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

Feedback-enhanced algorithm for aberration correction of holographic atom traps

We show that a phase-only spatial light modulator can be used to generate non-trivial light distributions suitable for trapping ultracold atoms, when the hologram calculation is included within a simple and robust feedback loop that corrects for imperfect device response and optical aberrations. This correction reduces the discrepancy between target and experimental light distribution to the level of a few percent (RMS error). We prove the generality of this algorithm by applying it to a variety of target light distributions of relevance for cold atomic physics.Comment: 5 pages, 4 figure

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

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

Collisional relaxation of Feshbach molecules and three-body recombination in 87Rb Bose-Einstein condensates

We predict the resonance enhanced magnetic field dependence of atom-dimer relaxation and three-body recombination rates in a $^{87}$Rb Bose-Einstein condensate (BEC) close to 1007 G. Our exact treatments of three-particle scattering explicitly include the dependence of the interactions on the atomic Zeeman levels. The Feshbach resonance distorts the entire diatomic energy spectrum causing interferences in both loss phenomena. Our two independent experiments confirm the predicted recombination loss over a range of rate constants that spans four orders of magnitude.Comment: 4 pages, 3 eps figures (updated references

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

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

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