Shortcut to adiabaticity in spinor condensates

We devise a method to shortcut the adiabatic evolution of a spin-1 Bose gas with an external magnetic field as the control parameter. An initial many-body state with almost all bosons populating the Zeeman sublevel m = 0 is evolved to a final state very close to a macroscopic spin-singlet condensate, a fragmented state with three macroscopically occupied Zeeman states. The shortcut protocol, obtained by an approximate mapping to a harmonic oscillator Hamiltonian, is compared to linear and exponential variations of the control parameter. We find a dramatic speedup of the dynamics when using the shortcut protocol

Fragmented condensation in Bose-Hubbard trimers with tunable tunnelling

We consider a Bose-Hubbard trimer, i.e. an ultracold Bose gas populating three quantum states. The latter can be either di erent sites of a triple-well potential or three internal states of the atoms. The bosons can tunnel between di erent states with variable tunnelling strength between two of them. This will allow us to study; i) di erent geometrical con gurations, i.e. from a closed triangle to three aligned wells and ii) a triangular con guration with a -phase, i.e. by setting one of the tunnellings negative. By solving the corresponding three-site Bose-Hubbard Hamiltonian we obtain the ground state of the system as a function of the trap topology. We characterise the di erent ground states by means of the coherence and entanglement properties. For small repulsive interactions, fragmented condensates are found for the -phase case. These are found to be robust against small variations of the tunnelling in the small interaction regime. A low-energy e ective many-body Hamiltonian restricted to the degenerate manifold provides a compelling description of the -phase degeneration and explains the low-energy spectrum as excitations of discrete semi uxon states

Robustness of discrete semifluxons in closed Bose-Hubbard chains

We present the properties of the ground state and low-energy excitations of Bose-Hubbard chains with a geometry that varies from open to closed and with a tunable twisted link. In the vicinity of the symmetric π-flux case the system behaves as an interacting gas of discrete semifluxons for finite chains and interactions in the Josephson regime. The energy spectrum of the system is studied by direct diagonalization and by solving the corresponding Bogoliubov-de Gennes equations. The atom-atom interactions are found to enhance the presence of strongly correlated macroscopic superpositions of semifluxons

Systematics of properties of the electron gas in deep-etched quantum wires

An efficient method is developed for an iterative solution of the Poisson and Schro¿dinger equations, which allows systematic studies of the properties of the electron gas in linear deep-etched quantum wires. A much simpler two-dimensional (2D) approximation is developed that accurately reproduces the results of the 3D calculations. A 2D Thomas-Fermi approximation is then derived, and shown to give a good account of average properties. Further, we prove that an analytic form due to Shikin et al. is a good approximation to the electron density given by the self-consistent methods

Linear relation between deuteron matter radius and the scattering length

We explain the empirical linear relations between the triplet scattering length, or the asymptotic normalization constant, and the deuteron matter radius using the effective range expansion in a manner similar to a recent paper by Bhaduri et al. We emphasize the corrections due to the finite force range and to shape dependence. The discrepancy between the experimental values and the empirical line shows the need for a larger value of the wound extension, a parameter which we introduce here. Short-distance nonlocality of the n-p interaction is a plausible explanation for the discrepancy

Continuum bound states as surface states of a finite periodic system

We discuss the relation between continuum bound states (CBSs) localized on a defect, and surface states of a finite periodic system. We model an experiment of Capasso et al. [F. Capasso, C. Sirtori, J. Faist, D. L. Sivco, S-N. G. Chu, and A. Y. Cho, Nature (London) 358, 565 (1992)] using the transfer-matrix method. We compute the rate for intrasubband transitions from the ground state to the CBS and derive a sum rule. Finally we show how to improve the confinement of a CBS while keeping the energy fixed

Systematics of properties of the electron gas in deep-etched quantum wires

An efficient method is developed for an iterative solution of the Poisson and Schro¿dinger equations, which allows systematic studies of the properties of the electron gas in linear deep-etched quantum wires. A much simpler two-dimensional (2D) approximation is developed that accurately reproduces the results of the 3D calculations. A 2D Thomas-Fermi approximation is then derived, and shown to give a good account of average properties. Further, we prove that an analytic form due to Shikin et al. is a good approximation to the electron density given by the self-consistent methods

Determination of the electron density in GaAs/AlxGa1-xAs heterostructures

An optimized self-consistent method for determination of the quantal electron density is presented. It is applied, in the zero-temperature case, to devices with either partial or full donor ionization. A Thomas-Fermi approximation for the T=0 limit is developed and shown to be appropriate for systematic studies of the two-dimensional electron density, σ − . A suitable linear approximation is found that provides simple and accurate analytic expressions for σ − in terms of the physical parameters of the device

Deuteron polarizability shifts and the deuteron matter radius

New laser-based measurements of the isotope shift between hydrogen and deuterium by Haensch [ital et] [ital al]. should determine accurately the deuteron matter radius [ital r][sub [ital m]]. We study the contribution of the deuteron polarizability energy shifts to the isotopic difference and show that this is known in a model independent way. We also make accurate determinations of the asymptotic normalization and the electric dipole polarizability by exploiting empirical linear relations between them and [ital r][sub [ital m]][sup 2]

Understanding quantum wires with circular bends

It is shown that propagation around a circular bend in a quantum wire is well approximated by a one¿dimensional problem with a square¿well potential replacing the bend. Simple analytic expressions are obtained for the transmission and bound states