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.

We present a universal method to create a tunable, artificial vector gauge potential for neutral particles trapped in an optical lattice. The necessary Peierls phase of the hopping parameters between neighboring lattice sites is generated by applying a suitable periodic inertial force such that the method does not rely on any internal structure of the particles. We experimentally demonstrate the realization of such artificial potentials, which generate ground state superfluids at arbitrary non-zero quasi-momentum. We furthermore investigate possible implementations of this scheme to create tuneable magnetic fluxes, going towards model systems for strong-field physics.First introduced in electromagnetism, gauge fields play a central role in the description of interactions in physics, from particle physics to condensed matter. Currently there is a large interest to introduce gauge fields into model systems in order to study fundamental aspects of physics [1]. Especially the emulation of synthetic electric and magnetic fields for of ultracold atomic systems is crucial in order to extend their proven quantum simulation abilities further, e.g. to quantum Hall physics or topological insulators. In this context, the analogy between inertial and Lorentz forces triggered the simulation of homogeneous artificial magnetic fields using rapidly rotating trapped ultracold gases [2]. Recently, several proposals ([3, 4] and references therein) and experimental realizations focused on the simulation of a gauge vector potential A either in a bulk system [5,6] or in optical lattices [7,8]. The realized schemes exploit the Berry phase which arises when the atomic ground state is split in several space-dependent sublevels, as in the presence of an electromagnetic field. Hence they rely on the coupling between internal and external degrees of freedom induced by laser fields. Here we demonstrate the generation of artificial gauge potentials for neutral atoms in an optical lattice without any requirements on the specific internal structure. As the realized scheme only relies on the trapability of the particle, it can be very widely applied to many atomic systems, in principle also to molecules and other complex particles. It is particularly interesting for fermionic systems, where in a many-body state governed by Pauli principle, the use of internal degrees of freedom often lead to conflicts with the creation of gauge potentials. As an important additional benefit, the internal degrees of freedom of the particles can be addressed independently, e.g. by real magnetic fields or microwave excitations. In general, the presence of a gauge vector potential modifies the kinetic part of the Hamiltonian describing the system. In a lattice, an artificial field can then be simulated by engineering a complex tunneling parameter J = |J| · e iθ , where θ is the Peierls phase. The central approach here is to control this phase via a suitable forcing of the lattice potential, acting at the single-particle level. We describe the general scheme for the...

Squeezing of quantum fluctuations by means of entanglement is a well-recognized goal in the field of quantum information science and precision measurements. In particular, squeezing the fluctuations via entanglement between 2-level atoms can improve the precision of sensing, clocks, metrology, and spectroscopy. Here, we demonstrate 3.4 dB of metrologically relevant squeezing and entanglement for 10 5 cold caesium atoms via a quantum nondemolition (QND) measurement on the atom clock levels. We show that there is an optimal degree of decoherence induced by the quantum measurement which maximizes the generated entanglement. A 2-color QND scheme used in this paper is shown to have a number of advantages for entanglement generation as compared with a single-color QND measurement. N A for the case of independent atoms also referred to as a coherent spin state (CSS). The CSS minimizes the Heisenberg uncertainty product so that, e.g., (δJ z ) 2 (δJ x ) 2 = 1 4| J y | 2 where J y is the expectation value of the spin projection operator. At the expense of an increase in (δJ x ) 2 , it is possible to reduce (δJ z ) 2 (or vice versa) below the projection noise limit while keeping their product constant. This constitutes an example of a spin squeezed state (SSS), for which the atoms need to be correlated. This correlation is ensured to be nonclassical ifwhere ξ defines the squeezing parameter. Under this condition, the atoms are entangled (3) and the prepared state improves the signal-to-noise ratio in spectroscopical and metrological applications (1). Systems of 2 to 3 ions have successfully been used to demonstrate spectroscopic performance with reduced quantum noise and entanglement (4, 5). The situation is somewhat different with macroscopic atomic ensembles where spin squeezing has been an active area of research in the past decade (6-13). To our knowledge, no results reporting ξ < 1 via interatomic entanglement in such ensembles have been reported so far, with a very recent exception of the paper (14) where entanglement in an external motional degree of freedom of 2 · 10 3 atoms via interactions in a Bose-Einstein condensate is demonstrated. Spin Squeezing by Quantum Nondemolition (QND) MeasurementsIn this article, we report on the generation of an SSS fulfilling Eq. 1 in an ensemble of ≈10 5 atoms via a QND measurement (7, 15-17) of J z . We show how to take advantage of the entanglement in this mesoscopic system by using Ramsey spectroscopy (1)-one of the methods of choice for precision measurements of time and frequency (18) (Fig. 1A). The figure presents the evolution of the pseudospin J whose tip is traveling over the Bloch sphere. The Ramsey method allows using the atomic ensemble as a sensor for external fields where the perturbation of the energy difference between the levels ΔE ↑↓ is measured, or as a clock where the frequency of an oscillator is locked to the transition frequency between the two states Ω = ΔE ↑↓ / . Fig. 1 B illustrates how a suitable SSS can improve the precision of the Ramsey measurement pr...

Atom interferometers covering macroscopic domains of space-time are a spectacular manifestation of the wave nature of matter. Because of their unique coherence properties, Bose-Einstein condensates are ideal sources for an atom interferometer in extended free fall. In this Letter we report on the realization of an asymmetric Mach-Zehnder interferometer operated with a Bose-Einstein condensate in microgravity. The resulting interference pattern is similar to the one in the far field of a double slit and shows a linear scaling with the time the wave packets expand. We employ delta-kick cooling in order to enhance the signal and extend our atom interferometer. Our experiments demonstrate the high potential of interferometers operated with quantum gases for probing the fundamental concepts of quantum mechanics and general relativity.