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arXiv:1408.0188 · Optics Express

Conjugate gradient minimisation approach to generating holographic traps for ultracold atoms

Tiffany Harte, Graham D. Bruce, Jonathan Keeling, Donatella Cassettari

Published Oct 20, 2014• 40 citations
arXivHTMLPDF

Abstract

Direct minimisation of a cost function can in principle provide a versatile and highly controllable route to computational hologram generation. 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.

DOI
10.1364/oe.22.026548

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Direct minimisation of a cost function can in principle provide a versatile and highly controllable route to computational hologram generation. 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.
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This thesis details the design, construction and characterisation of an ultracold atoms system, developed in conjunction with a flexible optical trapping scheme which utilises a Liquid Crystal Spatial Light Modulator (LC SLM). The ultracold atoms system uses a hybrid trap formed of a quadrupole magnetic field and a focused far-detuned laser beam to form a Bose-Einstein Condensate of 2×10⁵ ⁸⁷Rb atoms. Cold atoms confined in several arbitrary optical trapping geometries are created by overlaying the LC SLM trap on to the hybrid trap, where a simple feedback process using the atomic distribution as a metric is shown to be capable of compensating for optical aberrations. Two novel methods for creating flexible optical traps with the LC SLM are also detailed, the first of which is a multi-wavelength technique which allows several wavelengths of light to be smoothly shaped and applied to the atoms. The second method uses a computationally-efficient minimisation algorithm to create light patterns which are constrained in both amplitude and phase, where the extra phase constraint was shown to be crucial for controlling propagation effects of the LC SLM trapping beam.
Abstract 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 (root mean square error). We prove the generality of this algorithm by applying it to a variety of target light distributions of relevance for cold atomic physics.
We report the realization of a new iterative Fourier-transform algorithm for creating holograms that can diffract light into an arbitrary two-dimensional intensity profile. We show that the predicted intensity distributions are smooth with a fractional error from the target distribution at the percent level. We demonstrate that this new algorithm outperforms the most frequently used alternatives typically by one and two orders of magnitude in accuracy and roughness, respectively. The techniques described in this paper outline a path to creating arbitrary holographic atom traps in which the only remaining hurdle is physical implementation.
Arbitrary light potentials have proven to be a valuable and versatile tool in many quantum information and quantum simulation experiments with ultracold atoms. Using a phase-modulating spatial light modulator (SLM), we generate arbitrary light potentials holographically with measured efficiencies between 15 and 40% and an accuracy of [Formula: see text] root-mean-squared error. Key to the high accuracy is the modelling of pixel crosstalk of the SLM on a sub-pixel scale which is relevant especially for large light potentials. We employ conjugate gradient minimisation to calculate the SLM phase pattern for a given target light potential after measuring the intensity and wavefront at the SLM. Further, we use camera feedback to reduce experimental errors, we remove optical vortices and investigate the difference between the angular spectrum method and the Fourier transform to simulate the propagation of light. Using a combination of all these techniques, we achieved more accurate and efficient light potentials compared to previous studies, and generated a series of potentials relevant for cold atom experiments.