Polar Molecules with Three-Body Interactions on the Honeycomb Lattice

We study the phase diagram of ultra-cold bosonic polar molecules loaded on a two-dimensional optical lattice of hexagonal symmetry controlled by external electric and microwave fields. Following a recent proposal in Nature Physics \textbf{3}, 726 (2007), such a system is described by an extended Bose-Hubbard model of hard-core bosons, that includes both extended two- and three-body repulsions. Using quantum Monte-Carlo simulations, exact finite cluster calculations and the tensor network renormalization group, we explore the rich phase diagram of this system, resulting from the strongly competing nature of the three-body repulsions on the honeycomb lattice. Already in the classical limit, they induce complex solid states with large unit cells and macroscopic ground state degeneracies at different fractional lattice fillings. For the quantum regime, we obtain effective descriptions of the various phases in terms of emerging valence bond crystal states and quantum dimer models. Furthermore, we access the experimentally relevant parameter regime, and determine the stability of the crystalline phases towards strong two-body interactions

Measuring the eccentricity of the Earth orbit with a nail and a piece of plywood

I describe how to obtain a rather good experimental determination of the eccentricity of the Earth orbit, as well as the obliquity of the Earth rotation axis, by measuring, over the course of a year, the elevation of the Sun as a function of time during a day. With a very simple "instrument" consisting of an elementary sundial, first-year students can carry out an appealing measurement programme, learn important concepts in experimental physics, see concrete applications of kinematics and changes of reference frames, and benefit from a hands-on introduction to astronomy.Comment: 12 pages, 6 figure

Tuning the structural and dynamical properties of a dipolar Bose-Einstein condensate: Ripples and instability islands

It is now well established that the stability of aligned dipolar Bose gases can be tuned by varying the aspect ratio of the external harmonic confinement. This paper extends this idea and demonstrates that a Gaussian barrier along the strong confinement direction can be employed to tune both the structural properties and the dynamical stability of an oblate dipolar Bose gas aligned along the strong confinement direction. In particular, our theoretical mean-field analysis predicts the existence of instability islands immersed in otherwise stable regions of the phase diagram. Dynamical studies indicate that these instability islands, which can be probed experimentally with present-day technology, are associated with the going soft of a Bogoliubov--de Gennes excitation frequency with radial breathing mode character. Furthermore, we find dynamically stable ground state densities with ripple-like oscillations along the radial direction. These structured ground states exist in the vicinity of a dynamical radial roton-like instability.Comment: 9 pages, 11 figure

Off-diagonal correlations in a one-dimensional gas of dipolar bosons

We present a quantum Monte Carlo study of the one-body density matrix (OBDM) and the momentum distribution of one-dimensional dipolar bosons, with dipole moments polarized perpendicular to the direction of confinement. We observe that the long-range nature of the dipole interaction has dramatic effects on the off-diagonal correlations: although the dipoles never crystallize, the system goes from a quasi-condensate regime at low interactions to a regime in which quasi-condensation is discarded, in favor of quasi-solidity. For all strengths of the dipolar interaction, the OBDM shows an oscillatory behavior coexisting with an overall algebraic decay; and the momentum distribution shows sharp kinks at the wavevectors of the oscillations, $Q = \pm 2\pi n$ (where $n$ is the atom density), beyond which it is strongly suppressed. This \emph{momentum filtering} effect introduces a characteristic scale in the momentum distribution, which can be arbitrarily squeezed by lowering the atom density. This shows that one-dimensional dipolar Bose gases, realized e.g. by trapped dipolar molecules, show strong signatures of the dipolar interaction in time-of-flight measurements.Comment: 10 pages, 6 figures. v2: fixed a mistake in the comparison with Ref. 9, as well as several typos. Published versio

