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...

Emulation of gauge fields for ultracold atoms provides access to a class of exotic states arising in strong magnetic fields. Here we report on the experimental realisation of tunable staggered gauge fields in a periodically driven triangular lattice. For maximal staggered magnetic fluxes, the doubly degenerate superfluid ground state breaks both a discrete Z 2 (Ising) symmetry and a continuous U (1) symmetry. By measuring an Ising order parameter, we observe a thermally driven phase transition from an ordered antiferromagnetic to an unordered paramagnetic state and textbook-like magnetisation curves. Both the experimental and theoretical analysis of the coherence properties of the ultracold gas demonstrate the strong influence of the Z 2 symmetry onto the condensed phase.Phase transitions in systems with combined continuous and discrete symmetries are fundamentally different from their purely continuous and discrete counterparts. The interplay between different types of excitations in the various degrees of freedom can lead to a complex behaviour and coupling of the associated order parameters [1][2][3][4][5]. A paradigm example is the fully frustrated XY model on a triangular lattice. It combines vector spin-type symmetries with discrete chiral degrees of freedom, which result in the famous spin-chirality coupling at low temperatures [6]. However, experimental studies in solid-state systems are challenging in view of implementing and isolating an XY model Hamiltonian [7][8][9].Ultracold bosonic quantum gases in optical lattices, on the other hand, constitute a highly versatile system with an extraordinary degree of control [10,11]. In particular, the recent experimental realisations of artificial gauge potentials for bulk [12][13][14][15] and optical lattice systems [16][17][18][19] allow for the investigation of new physical regimes, not realisable in condensed matter systems.Here, we demonstrate the realisation of a system with combined U (1) and Z 2 symmetries using ultracold atoms submitted to artificial gauge fields. Our experimental setup consists of an ultracold gas of 87 Rb atoms held in a two-dimensional triangular lattice [20] (see Fig. 1a). At each lattice site j with particle number N j , the weakly interacting superfluid gas can be described by the local order parameter a j = N j e iϕj . As a central aspect, the local phases ϕ j are mapped onto classical XY spins s j = (cos ϕ j , sin ϕ j ), where the tunneling matrix elements between neighbouring lattice sites correspond to the spinspin coupling parameters. Such classical spins possess a continuous degree of freedom. In presence of a long-range order, analogous to the onset of Bose-Einstein condensation (BEC), the order parameter assumes an arbitrary, but fixed phase, thus breaking the continuous U (1) symmetry [21].Beyond that, we experimentally engineer strong staggered gauge fields, which generate an additional discrete Z 2 symmetry in our system. The resulting magnetic flux induces cyclotron-like mass currents around each plaquette. The two poss...

Time-periodic driving like lattice shaking offers a low-demanding method to generate artificial gauge fields in optical lattices. We identify the relevant symmetries that have to be broken by the driving function for that purpose and demonstrate the power of this method by making concrete proposals for its application to two-dimensional lattice systems: We show how to tune frustration and how to create and control band touching points like Dirac cones in the shaken kagome lattice. We propose the realization of a topological and a quantum spin Hall insulator in a shaken spin-dependent hexagonal lattice. We describe how strong artificial magnetic fields can be achieved for example in a square lattice by employing superlattice modulation. Finally, exemplified on a shaken spin-dependent square lattice, we develop a method to create strong non-abelian gauge fields.

Precision spectroscopy of simple atomic systems has refined our understanding of the fundamental laws of quantum physics. In particular, helium spectroscopy has played a crucial role in describing two-electron interactions, determining the fine-structure constant and extracting the size of the helium nucleus. Here we present a measurement of the doubly-forbidden 1557-nanometer transition connecting the two metastable states of helium (the lowest energy triplet state 2 3 S 1 and first excited singlet state 2 1 S 0 ), for which quantum electrodynamic and nuclear size effects are very strong. This transition is fourteen orders of magnitude weaker than the most predominantly measured transition in helium. Ultracold, sub-microkelvin, fermionic 3 He and bosonic 4 He atoms are used to obtain a precision of 8×10 −12 , providing a stringent test of two-electron quantum electrodynamic theory and of nuclear few-body theory.

