André Eckardt

Quantum Simulation of Frustrated Classical Magnetism in Triangular Optical Lattices

An optical lattice of trapped atoms provides a tractable and tunable setup to study complex magnetic interactions. 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.

Tunable gauge potential for neutral and spinless particles in driven optical lattices.

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 nonzero quasimomentum. We furthermore investigate possible implementations of this scheme to create tunable magnetic fluxes, going towards model systems for strong-field physics.

Superfluid-insulator transition in a periodically driven optical lattice.

We demonstrate that the transition from a superfluid to a Mott insulator in the Bose-Hubbard model can be induced by an oscillating force through an effective renormalization of the tunneling matrix element. The mechanism involves adiabatic following of Floquet states, and can be tested experimentally with Bose-Einstein condensates in periodically driven optical lattices. Its extension from small to very large systems yields nontrivial information on the condensate dynamics.

Non-Abelian gauge fields and topological insulators in shaken optical lattices

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.

Colloquium: Atomic quantum gases in periodically driven optical lattices

Time periodic forcing in the form of coherent radiation is a standard tool for the coherent manipulation of small quantum systems like single atoms. In the last years, periodic driving has more and more also been considered as a means for the coherent control of many-body systems. In particular, experiments with ultracold quantum gases in optical lattices subjected to periodic driving in the lower kilohertz regime have attracted a lot of attention. Milestones include the observation of dynamic localization, the dynamic control of the quantum phase transition between a bosonic superfluid and a Mott insulator, as well as the dynamic creation of strong artificial magnetic fields and topological band structures. This article reviews these recent experiments and their theoretical description. Moreover, fundamental properties of periodically driven many-body systems are discussed within the framework of Floquet theory, including heating, relaxation dynamics, anomalous topological edge states, and the response to slow parameter variations.

Engineering Ising-XY spin-models in a triangular lattice using tunable artificial gauge fields

A quantum gas trapped in an optical lattice of triangular symmetry can now be driven from a paramagnetic to an antiferromagnetic state by a tunable artificial magnetic field.

High-frequency approximation for periodically driven quantum systems from a Floquet-space perspective

We derive a systematic high-frequency expansion for the effective Hamiltonian and the micromotion operator of periodically driven quantum systems. Our approach is based on the block diagonalization of the quasienergy operator in the extended Floquet Hilbert space by means of degenerate perturbation theory. The final results are equivalent to those obtained within a different approach [Phys.\ Rev.\ A {\bf 68}, 013820 (2003), Phys.\ Rev.\ X {\bf 4}, 031027 (2014)] and can also be related to the Floquet-Magnus expansion [J.\ Phys.\ A {\bf 34}, 3379 (2000)]. We discuss that the dependence on the driving phase, which plagues the latter, can lead to artifactual symmetry breaking. The high-frequency approach is illustrated using the example of a periodically driven Hubbard model. Moreover, we discuss the nature of the approximation and its limitations for systems of many interacting particles.

Analog of photon-assisted tunneling in a Bose-Einstein condensate.

We study many-body tunneling of a small Bose-Einstein condensate in a periodically modulated, tilted double-well potential. Periodic modulation of the trapping potential leads to an analog of photon-assisted tunneling, with distinct signatures of the interparticle interaction visible in the amount of particles transferred from one well to the other. In particular, under experimentally accessible conditions there exist well-developed half-integer Shapiro-like resonances.

Exploring dynamic localization with a Bose-Einstein condensate

We report on the experimental observation of dynamic localization of a Bose-Einstein condensate in a shaken optical lattice, both for sinusoidal and square-wave forcing. The formulation of this effect in terms of a quasienergy band collapse, backed by the excellent agreement of the observed collapse points with the theoretical predictions, suggests the feasibility of systematic quasienergy band engineering.

Frustrated quantum antiferromagnetism with ultracold bosons in a triangular lattice

We propose to realize the anisotropic triangular-lattice Bose-Hubbard model with positive tunneling matrix elements by using ultracold atoms in an optical lattice dressed by a fast lattice oscillation. This model exhibits frustrated antiferromagnetism at experimentally feasible temperatures; it interpolates between a classical rotor model for weak interaction, and a quantum spin-(1/2) XY-model in the limit of hard-core bosons. This allows to explore experimentally gapped spin-liquid phases predicted recently (Schmied R. et al., New J. Phys., 10 (2008) 045017).