Nonlinear Schr\"odinger equation for a PT symmetric delta-functions double well

The time-independent nonlinear Schr\"odinger equation is solved for two attractive delta-function shaped potential wells where an imaginary loss term is added in one well, and a gain term of the same size but with opposite sign in the other. We show that for vanishing nonlinearity the model captures all the features known from studies of PT symmetric optical wave guides, e.g., the coalescence of modes in an exceptional point at a critical value of the loss/gain parameter, and the breaking of PT symmetry beyond. With the nonlinearity present, the equation is a model for a Bose-Einstein condensate with loss and gain in a double well potential. We find that the nonlinear Hamiltonian picks as stationary eigenstates exactly such solutions which render the nonlinear Hamiltonian itself PT symmetric, but observe coalescence and bifurcation scenarios different from those known from linear PT symmetric Hamiltonians.Comment: 16 pages, 9 figures, to be published in Journal of Physics

Dynamics of gap solitons in a dipolar Bose-Einstein condensate on a three-dimensional optical lattice

We suggest and study the stable disk- and cigar-shaped gap solitons of a dipolar Bose-Einstein condensate of $^{52}$Cr atoms localized in the lowest band gap by three optical-lattice (OL) potentials along orthogonal directions. The one-dimensional version of these solitons of experimental interest confined by an OL along the dipole moment direction and harmonic traps in transverse directions is also considered. Important dynamics of (i) breathing oscillation of a gap soliton upon perturbation and (ii) dragging of a gap soliton by a moving lattice along axial $z$ direction demonstrates the stability of gap solitons. A movie clip of dragging of three-dimensional gap soliton is included.Comment: To see the dragging movie clip please download sourc

Dynamics of quasi-one-dimensional bright and vortex solitons of a dipolar Bose-Einstein condensate with repulsive atomic interaction

By numerical and variational analysis of the three-dimensional Gross-Pitaevskii equation we study the formation and dynamics of bright and vortex-bright solitons in a cigar-shaped dipolar Bose-Einstein condensate for large repulsive atomic interactions. Phase diagram showing the region of stability of the solitons is obtained. We also study the dynamics of breathing oscillation of the solitons as well as the collision dynamics of two solitons at large velocities. Two solitons placed side-by-side at rest coalesce to form a stable bound soliton molecule due to dipolar attraction.Comment: To obtain the included video clips S1, S2, S3 and S4, please download sourc

A 1.85 Ga volcanic arc offshore the proto-continent Fennoscandia in southern Sweden

The Fröderyd Group forms part of the Vetlanda-Oskarshamn belt (also known as the Oskarshamn-Jönköping Belt), which is a piece of Palaeoproterozoic crust that is completely encapsulated by 1.81–1.77 Ga granitoids of the Transscandinavian Igneous Belt in the southern part of the Fennoscandian Shield. New U-Pb zircon data from a felsic metavolcanic rock in the Fröderyd Group have been acquired using LA-ICP-MS single collector. The age is determined to 1853 ± 11 Ma. The Fröderyd Group is interpreted to represent a volcanic arc that was located southwest of the margin to the proto-continent Fennoscandia. Tonalitic magma, identified in the Eksjö-Bäckaby regions, formed the middle crust in this arc complex and intruded the volcanic arc rocks at ca. 1.83–1.82 Ga. When this arc complex gradually approached the margin to the proto-continent Fennoscandia, parts of it were uplifted above sea level and initiated lacustrine sedimentation in restricted basins, which now are found in the Vetlanda region. Parallel with the development of this arc complex, 1.86–1.85 Ga granitoids intruded the margin to the proto-continent Fennoscandia and 1.87–1.86 Ga clastic metasedimentary rocks in the Västervik area in an Andean-type active continental margin.It can be concluded that the Vetlanda and Västervik sedimentary basins formed in two completely different geological environments during two separate events. The Västervik sediments formed along the margin to the proto-continent Fennoscandia before the Fröderyd arc system had developed while the Vetlanda sediments formed in a post-arc environment outboard to the southwest of the margin to the proto-continent Fennoscandia. It is suggested that the mafic volcanic rocks close to the lake Nömmen should be excluded from the Vetlanda supergroup and instead be related in time to the Fröderyd Group. This paper presents an interpretation of the tectonic evolution including volcanic arc and rifted volcanic arc during the 1.87 to 1.77 Ga time span with relevance to the evolution of the active southwestern margin of the proto-continent Fennoscandia depicted as a sequence of schematic profiles.</p