We report on the observation of multiphoton interband absorption processes for quantum gases in shaken light crystals. Periodic inertial forcing, induced by a spatial motion of the lattice potential, drives multiphoton interband excitations of up to the ninth order. The occurrence of such excitation features is systematically investigated with respect to the potential depth and the driving amplitude. Ab initio calculations of resonance positions as well as numerical evaluation of their strengths exhibit good agreement with experimental data. In addition our findings could make it possible to reach novel phases of quantum matter by tailoring appropriate driving schemes.

We propose a method for the emulation of artificial spin-orbit coupling in a system of ultracold, neutral atoms trapped in a tight-binding lattice. This scheme does not involve near-resonant laser fields, avoiding the heating processes connected to the spontaneous emission of photons. In our case, the necessary spin-dependent tunnel matrix elements are generated by a rapid, spin-dependent, periodic force, which can be described in the framework of an effective, time-averaged Hamiltonian. An additional radio-frequency coupling between the spin states leads to a mixing of the spin bands.PACS numbers: 03.65.Vf, 71.70.Ej, 37.10.Jk The phenomenon of spin-orbit coupling (SOC) generally describes an interplay between the spin state of a particle and its motional degrees of freedom. This effect naturally arises in the framework of relativistic quantum mechanics described by the Dirac equation. A spinful particle moving through an electric field experiences a magnetic field in the co-moving reference frame. The resulting interaction between the spin and the magnetic field depends on the amplitude of the field and thus on the velocity of the particle, leading to the coupling of motion and spin. In solid state materials, SOC can result in exotic phases and phenomena, such as topological insulators [1,2] or the spin Hall effect [3][4][5][6][7].The experimental realization of synthetic spin-orbit interactions with equal Rashba [8] and Dresselhaus [9] contributions for bosonic [10,11] and fermionic quantum gases [12,13] has raised considerable interest over the last years ([14] and references therein). For ultracold atomsinteracting via s-wave scattering -SOC can lead to effective interactions with higher partial wave contributions [15][16][17]. In a single-component Fermi gas this could lead to stable p-wave interactions and topological superfluids [18][19][20]. All of the experimentally implemented schemes rely on near-resonant Raman-laser coupling schemes and thus suffer from spontaneous emission, leading to excitations and particle loss. Currently a lot of effort is directed towards novel methods for the creation of artificial SOC avoiding this issue, e.g., by using magnetic field pulses [21,22] or far-off-resonant light [23].As thoroughly investigated over the last years a rapid, periodic lattice drive coherently manipulates the tunneling processes in an optical lattice. This allows for, e.g., the coherent destruction of tunneling and sign inversion of the tunnel elements [24-27], photon assisted tunneling [28,29], and the creation of artificial gauge fields [30][31][32][33][34][35][36][37][38]. In this manuscript, we propose to engineer a * E-mail address: jstruck@mit.edu; HKin represents the spin-independent nearest-neighbour tunneling processes, HRF describes the radio frequency coupling of the two spin states and HForce corresponds to the spin-dependent driving of the atoms in the lattice. The drive originates from an oscillating magnetic field gradient.time-periodic and spin-dependent drive in order to realize ...

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We study the ground-state properties of ultracold bosonic atoms in a state-dependent graphene-like honeycomb optical lattice, where the degeneracy between the two triangular sublattices A and B can be lifted. We discuss the various geometries accessible with this lattice setup and present a novel scheme to control the energy offset with external magnetic fields. The competition of the on-site interaction with the offset energy leads to Mott phases characterized by population imbalances between the sublattices. For the definition of an optimal Hubbard model, we demonstrate a scheme that allows for the efficient computation of Wannier functions. Using a cluster mean-field method, we compute the phase diagrams and provide a universal representation for arbitrary energy offsets. We find good agreement with the experimental data for the superfluid to Mott insulator transition