Quantum simulation of the Anderson Hamiltonian with an array of coupled nanoresonators: delocalization and thermalization effects

The possibility of using nanoelectromechanical systems as a simulation tool for quantum many-body effects is explored. It is demonstrated that an array of electrostatically coupled nanoresonators can effectively simulate the Bose-Hubbard model without interactions, corresponding in the single-phonon regime to the Anderson tight-binding model. Employing a density matrix formalism for the system coupled to a bosonic thermal bath, we study the interplay between disorder and thermalization, focusing on the delocalization process. It is found that the phonon population remains localized for a long time at low enough temperatures; with increasing temperatures the localization is rapidly lost due to thermal pumping of excitations into the array, producing in the equilibrium a fully thermalized system. Finally, we consider a possible experimental design to measure the phonon population in the array by means of a superconducting transmon qubit coupled to individual nanoresonators. We also consider the possibility of using the proposed quantum simulator for realizing continuous-time quantum walks.Comment: Replaced with new improved version. To appear in EPJ Q

Vortex dynamics of rotating dipolar Bose-Einstein condensates

We study the influence of dipole-dipole interaction on the formation of vortices in a rotating dipolar Bose-Einstein condensate (BEC) of $^{52}$Cr and $^{164}$Dy atoms in quasi two-dimensional geometry. By numerically solving the corresponding time-dependent mean-field Gross-Pitaevskii equation, we show that the dipolar interaction enhances the number of vortices while a repulsive contact interaction increases the stability of the vortices. Further, an ordered vortex lattice of relatively large number of vortices is found in a strongly dipolar BEC.Comment: 15 pages, 10 figures, 1 tabl

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

Scissors mode of trapped dipolar gases

We study the scissors modes of dipolar boson and fermion gases trapped in a spherically symmetric potential. We use the harmonic oscillator states to solve the time-dependent Gross-Pitaevskii equation for bosons and the time-dependent Hartree-Fock equation for fermions. It is pointed out that the scissors modes of bosons and fermions can be of quite different nature

1.90-1.88Ga arc magmatism of central Fennoscandia: geochemistry, U-Pb geochronology, Sm-Nd and Lu-Hf isotope systematics of plutonic-volcanic rocks from southern Finland

The earliest Svecofennian magmatism in southern Finland has been dated at 1.90-1.88Ga. As an example of this, the Orijärvi (ca. 1.89Ga) and Enklinge (ca. 1.88Ga) volcanic centres comprise bimodal plutonic batholiths surrounded by volcanic rocks of comparable ages and chemical compositions. Here, we report geochemical and Sm-Nd isotope data from intrusive and extrusive samples, combined with zircon U-Pb and Lu-Hf isotopes for granodiorites from both study areas. The samples range from gabbros to granites and indicate a subduction-related continental margin setting. The zircons from the Orijärvi granodiorite define an age of 1892±4Ma whereas the Enklinge granodiorite yields an age of 1882±6Ma. Several inherited ages of 2.25-1.95Ga as well as younger ages of 1.86-1.80Ga were found in the Enklinge granodiorite. The initial εNd values from the mafic rocks from both locations fall in the range +1.1 to +2.9 whereas the felsic rocks exhibit initial εNd values of -0.4 to +1.2. The magmatic zircons from the Orijärvi and Enklinge granodiorites show average initial εHf values of -1.1 (at 1892Ma) and zero (at 1882Ma), respectively, each with a spread of about 7 ε-units. The initial εHf values for the inherited zircons from Enklinge range from +3.5 to +7.6 with increasing age. The Sm-Nd data indicate that the mafic rocks were derived from a “mildly depleted” mantle source while the felsic rocks show larger crustal contribution. Also, the variation in εHf values indicates minor mixing between mildly depleted mantle derived magmas and crustal sources. U-Pb ages and Hf isotopes for inherited zircons in the Enklinge granodiorite suggest the presence of juvenile Svecofennian “proto-crust” at depth

Localization of a dipolar Bose-Einstein condensate in a bichromatic optical lattice

By numerical simulation and variational analysis of the Gross-Pitaevskii equation we study the localization, with an exponential tail, of a dipolar Bose-Einstein condensate (DBEC) of $^{52}$Cr atoms in a three-dimensional bichromatic optical-lattice (OL) generated by two monochromatic OL of incommensurate wavelengths along three orthogonal directions. For a fixed dipole-dipole interaction, a localized state of a small number of atoms ($\sim 1000$) could be obtained when the short-range interaction is not too attractive or not too repulsive. A phase diagram showing the region of stability of a DBEC with short-range interaction and dipole-dipole interaction is given

Density wave instabilities of tilted fermionic dipoles in a multilayer geometry

We consider the density wave instability of fermionic dipoles aligned by an external field, and moving in equidistant layers at zero temperature. Using a conserving Hartree-Fock approximation, we show that correlations between dipoles in different layers significantly decrease the critical coupling strength for the formation of density waves when the distance between the layers is comparable to the inter-particle distance within each layer. This effect, which is strongest when the dipoles are oriented perpendicular to the planes, causes the density waves in neighboring layers to be in-phase for all orientations of the dipoles. We furthermore demonstrate that the effects of the interlayer interaction can be understood from a classical model. Finally, we show that the interlayer correlations are important for experimentally relevant dipolar molecules, including the chemically stable $^{23}$Na$^{40}$K and $^{40}$K$^{133}$Cs, where the density wave regime is within experimental reach.Comment: 18 pages, 11 figures; new version with expanded discussion on experimental relevance including one new figur

Collective Electronic Excitation Coupling between Planar Optical Lattices using Ewald's Method

Using Ewald's summation method we investigate collective electronic excitations (excitons) of ultracold atoms in parallel planar optical lattices including long range interactions. The exciton dispersion relation can then be suitably rewritten and efficiently calculated for long range resonance dipole-dipole interactions. Such in-plane excitons resonantly couple for two identical optical lattices, with an energy transfer strength decreasing exponentially with the distance between the lattices. This allows a restriction of the transfer to neighboring planes and gives rise to excitons delocalized between the lattices. In general equivalent results will hold for any planar system containing lattice layers of optically active and dipolar materials.Comment: 6 pages, and 7 figure