Orbital-driven melting of a bosonic Mott insulator in a shaken optical lattice

In order to study the interplay between localized and dispersive orbital states in a system of ultracold atoms in an optical lattice, we investigate the possibility to coherently couple the lowest two Bloch bands by means of resonant periodic forcing. Considering bosons in one dimension, it is shown that a strongly interacting Floquet system can be realized, where at every lattice site two (and only two) near-degenerate orbital states are relevant. By smoothly tuning both states into resonance we find that the system can undergo an orbital-driven Mott-insulator-to-superfluid transition. As an intriguing consequence of the kinetic frustration in the system, this transition can be either continuous or first-order, depending on parameters such as lattice depth and filling.Comment: 7 pages, 3 figure

Interband heating processes in a periodically driven optical lattice

We investigate multi-"photon" interband excitation processes in an optical lattice that is driven periodically in time by a modulation of the lattice depth. Assuming the system to be prepared in the lowest band, we compute the excitation spectrum numerically. Moreover, we estimate the effective coupling parameters for resonant interband excitation processes analytically, employing degenerate perturbation theory in Floquet space. We find that below a threshold driving strength, interband excitations are suppressed exponentially with respect to the inverse driving frequency. For sufficiently low frequencies, this leads to a rather sudden onset of interband heating, once the driving strength reaches the threshold. We argue that this behavior is rather generic and should also be found in lattice systems that are driven by other forms of periodic forcing. Our results are relevant for Floquet engineering, where a lattice system is driven periodically in time in order to endow it with novel properties like the emergence of a strong artificial magnetic field or a topological band structure. In this context, interband excitation processes correspond to detrimental heating.Comment: 11 pages, 4 figure

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.Comment: 48 pages, 7 figure

Point patterns occurring on complex structures in space and space-time: An alternative network approach

This paper presents an alternative approach of analyzing possibly multitype point patterns in space and space-time that occur on network structures, and introduces several different graph-related intensity measures. The proposed formalism allows to control for processes on undirected, directional as well as partially directed network structures and is not restricted to linearity or circularity

The optimal frequency window for Floquet engineering in optical lattices

The concept of Floquet engineering is to subject a quantum system to time-periodic driving in such a way that it acquires interesting novel properties. It has been employed, for instance, for the realization of artificial magnetic fluxes in optical lattices and, typically, it is based on two approximations. First, the driving frequency is assumed to be low enough to suppress resonant excitations to high-lying states above some energy gap separating a low energy subspace from excited states. Second, the driving frequency is still assumed to be large compared to the energy scales of the low-energy subspace, so that also resonant excitations within this space are negligible. Eventually, however, deviations from both approximations will lead to unwanted heating on a time scale $\tau$. Using the example of a one-dimensional system of repulsively interacting bosons in a shaken optical lattice, we investigate the optimal frequency (window) that maximizes $\tau$. As a main result, we find that, when increasing the lattice depth, $\tau$ increases faster than the experimentally relevant time scale given by the tunneling time $\hbar/J$, so that Floquet heating becomes suppressed.Comment: 11 pages, 8 figure

Quantum crystal growing: Adiabatic preparation of a bosonic antiferromagnet in the presence of a parabolic inhomogeneity

We theoretically study the adiabatic preparation of an antiferromagnetic phase in a mixed Mott insulator of two bosonic atom species in a one-dimensional optical lattice. In such a system one can engineer a tunable parabolic inhomogeneity by controlling the difference of the trapping potentials felt by the two species. Using numerical simulations we predict that a finite parabolic potential can assist the adiabatic preparation of the antiferromagnet. The optimal strength of the parabolic inhomogeneity depends sensitively on the number imbalance between the two species. We also find that during the preparation finite size effects will play a crucial role for a system of realistic size. The experiment that we propose can be realized, for example, using atomic mixtures of Rubidium 87 with Potassium 41 or Ytterbium 168 with Ytterbium 174.Comment: 25 pages, 6 figure

Bath-induced decay of Stark many-body localization

We investigate the relaxation dynamics of an interacting Stark-localized system coupled to a dephasing bath, and compare its behavior to the conventional disorder-induced many body localized system. Specifically, we study the dynamics of population imbalance between even and odd sites, and the growth of the von Neumann entropy. For a large potential gradient, the imbalance is found to decay on a time scale that grows quadratically with the Wannier-Stark tilt. For the non-interacting system, it shows an exponential decay, which becomes a stretched exponential decay in the presence of finite interactions. This is different from a system with disorder-induced localization, where the imbalance exhibits a stretched exponential decay also for vanishing interactions. As another clear qualitative difference, we do not find a logarithmically slow growth of the von-Neumann entropy as it is found for the disordered system. Our findings can immediately be tested experimentally with ultracold atoms in optical lattices

Avoided level crossing spectroscopy with dressed matter waves

We devise a method for probing resonances of macroscopic matter waves in shaken optical lattices by monitoring their response to slow parameter changes, and show that such resonances can be disabled by particular choices of the driving amplitude. The theoretical analysis of this scheme reveals far-reaching analogies between dressed atoms and time-periodically forced matter waves.Comment: 4 pages, 3 figure

Process chain approach to high-order perturbation calculus for quantum lattice models

A method based on Rayleigh-Schroedinger perturbation theory is developed that allows to obtain high-order series expansions for ground-state properties of quantum lattice models. The approach is capable of treating both lattice geometries of large spatial dimensionalities d and on-site degrees of freedom with large state space dimensionalities. It has recently been used to accurately compute the zero-temperature phase diagram of the Bose-Hubbard model on a hypercubic lattice, up to arbitrary large filling and for d=2, 3 and greater [Teichmann et al., Phys. Rev. B 79, 100503(R) (2009)].Comment: 11 pages, 6 figure

Tomography of band insulators from quench dynamics

We propose a simple scheme for tomography of band-insulating states in one- and two-dimensional optical lattices with two sublattice states. In particular, the scheme maps out the Berry curvature in the entire Brillouin zone and extracts topological invariants such as the Chern number. The measurement relies on observing---via time-of-flight imaging---the time evolution of the momentum distribution following a sudden quench in the band structure. We consider two examples of experimental relevance: the Harper model with $\pi$-flux and the Haldane model on a honeycomb lattice. Moreover, we illustrate the performance of the scheme in the presence of a parabolic trap, noise, and finite measurement resolution.Comment: v2: 5+5 pages, 3+5 figures; added analytical and numerical results for the presence of a harmonic confinement. v3: Minor changes; as accepted in PR