainty, 4,5,6,7 are already being used to test physical theories 8,9 and herald a revision of the International System of units (SI). 10,11 However, to unlock their potential for cross-disciplinary applications such as relativistic geodesy, 12 a major challenge remains. This is their transformation from highly specialized instruments restricted to national metrology laboratories into flexible devices deployable in different locations. 13,14,15 Here we report the first field measurement campaign performed with a ubiquitously applicable 87 Sr optical lattice clock. 13 We use it to determine the gravity potential difference between the middle of a mountain and a location 90 km apart, exploiting both local and remote clock comparisons to eliminate potential clock errors. A local comparison with a 171 Yb lattice clock 16 also serves as an important check on the international consistency of independently developed optical clocks. This campaign demonstrates the exciting prospects for transportable optical clocks.The application of clocks in geodesy fulfils long-standing proposals to interpret a measurement of the fractional relativistic redshift Δνrel/ν0 to determine the gravity potential difference ΔU = c 2 Δνrel/ν0 between clocks at two sites (c being the speed of light). 12 National geodetic height systems based on classical terrestrial and satellite-based measurements exhibit discrepancies at the decimetre level. 17 Optical clocks, combined with high performance frequency dissemination techniques 18,19 offer an attractive way to resolve these discrepancies, as they combine the advantage of high spectral resolution with small error accumulation over long distances. 18,20 However, to achieve competitive capability requires high clock performance: a fractional frequency accuracy of 1×10 17 corresponds to a resolution of about 10 cm in height. Furthermore, it is important to realize that the sideby-side frequency ratio has to be known to determine the remote frequency shift Δνrel. Taking the uncertainty budgets of optical clocks for granted, harbours the possibility of errors, because very few have been verified experimentally to the low 10 17 region or beyond. 5,7,18,21 A transportable optical clock not only increases the flexibility in measurement sites but mitigates the risk of undetected errors by enabling local calibrations to be performed.The test site chosen for our demonstration of chronometric levelling 12 with optical clocks was the Laboratoire Souterrain de Modane (LSM) in France, with the Italian metrology institute INRIM in Torino serving as the reference site. The height difference between the two sites is approximately 1000 m, corresponding to a fractional redshift of about 10 -13 . From a geodetic point of view, LSM is a challenging and interesting location in which to perform such measurements: firstly, it is located in the middl...
We report on the first direct observation of fast spin-exchange coherent oscillations between different long-lived electronic orbitals of ultracold 173 Yb fermions. We measure, in a model-independent way, the strength of the exchange interaction driving this coherent process. This observation allows us to retrieve important information on the interorbital collisional properties of 173 Yb atoms and paves the way to novel quantum simulations of paradigmatic models of two-orbital quantum magnetism. DOI: 10.1103/PhysRevLett.113.120402 PACS numbers: 03.75.Ss, 34.50.Cx, 37.10.Jk, 67.85.Lm Alkaline-earth-like (AEL) atoms are providing a new valuable experimental platform for advancing the possibilities of quantum simulation with ultracold gases [1]. For instance, the purely nuclear spin of ground-state AEL fermionic isotopes results in the independence of the atom-atom scattering properties from the nuclear spin projection. This feature has enabled the investigation of multicomponent 173 Yb fermions with SUðNÞ interaction symmetry both in optical lattices [2] and in onedimensional quantum wires [3]. In addition to their nuclear spin, AEL atoms offer experimental access to supplementary degrees of freedom, in particular, to a long-lived electronically excited state jei ¼ j 3 P 0 i which can be coherently populated from the ground state jgi ¼ j 1 S 0 i by optical excitation on an ultranarrow clock transition. The possibility of coherently manipulating both the orbital and the spin degree of freedom has recently been envisioned to grant the realization of paradigmatic models of two-orbital magnetism, like the Kondo model [4]. In