Order parameter and detection for crystallized dipolar bosons in lattices

We explore the ground-state properties of bosons with dipole-dipole interactions in a one-dimensional optical lattice. Remarkably, a crystallization process happens for strong dipolar interactions. Herein, we provide a detailed characterization and a way to measure the resulting crystal phase. Using the eigenvalues of the reduced one-body density matrix we define an order parameter that yields a phase diagram in agreement with an analysis of the density and two-body density. We demonstrate that the phase diagram can be detected experimentally using the variance of single-shot measurements.Comment: 6 pages, 3 figures. Supplementary Information included. Software available at http://ultracold.org

Condensate fragmentation as a sensitive measure of the quantum many-body behavior of bosons with long-range interactions

The occupation of more than one single-particle state and hence the emergence of fragmentation is a many-body phenomenon universal to systems of spatially confined interacting bosons. In the present study, we investigate the effect of the range of the interparticle interactions on the fragmentation degree of one- and two-dimensional systems. We solve the full many-body Schr\"odinger equation of the system using the recursive implementation of the multiconfigurational time-dependent Hartree for bosons method, R-MCTDHB. The dependence of the degree of fragmentation on dimensionality, particle number, areal or line density and interaction strength is assessed. It is found that for contact interactions, the fragmentation is essentially density independent in two dimensions. However, fragmentation increasingly depends on density the more long-ranged the interactions become. The degree of fragmentation is increasing, keeping the particle number $N$ fixed, when the density is decreasing as expected in one spatial dimension. We demonstrate that this remains, nontrivially, true also for long-range interactions in two spatial dimensions. We, finally, find that within our fully self-consistent approach, the fragmentation degree, to a good approximation, decreases universally as $N^{-1/2}$ when only $N$ is varied.Comment: 8 pages of RevTex4-1, 5 figure

Detecting One-Dimensional Dipolar Bosonic Crystal Orders via Full Distribution Functions

We explore the groundstates of a few dipolar bosons in optical lattices with incommensurate filling. The competition of kinetic, potential, and interaction energies leads to the emergence of a variety of crystal state orders with characteristic one- and two-body densities. We probe the transitions between these orders and construct the emergent state diagram as a function of the dipolar interaction strength and the lattice depth. We show that the crystal state orders can be observed using the full distribution functions of the particle number extracted from simulated single-shot images.Comment: 6 pages, 3 Figures in main text. Supplementary Information included. This version accepted for publication at Physical Review Letters. Software for the computations available at http://www.ultracold.or

Superlattice switching from parametric instabilities in a driven-dissipative BEC in a cavity

We numerically obtain the full time-evolution of a parametrically-driven dissipative Bose-Einstein condensate in an optical cavity and investigate the implications of driving for the phase diagram. Beyond the normal and superradiant phases, a third nonequilibrium phase emerges as a manybody parametric resonance. This dynamical normal phase switches between two symmetry-broken superradiant configurations. The switching implies a breakdown of the system's mapping to the Dicke model. Unlike the other phases, the dynamical normal phase shows features of nonintegrability and thermalization.Comment: 5 pages, 3 figure

Breaking the resilience of a two-dimensional Bose-Einstein condensate to fragmentation

A two-dimensional Bose-Einstein condensate (BEC) split by a radial potential barrier is investigated. We determine on an accurate many-body level the system's ground-state phase diagram as well as a time-dependent phase diagram of the splitting process. Whereas the ground state is condensed for a wide range of parameters, the time-dependent splitting process leads to substantial fragmentation. We demonstrate for the first time the dynamical fragmentation of a BEC despite its ground state being condensed. The results are analyzed by a mean-field model and suggest that a large manifold of low-lying fragmented excited states can significantly impact the dynamics of trapped two-dimensional BECs.Comment: 5+eps pages, 4 figure

Phases, many-body entropy measures and coherence of interacting bosons in optical lattices

Already a few bosons with contact interparticle interactions in small optical lattices feature a variety of quantum phases: superfluid, Mott-insulator and fermionized Tonks gases can be probed in such systems. To detect these phases -- pivotal for both experiment and theory -- as well as their many-body properties we analyze several distinct measures for the one-body and many-body Shannon information entropies. We exemplify the connection of these entropies with spatial correlations in the many-body state by contrasting them to the Glauber normalized correlation functions. To obtain the ground-state for lattices with commensurate filling (i.e. an integer number of particles per site) for the full range of repulsive interparticle interactions we utilize the multiconfigurational time-dependent Hartree method for bosons (MCTDHB) in order to solve the many-boson Schr\"odinger equation. We demonstrate that all emergent phases -- the superfluid, the Mott insulator, and the fermionized gas can be characterized equivalently by our many-body entropy measures and by Glauber's normalized correlation functions. In contrast to our many-body entropy measures, single-particle entropy cannot capture these transitions.Comment: 11 pages, 7 figures, software available at http://ultracold.or