Abstract

ABSTRACTWe discuss and compare three methods to generate holograms for optical tweezers: simple rounding, Floyd–Steinberg error diffusion dithering and mixed-region amplitude freedom (MRAF). These schemes are optimized for producing large arrays of tightly focused luminous spots. The algorithms are compared in terms of their speed, efficiency and accuracy, for periodic arrangements of traps; an arrangement of particular interest for the trapping and manipulation of single laser-cooled atoms in the field of quantum computing. We simulate the image formation using each of a binary amplitude modulating digital mirror device (DMD) and a phase modulating spatial light modulator (PSLM) as the display element. While a DMD allows for fast frame rates, the slower PSLM is more efficient and provides higher accuracy with a quasi-continuous variation of phase. We discuss the relative merits of each algorithm for use with both a DMD and a PSLM, allowing one to choose the ideal approach depending on the circumstances.

Highlights

  • Since their invention by Ashkin [1], optical tweezers have had an enormous impact in diverse fields from biology to quantum physics

  • We discuss the relative merits of each algorithm for use with both a digital mirror device (DMD) and a phase modulating spatial light modulator (PSLM), allowing one to choose the ideal approach depending on the circumstances

  • We investigate the feasibility of using either a PSLM, which is quasi-continuous with m > 200 phase levels between 0 and 2π, or a binary amplitude modulating DMD, for the controlled dipole trapping of lasercooled atoms in a holographic optical tweezers arrangement

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Summary

Introduction

Since their invention by Ashkin [1], optical tweezers have had an enormous impact in diverse fields from biology to quantum physics (see [2] for a review). Holographic optical tweezers typically use a PSLM, with an iterative phase retrieval algorithm such as the Gerchberg–Saxton algorithm [22], variants thereof [23], mixed-region amplitude freedom (MRAF) [24], offset MRAF [25], or conjugate gradient minimization [26] to calculate the hologram. We investigate the feasibility of using either a PSLM, which is quasi-continuous with m > 200 phase levels between 0 and 2π , or a binary amplitude modulating DMD, for the controlled dipole trapping of lasercooled atoms in a holographic optical tweezers arrangement. The simulation and benchmarking of algorithms presented here has been the key to successfully trap and manipulate single atoms laser-cooled to less than 100 μK in a DMD-controlled arrangement of optical dipole-force traps [15], and only recently our considerations lead to the implementation of arbitrary trapping patterns for single atoms using a PSLM, see Figure 3(b). We present a benchmark of the different algorithms comparing their numerical complexity, efficiency of use of laser power and accuracy of the resulting trapping potentials

Principles of holographic imaging
The hologram of a single trap
Representing a complex-valued hologram
Algorithms for improved hologram generation
Floyd–Steinberg error diffusion dithering
Mixed-region amplitude freedom
Comparison of the algorithms
Findings
Conclusion
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