Phase dynamics of Bose-Einstein condensates: Losses versus revivals

In the absence of losses the phase of a Bose-Einstein condensate undergoes collapses and revivals in time due to elastic atomic interactions. As experiments necessarily involve inelastic collisions, we develop a model to describe the phase dynamics of the condensates in presence of collisional losses. We find that a few inelastic processes are sufficient to damp the revivals of the phase. For this reason the observability of phase revivals for present experimental conditions is limited to condensates with a few hundreds of atoms. Received: 23 February 1998 / Revised: 21 July 1998 / Accepted: 23 July 1998     

Vortex lattice formation in Bose-Einstein condensates

We show that the formation of a vortex lattice in a weakly interacting Bose condensed gas can be modeled with the nonlinear Schr?dinger equation for both T=0 and finite temperatures without the need for an explicit damping term. Applying a weak rotating anisotropic harmonic potential, we find numerically that the turbulent dynamics of the field produces an effective dissipation of the vortex motion and leads to the formation of a lattice. For T=0, this turbulent dynamics is triggered by a rotational dynamic instability of the condensate. For finite temperatures, noise is present at the start of the simulation and allows the formation of a vortex lattice at a lower rotation frequency, the Landau frequency. These two regimes have different vortex dynamics. We show that the multimode interpretation of the classical field is essential.     

Binary mixtures of Bose-Einstein condensates: Phase dynamics and spatial dynamics

We investigate the relative phase coherence properties and the occurrence of demixing instabilities for two mutually interacting and time evolving Bose-Einstein condensates in traps. Our treatment naturally includes the additional decoherence effect due to fluctuations in the total number of particles. Analytical results are presented for the breathe-together solution, an extension of previously known scaling solution to the case of a binary mixture of condensates. When the three coupling constants describing the elastic interactions among the atoms in the two states are close to each other, a dramatic increase of the phase coherence time is predicted. Numerical results are presented for the parameters of the recent JILA experiments. Received 23 April 1999 and Received in final form 21 September 1999     

XPS and AFM characterization of the enzyme glucose oxidase immobilized on SiO(2) surfaces

A process to immobilize the enzyme glucose oxidase on SiO2 surfaces for the realization of integrated microbiosensors was developed. The sample characterization was performed by monitoring, step by step, oxide activation, silanization, linker molecule (glutaraldehyde) deposition, and enzyme immobilization by means of XPS, AFM, and contact angle measurements. The control of the environment during the procedure, to prevent silane polymerization, and the use of oxide activation to obtain a uniform enzyme layer are issues of crucial importance. The correct protocol application gives a uniform layer of the linker molecule and the maximum sample surface coverage. This result is fundamental for maximizing the enzyme bonding sites on the sample surface and achieving the maximum surface coverage. Thin SiO2 layers thermally grown on a Si substrate were used. The XPS Si 2p signal of the substrate was monitored during immobilization. Such a signal is not completely shielded by the thin oxide layer and it is fully suppressed after the completion of the whole protocol. A power spectral density analysis on the AFM measurements showed the crucial role of both the oxide activation and the intermediate steps (silanization and linker molecule deposition) to obtain uniform immobilized enzyme coverage. Finally, enzymatic activity measurements confirmed the suitability of the optimized protocol.     

Spin squeezing in finite temperature Bose-Einstein condensates: Scaling with the system size

We perform a multimode treatment of spin squeezing induced by interactions in atomic condensates, and we show that, at finite temperature, the maximum spin squeezing has a finite limit when the atom number N →∞ at fixed density and interaction strength. To calculate the limit of the squeezing parameter for a spatially homogeneous system we perform a double expansion with two small parameters: 1/N in the thermodynamic limit and the non-condensed fraction ⟨N _nc⟩/N in the Bogoliubov limit. To test our analytical results beyond the Bogoliubov approximation, and to perform numerical experiments, we use improved classical field simulations with a carefully chosen cut-off, such that the classical field model gives for the ideal Bose gas the correct non-condensed fraction in the Bose-condensed regime.     

Penning collisions of laser-cooled metastable helium atoms

We present experimental results on the two-body loss rates in a magneto-optical trap of metastable helium atoms. Absolute rates are measured in a systematic way for several laser detunings ranging from -5 to -30 MHz and at different intensities, by monitoring the decay of the trap fluorescence. The dependence of the two-body loss rate coefficient β on the excited state ( 2³ P ₂) and metastable state ( 2³ S ₁) populations is also investigated. From these results we infer a rather uniform rate constant K _sp = (1±0.4)×10^-7 cm³/s. Received 8 September 2000 and Received in final form 19 December 2000     

Singularity Curves of a Parallel Pointing System

This paper studies a parallel pointing system used in aerospace applications for orientating parabolic antennas. In the literature [6, 7], the position analysis of this device has been already solved in closed form, whereas simple and efficient tools to address singularities distribution are still lacking. In this paper, its velocity analysis is addressed, and a singularity locus analytic expression, containing the manipulator geometric parameters and the end-effector orientation parameters, is derived. Moreover, it is shown that the determined singularity locus can be represented by curves (singularity curves) on a Cartesian plane having the generalized coordinates of the mechanism on the coordinate axes. Finally, an example showing the use of the proposed relationships is given and discussed.     

Optical measurement of <Superscript>3</Superscript>He nuclear polarization for metastable exchange optical pumping studies at high magnetic field

An accurate optical method to measure the nuclear polarization of ³He atoms in the 1¹S ground state is described. The absorption of a weak, probe laser beam is used to measure the relative populations of two hyperfine sublevels of the 2³S metastable state that are not addressed by the pumping laser beam. Since a common spin temperature between the ground and metastable states is established by metastable exchange collisions, the nuclear polarization can be derived from these absorption measurements. The method is highly sensitive, robust, and can be used to monitor the dynamics of optical pumping and relaxation processes without interfering with them. It was successfully implemented and tested in the 0.45–2.0 T magnetic field range at the ³He gas pressure up to 67 mbar.     

Limit of spin squeezing in finite-temperature Bose-Einstein condensates

We show that, at finite temperature, the maximum spin squeezing achievable using interactions in Bose-Einstein condensates has a finite limit when the atom number N→∞ at fixed density and interaction strength. We calculate the limit of the squeezing parameter for a spatially homogeneous system and show that it is bounded from above by the initial noncondensed fraction.