this context, the two electronic states jgi and jei play the roles of two different orbitals.Recent experiments have investigated the SUðNÞ symmetry in jgi-jei ultracold collisions of two-electron atoms [5] and reported on first signatures of spin-exchange interactions between atoms in the two electronic states [6]. Spin-exchange interactions arise from the difference in the spin-singlet and spin-triplet potential curves in the scattering of one jgi and one jei atom. Let us assume that the two interacting atoms are in different nuclear spin states j↑i and j↓i (where the arrows are placeholders for two arbitrary nuclear spin states) and that they share the same spatial wave function. At zero magnetic field, the degeneracy of the configurations jg↑; e↓i and jg↓; e↑i, which are associated with a well-defined spin in each orbital [7], is lifted by the atom-atom interaction and the eigenstates are the orbital-symmetric (spin-singlet) jeg þ i and the orbitalantisymmetric (spin-triplet) jegFIG. 1 (color online). Two-orbital spin-exchange interaction in AEL atoms. (a) One atom in the ground state jgi and one atom in the long-lived electronic state jei periodically "exchange" their nuclear spins because of the different interaction energy in the spin-singlet jeg þ i and spin-triplet jeg − i two-particle states (note that in the graphical notation, the two-particle exchange symmetry is implicit [7]). (b...
Over five years we have compared the hyperfine frequencies of 133 Cs and 87 Rb atoms in their electronic ground state using several laser cooled 133 Cs and 87 Rb atomic fountains with an accuracy of ∼ 10 −15 . These measurements set a stringent upper bound to a possible fractional time variation of the ratio between the two frequencies :d dt ln ν Rb ν Cs = (0.2 ± 7.0) × 10 −16 yr −1 (1σ uncertainty).The same limit applies to a possible variation of the quantity (µ Rb /µCs)α −0.44 , which involves the ratio of nuclear magnetic moments and the fine structure constant.PACS numbers: 06.30. Ft, 32.80.Pj, 06.20.Jr Since Dirac's 1937 formulation of his large number hypothesis aiming at tying together the fundamental constants of physics [1], large amount of work has been devoted to test if these constants were indeed constant over time [2,3].In General Relativity and in all metric theories of gravitation, variations with time and space of non gravitational fundamental constants such as the fine structure constant α = e 2 /4πǫ 0 c are forbidden. They would violate Einstein's Equivalence Principle (EEP). EEP imposes the Local Position Invariance stating that in a local freely falling reference frame, the result of any local non gravitational experiment is independent of where and when it is performed. On the other hand, almost all modern theories aiming at unifying gravitation with the three other fundamental interactions predict violation of EEP at levels which are within reach of near-future experiments [4,5]. As the internal energies of atoms or molecules depend on electromagnetic, as well as strong and weak interactions, comparing the frequency of electronic transitions, fine structure transitions and hyperfine transitions as a function of time or gravitational potential provides an interesting test of the validity of EEP.To date, very stringent tests exist on geological and cosmological timescales. The analysis of the Oklo nuclear reactor showed that, 2 × 10 9 years ago, α did not differ from the present value by more than 10 −7 of its value [6]. Light emitted by distant quasars has been used to perform absorption spectroscopy of interstellar clouds. For instance, measurements of the wavelengths of molecular hydrogen transitions test a possible variation of the electron to proton mass ratio m e /m p [7]. Comparisons between the gross structure and the fine structure of neutral atoms and ions would indicate that α for a redshift z ∼ 1.5 (∼ 10 Gyr) differed from the present value: ∆α/α = (−7.2 ± 1.8) × 10 −6 [8]. Today this is the only claim that fundamental constants might change.On much shorter timescales, several tests using frequency standards have been performed [9,10,11]. These laboratory tests have a very high sensitivity to changes in fundamental constants. They are repeatable, systematic errors can be tracked as experimental conditions can be changed.In this letter we present results that place a new stringent limit to the time variation of fundamental constants. By comparing the hyperfine energies of 13...
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