A conjugate gradient minimisation approach to generating holographic traps for ultracold atoms

Direct minimisation of a cost function can in principle provide a versatile and highly controllable route to computational hologram generation. However, to date iterative Fourier transform algorithms have been predominantly used. Here we show that the careful design of cost functions, combined with numerically efficient conjugate gradient minimisation, establishes a practical method for the generation of holograms for a wide range of target light distributions. This results in a guided optimisation process, with a crucial advantage illustrated by the ability to circumvent optical vortex formation during hologram calculation. We demonstrate the implementation of the conjugate gradient method for both discrete and continuous intensity distributions and discuss its applicability to optical trapping of ultracold atoms.Comment: 11 pages, 4 figure

Multi-wavelength holography with a single spatial light modulator for ultracold atom experiments

The authors acknowledge funding from the Leverhulme Trust Research Project Grant RPG-2013-074 and from the EPSRC grant GR/T08272/01.We demonstrate a method to independently and arbitrarily tailor the spatial profile of light of multiple wavelengths and we show possible applications to ultracold atoms experiments. A single spatial light modulator is programmed to create a pattern containing multiple spatially separated structures in the Fourier plane when illuminated with a single wavelength. When the modulator is illuminated with overlapped laser beams of different wavelengths, the position of the structures is wavelength-dependent. Hence, by designing their separations appropriately, a desired overlap of different structures at different wavelengths is obtained. We employ regional phase calculation algorithms and demonstrate several possible experimental scenarios by generating light patterns with 670 nm, 780 nm and 1064 nm laser light which are accurate to the level of a few percent. This technique is easily integrated into cold atom experiments, requiring little optical access.PostprintPeer reviewe

Axially open nonradiative structures: an example of single-mode resonator based on the sample holder

The concept of nonradiative dielectric resonator is generalized in order to include axially open configurations having rotational invariance. The resulting additional nonradiative conditions are established for the different resonance modes on the basis of their azimuthal modal index. An approximate chart of the allowed dielectric and geometrical parameters for the TE011 mode is given. A practical realization of the proposed device based on commercial fused quartz tubes is demonstrated at millimeter wavelengths, together with simple excitation and tuning mechanisms. The observed resonances are characterized in their basic parameters, as well as in the field distribution by means of a finite element method. The predictions of the theoretical analysis are well confirmed, both in the general behaviour and in the expected quality factors. The resulting device, in which the sample holder acts itself as single-mode resonating element, combines an extreme ease of realization with state-of-the-art performances. The general benefits of the proposed open single-mode resonators are finally discussed.Comment: 18 pages, 10 figure

Wave function recombination instability in cold atom interferometers

Cold atom interferometers use guiding potentials that split the wave function of the Bose-Einstein condensate and then recombine it. We present theoretical analysis of the wave function recombination instability that is due to the weak nonlinearity of the condensate. It is most pronounced when the accumulated phase difference between the arms of the interferometer is close to an odd multiple of PI and consists in exponential amplification of the weak ground state mode by the strong first excited mode. The instability exists for both trapped-atom and beam interferometers.Comment: 4 pages, 5 figure

Transport of Bose-Einstein Condensates with Optical Tweezers

We have transported gaseous Bose-Einstein condensates over distances up to 44 cm. This was accomplished by trapping the condensate in the focus of an infrared laser and translating the location of the laser focus with controlled acceleration. Condensates of order 1 million atoms were moved into an auxiliary chamber and loaded into a magnetic trap formed by a Z-shaped wire. This transport technique avoids the optical and mechanical access constraints of conventional condensate experiments and creates many new scientific opportunities.Comment: 5 pages, 3 figure

An accelerator mode based technique for studying quantum chaos

We experimentally demonstrate a method for selecting small regions of phase space for kicked rotor quantum chaos experiments with cold atoms. Our technique uses quantum accelerator modes to selectively accelerate atomic wavepackets with localized spatial and momentum distributions. The potential used to create the accelerator mode and subsequently realize the kicked rotor system is formed by a set of off-resonant standing wave light pulses. We also propose a method for testing whether a selected region of phase space exhibits chaotic or regular behavior using a Ramsey type separated field experiment.Comment: 5 pages, 3 figures, some modest revisions to previous version (esp. to the figures) to aid clarity; accepted for publication in Physical Review A (due out on January 1st 2003

Reflection of Channel-Guided Solitons at Junctions in Two-Dimensional Nonlinear Schroedinger Equation

Solitons confined in channels are studied in the two-dimensional nonlinear Schr\"odinger equation. We study the dynamics of two channel-guided solitons near the junction where two channels are merged. The two solitons merge into one soliton, when there is no phase shift. If a phase difference is given to the two solitons, the Josephson oscillation is induced. The Josephson oscillation is amplified near the junction. The two solitons are reflected when the initial velocity is below a critical value.Comment: 3 pages, 2 figure

Trapped-Atom-Interferometer in a Magnetic Microtrap

We propose a configuration of a magnetic microtrap which can be used as an interferometer for three-dimensionally trapped atoms. The interferometer is realized via a dynamic splitting potential that transforms from a single well into two separate wells and back. The ports of the interferometer are neighboring vibrational states in the single well potential. We present a one-dimensional model of this interferometer and compute the probability of unwanted vibrational excitations for a realistic magnetic potential. We optimize the speed of the splitting process in order suppress these excitations and conclude that such interferometer device should be feasible with currently available microtrap technique.Comment: 6 pages, 6 figures, submitted to PR

Surface Effects in Magnetic Microtraps

We have investigated Bose-Einstein condensates and ultra cold atoms in the vicinity of a surface of a magnetic microtrap. The atoms are prepared along copper conductors at distances to the surface between 300 um and 20 um. In this range, the lifetime decreases from 20 s to 0.7 s showing a linear dependence on the distance to the surface. The atoms manifest a weak thermal coupling to the surface, with measured heating rates remaining below 500 nK/s. In addition, we observe a periodic fragmentation of the condensate and thermal clouds when the surface is approached.Comment: 4 pages, 4 figures; v2: corrected references; v3: final versio

A Storage Ring for Neutral Atoms

We have demonstrated a storage ring for ultra-cold neutral atoms. Atoms with mean velocities of 1 m/s corresponding to kinetic energies of ~100 neV are confined to a 2 cm diameter ring by magnetic forces produced by two current-carrying wires. Up to 10^6 atoms are loaded at a time in the ring, and 7 revolutions are clearly observed. Additionally, we have demonstrated multiple loading of the ring and deterministic manipulation of the longitudinal velocity distribution of the atoms using applied laser pulses. Applications of this ring include large area atom interferometers and cw monochromatic atomic beam generation.Comment: 4 pages, 5 figure