Collision-assisted Zeeman cooling of neutral atoms

We propose a new method to cool gaseous samples of neutral atoms. The gas is confined in a non dissipative optical trap in the presence of an homogeneous magnetic field. The method accumulates atoms in the $m_F=0$ Zeeman sub-level. Cooling occurs via collisions that produce atoms in $m_F\neq 0$ states. Thanks to the second order Zeeman effect kinetic energy is transformed into internal energy and recycling of atoms is ensured by optical pumping. This method may allow quantum degeneracy to be reached by purely optical means.Comment: 5 figure

Dynamic structure factor of a superfluid Fermi gas

We describe the excitation spectrum of a two-component neutral Fermi gas in the superfluid phase at finite temperature by deriving a suitable Random-Phase approximation with the technique of functional derivatives. The obtained spectrum for the homogeneous gas at small wavevectors contains the Bogoliubov-Anderson phonon and is essentially different from the spectrum predicted by the static Bogoliubov theory, which instead shows an unphysically large response. We adapt the results for the homogeneous system to obtain the dynamic structure factor of a harmonically confined superfluid and we identify in the spectrum a unique feature of the superfluid phase.Comment: 8 pages, 2 figure

Optimal Dynamic Procurement Policies for a Storable Commodity with L\'evy Prices and Convex Holding Costs

In this paper we study a continuous time stochastic inventory model for a commodity traded in the spot market and whose supply purchase is affected by price and demand uncertainty. A firm aims at meeting a random demand of the commodity at a random time by maximizing total expected profits. We model the firm's optimal procurement problem as a singular stochastic control problem in which controls are nondecreasing processes and represent the cumulative investment made by the firm in the spot market (a so-called stochastic "monotone follower problem"). We assume a general exponential L\'evy process for the commodity's spot price, rather than the commonly used geometric Brownian motion, and general convex holding costs. We obtain necessary and sufficient first order conditions for optimality and we provide the optimal procurement policy in terms of a "base inventory" process; that is, a minimal time-dependent desirable inventory level that the firm's manager must reach at any time. In particular, in the case of linear holding costs and exponentially distributed demand, we are also able to obtain the explicit analytic form of the optimal policy and a probabilistic representation of the optimal revenue. The paper is completed by some computer drawings of the optimal inventory when spot prices are given by a geometric Brownian motion and by an exponential jump-diffusion process. In the first case we also make a numerical comparison between the value function and the revenue associated to the classical static "newsvendor" strategy.Comment: 28 pages, 3 figures; improved presentation, added new results and section

Creation and counting of defects in a temperature quenched Bose-Einstein Condensate

We study the spontaneous formation of defects in the order parameter of a trapped ultracold bosonic gas while crossing the critical temperature for Bose-Einstein Condensation (BEC) at different rates. The system has the shape of an elongated ellipsoid, whose transverse width can be varied to explore dimensionality effects. For slow enough temperature quenches we find a power-law scaling of the average defect number with the quench rate, as predicted by the Kibble-Zurek mechanism. A breakdown of such a scaling is found for fast quenches, leading to a saturation of the average defect number. We suggest an explanation for this saturation in terms of the mutual interactions among defects.Comment: 9 pages, 10 figure

Observation of Solitonic Vortices in Bose-Einstein Condensates

We observe solitonic vortices in an atomic Bose-Einstein condensate after free expansion. Clear signatures of the nature of such defects are the twisted planar density depletion around the vortex line, observed in absorption images, and the double dislocation in the interference pattern obtained through homodyne techniques. Both methods allow us to determine the sign of the quantized circulation. Experimental observations agree with numerical simulations. These solitonic vortices are the decay product of phase defects of the BEC order parameter spontaneously created after a rapid quench across the BEC transition in a cigar-shaped harmonic trap and are shown to have a very long lifetime.Comment: 7 pages, 7 figure

Solitonic Vortices in Bose-Einstein Condensates

We analyse, theoretically and experimentally, the nature of solitonic vortices (SV) in an elongated Bose-Einstein condensate. In the experiment, such defects are created via the Kibble-Zurek mechanism, when the temperature of a gas of sodium atoms is quenched across the BEC transition, and are imaged after a free expansion of the condensate. By using the Gross-Pitaevskii equation, we calculate the in-trap density and phase distributions characterizing a SV in the crossover from an elongate quasi-1D to a bulk 3D regime. The simulations show that the free expansion strongly amplifies the key features of a SV and produces a remarkable twist of the solitonic plane due to the quantized vorticity associated with the defect. Good agreement is found between simulations and experiments.Comment: 6 pages, 4 figure

Dynamics and interaction of vortex lines in an elongated Bose-Einstein condensate

We study the real-time dynamics of vortex lines in a large elongated Bose-Einstein condensate (BEC) of sodium atoms using a stroboscopic technique. Vortices are spontaneously produced via the Kibble-Zurek mechanism in a quench across the BEC transition and then they slowly precess keeping their orientation perpendicular to the long axis of the trap as expected for solitonic vortices in a highly anisotropic condensate. Good agreement with theoretical predictions is found for the precession period as a function of the orbit amplitude and the number of condensed atoms. In configurations with two or more vortex lines, we see signatures of vortex-vortex interaction in the shape and visibility of the orbits. In addition, when more than two vortices are present, their decay is faster than the thermal decay observed for one or two vortices. The possible role of vortex reconnection processes is discussed.Comment: 4 pages, 4 figure