Magnetism plays a key role in modern technology and stimulates research in several branches of condensed matter physics. Although the theory of classical magnetism is well developed, the demonstration of a widely tunable experimental system has remained an elusive goal. Here, we present the realization of a large-scale simulator for classical magnetism on a triangular lattice by exploiting the particular properties of a quantum system. We use the motional degrees of freedom of atoms trapped in an optical lattice to simulate a large variety of magnetic phases: ferromagnetic, antiferromagnetic, and even frustrated spin configurations. A rich phase diagram is revealed with different types of phase transitions. Our results provide a route to study highly debated phases like spin-liquids as well as the dynamics of quantum phase transitions.

Leveraging the unrivalled performance of optical clocks as key tools for geo-science, for astronomy and for fundamental physics beyond the standard model requires comparing the frequency of distant optical clocks faithfully. Here, we report on the comparison and agreement of two strontium optical clocks at an uncertainty of 5 × 10−17 via a newly established phase-coherent frequency link connecting Paris and Braunschweig using 1,415 km of telecom fibre. The remote comparison is limited only by the instability and uncertainty of the strontium lattice clocks themselves, with negligible contributions from the optical frequency transfer. A fractional precision of 3 × 10−17 is reached after only 1,000 s averaging time, which is already 10 times better and more than four orders of magnitude faster than any previous long-distance clock comparison. The capability of performing high resolution international clock comparisons paves the way for a redefinition of the unit of time and an all-optical dissemination of the SI-second.

Progress in realizing the SI second had multiple technological impacts and enabled further constraint of theoretical models in fundamental physics. Caesium microwave fountains, realizing best the second according to its current definition with a relative uncertainty of 2-4 Â 10 À 16 , have already been overtaken by atomic clocks referenced to an optical transition, which are both more stable and more accurate. Here we present an important step in the direction of a possible new definition of the second. Our system of five clocks connects with an unprecedented consistency the optical and the microwave worlds. For the first time, two state-of-the-art strontium optical lattice clocks are proven to agree within their accuracy budget, with a total uncertainty of 1.5 Â 10 À 16 . Their comparison with three independent caesium fountains shows a degree of accuracy now only limited by the best realizations of the microwave-defined second, at the level of 3.1 Â 10 À 16 .

The 1S0-3P0 clock transition frequency nuSr in neutral 87Sr has been measured relative to the Cs standard by three independent laboratories in Boulder, Paris, and Tokyo over the last three years. The agreement on the 1 x 10(-15) level makes nuSr the best agreed-upon optical atomic frequency. We combine periodic variations in the 87Sr clock frequency with 199Hg+ and H-maser data to test local position invariance by obtaining the strongest limits to date on gravitational-coupling coefficients for the fine-structure constant alpha, electron-proton mass ratio mu, and light quark mass. Furthermore, after 199Hg+, 171Yb+, and H, we add 87Sr as the fourth optical atomic clock species to enhance constraints on yearly drifts of alpha and mu.

The first Earth-scale quantum sensor network based on optical atomic clocks is looking for dark matter candidates.

Phase compensated optical fiber links enable high accuracy atomic clocks separated by thousands of kilometers to be compared with unprecedented statistical resolution. By searching for a daily variation of the frequency difference between four strontium optical lattice clocks in different locations throughout Europe connected by such links, we improve upon previous tests of time dilation predicted by special relativity. We obtain a constraint on the Robertson-Mansouri-Sexl parameter |α| 1.1 × 10 −8 quantifying a violation of time dilation, thus improving by a factor of around two the best known constraint obtained with Ives-Stilwell type experiments, and by two orders of magnitude the best constraint obtained by comparing atomic clocks. This work is the first of a new generation of tests of fundamental physics using optical clocks and fiber links. As clocks improve, and as fiber links are routinely operated, we expect that the tests initiated in this paper will improve by orders of magnitude in the near future.

We report a frequency measurement of the 1 S0 − 3 P0 transition of 87 Sr atoms in an optical lattice clock. The frequency is determined to be 429 228 004 229 879 (5) Hz with a fractional uncertainty that is comparable to state-of-the-art optical clocks with neutral atoms in free fall. Two previous measurements of this transition were found to disagree by about 2 × 10 −13 , i.e. almost four times the combined error bar, instilling doubt on the potential of optical lattice clocks to perform at a high accuracy level. In perfect agreement with one of these two values, our measurement essentially dissipates this doubt.PACS numbers: 06.30. Ft,42.50.Hz,42.62.Fi Recent advances in the field of optical frequency metrology make measurements with a fractional accuracy of 10 −17 or better a realistic short term goal [1]. Among other possible applications (e.g. a redefinition of the S.I. second, optical very long baseline interferometry in space, direct mapping of the earth gravitational using the Einstein effect,...), a very interesting prospect with measurements at that level is a reproducible test of Einstein Equivalence Principle by the repeated determination of the frequency ratio of different atomic and molecular transitions [2,3,4,5,6,7]. The topicality of such a test has recently been renewed by measurements at the cosmological scale which seem to indicate a slow variation of the electron to proton mass ratio [8]. The richness of the test directly depends on the performance of the clocks that are used but also on the variety of clock transitions and atomic species on which high accuracy frequency standards are based.In that context, optical lattice clocks are expected to play a central role in the future of this field. They use a large number of atoms confined in the Lamb-Dicke regime by an optical lattice in which the first order perturbation of the clock transition cancels [9]. Due to the lattice confinement motional effects, which set a severe limitation to standards with neutral atoms in free fall [10,11], essentially vanish [12]. This gives hope for a ultimate fractional accuracy better than 10 −17 . On the other hand, the large number of atoms in an optical lattice clock in principle opens the way to a short term fractional frequency stability significantly better than 10 −15 τ −1/2 with τ the averaging time in seconds. In this regime the coherence time of the laser frequency locked to the clock transition would be several seconds, possibly tens of seconds [25]. Such a long coherence time could for instance be used to reduce the width of the optical resonances in single ion clocks down to or below the 0.1 Hz range opening new prospects for these devices also. Finally, the optical lattice clock scheme is in principle applicable to a large number of atomic species (Sr, Yb, Hg, Ca, Mg,...) which is a key feature for the fundamental test discussed above. It is then particularly problematic that the frequency delivered by the first two evaluated optical lattice clocks, which both use 87 Sr, disagree by about 2 × ...

We report the observation of the higher order frequency shift due to the trapping field in a 87 Sr optical lattice clock. We show that at the magic wavelength of the lattice, where the first order term cancels, the higher order shift will not constitute a limitation to the fractional accuracy of the clock at a level of 10 −18 . This result is achieved by operating the clock at very high trapping intensity up to 400 kW/cm 2 and by a specific study of the effect of the two two-photon transitions near the magic wavelength.PACS numbers: 06.30. Ft,42.50.Hz,42.62.Fi The recent proposal and preliminary realizations of optical lattice clocks open a promising route towards frequency standards with a fractional accuracy better than 10 −17 [1,2,3,4]. A large number of atoms are confined in micro-traps formed by the interference pattern of laser beams which in principle allows both the high signal to noise ratio of optical clocks with neutral atoms [5] and the cancellation of motional effects of trapped ion devices [6, 7, 8, 9]. In contrast to the ion case an optical lattice clock requires high trapping fields. The evaluation of their effects on the clock transition is a major concern and is the subject of this letter. For a Sr optical lattice clock, the typical requirement in terms of trapping depth is about 10 E r with E r the recoil energy associated to the absorption of a lattice photon [10]. The corresponding frequency shift of both clock states amounts to 36 kHz at 800 nm, while a relative accuracy goal of 10 −18 implies a control of the differential shift at the 0.5 mHz level, or 10 −8 in fractional units.The frequency of the clock transition in a laser trap of depth U 0 is shifted with respect to the unperturbed frequency ν 0 according towith ν 1 and ν 2 proportional to the (dynamic) polarizability and hyperpolarizability difference between both states of the clock transition [1]. By principle of the optical lattice clock, ν 1 cancels when the laser which forms the lattice is tuned to the "magic wavelength" λ m . Although this remains to be demonstrated experimentally, a control of this first order term to better than 1 mHz seems achievable [1]. The higher order term is a priori more problematic with no expected cancellation. A theoretical calculation of the effect is reported in Ref.[1] predicting a frequency shift of −2 µHz/E 2 r for a linear polarization of the lattice. The calculation however was performed at the theoretical magic wavelength of 800 nm. The actual value [17], λ m = 813.428 (1) effect and impede the realization of an accurate clock. The first one couples 5s5p 3 P 0 to 5s7p 1 P 1 (Fig. 1) and is at a wavelength of 813.36 nm, or equivalently 30 GHz away from the magic wavelength. Although this J = 0 → J = 1 two-photon transition is forbidden to leading order for two photons of identical frequencies [11], it is so close to the magic wavelength that it has to be a priori considered. The second one resonantly couples 5s5p 3 P 0 to 5s4f 3 F 2 at 818.57 nm and is fully allowed. We report here an expe...