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Journal of Modern Optics

Benchmarking modern algorithms to holographically create optical tweezers for laser-cooled atoms

Naomi C Holland, Dustin Stuart, Oliver Barter, Axel Kuhn

Published Jul 20, 2018• 9 citations
Publisher

Abstract

We 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.

DOI
10.1080/09500340.2018.1499978

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We 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.
Single atoms are promising candidates for physically implementing quantum bits, the fundamental unit of quantum information. We have built an apparatus for cooling, trapping and imaging single rubidium atoms in microscopic optical tweezers. The traps are formed from a tightly focused off-resonant laser beam, which traps atoms using the optical dipole force. The traps have a diameter of ~1 μm and a depth of ~1 mK. The novelty of our approach is the use a digital mirror device (DMD) to generate multiple independently movable tweezers from a single laser beam. The DMD consists of an array of micro-mirrors that can be switched on and off, thus acting as a binary amplitude modulator. We use the DMD to imprint a computer-generated hologram on the laser beam, which is converted in to the desired arrangement of traps in the focal plane of a lens. We have developed fast algorithms for calculating binary holograms suitable for the DMD. In addition, we use this method to measure and correct for errors in the phase of the wavefront caused by optical aberrations, which is necessary for producing diffraction-limited focal spots. Using this apparatus, we have trapped arrays of up to 20 atoms with arbitrary geometrical arrangements. We exploit light-assisted collisions between atoms to ensure there is at most one atom per trapping site. We measure the temperature of the atoms in the traps to be 12 μK, and their lifetime to be 1.4 s. Finally, we demonstrate the ability to select individual atoms from an array and transport them over a distance of 14μm with laser cooling, and 5 μm without.
We demonstrate the trapping and manipulation of single neutral atoms in reconfigurable arrays of optical tweezers. Our approach offers unparalleled speed by using a Texas instruments digital micro-mirror device as a holographic amplitude modulator with a frame rate of 20 000 per second. We show the trapping of static arrays of up to 20 atoms, as well as transport of individually selected atoms over a distance of 25 μ m with laser cooling and 4 μ m without. We discuss the limitations of the technique and the scope for technical improvements.
Neutral atoms trapped in microscopic optical tweezers have emerged as a growing platform for quantum science. Achieving homogeneity over the tweezers array is an important technical requirement, and our research focuses on improving it for holographic arrays generated with a spatial light modulator. We present a series of optimization methods to calculate better holograms, fueled by precise measurement schemes. These innovations enable to achieve intensity homogeneity with a relative standard deviation of 0.3%, shape variations below 0.5%, and positioning errors within 70 nm. Such ultraprecise holographic optical tweezers arrays allow for the most demanding applications in quantum science with atomic arrays.
Trapped ion is one of the leading platforms for quantum simulation experiment due to its long coherence time and high fidelity state initialization, detection, and manipulation. To individually address ions at a single-ion level, it requires sophisticated optical engineering. In the thesis, we present a novel single qubit addressing system that is immune to imperfections of optical imaging and can scale to different size of the system. The technique is based on digital light processing with a commercially available digital micro-mirror device (DMD). \n \nA DMD is a 2D array that consists of tiny micro-mirrors that can be individually manipulated. It is commonly used in movie projectors to modulate the intensity of the light to create the desired image. However, using this technology to ions will require more sophisticated controls over optical wavefronts of the laser beams, for example, the necessity to manipulate the optical phase. It can be achieved by using the DMD as a programmable hologram, which can then be used to characterize and compensate for any imaging imperfections as well. We developed a new iterative Fourier transform algorithm (IFTA) for calculating the holograms. In the simulation, our algorithm shows more than one order of magnitude improvement in accuracy comparing to previously proposed algorithms. We experimentally demonstrated this holographic beam shaping technique with the optical aberration being compensated. The laser we used in the experiment is in the ultraviolet (UV) regime that is close to the optical transition used for manipulating 171mathrmYb+^{171}\\mathrm{Yb}^+171mathrmYb+ qubits. The short wavelength makes it more susceptible to environmental disturbance. \n \nAlso, we proposed and experimentally demonstrated a new scheme that enables holographic controls over lights with multiple laser frequencies simultaneously by combing the DMD with an acousto-optical modulator (AOM). The AOM splits the light and illuminates different zones of the DMD. Each zone has its own hologram forming one frequency channel for addressing. This opens the possibility to engineer more complex Hamiltonian for quantum simulation. For example, we can engineer arbitrary spin-spin interaction graphs by applying the M\\o lmer-S\\o rensen scheme on this new setup.
Assembling defect-free arrays of neutral atoms requires real-time rearrangement of stochastically loaded optical tweezers. Conventional rearrangement methods shuttle atoms sequentially, whereas high-speed spatial light modulators (SLMs) can move all atoms in parallel, which scales more favorably as the array size grows. For fast parallel rearrangement, the sequence of holograms displayed on the SLM should be computed more rapidly than the SLM refresh rate, and there should be phase continuity between successive holograms to minimize transient intensity fluctuations. We calculate holograms analytically by adding together the complex fields needed to produce each individual trap, and we ramp the phase of each trap linearly as it moves to its target location. Trap positions enter as continuous variables, rather than tied to points on a grid, so the method provides high positioning accuracy. Using a single GPU, we compute each intermediate hologram in 0.284 ms, considerably faster than the SLM refresh time of 0.696 ms, so the rearrangement speed is hardware-limited. In each step, we use the free processing time to iteratively optimize the holograms for equal intensity across the traps, decreasing trap non-uniformity to 1.24% during rearrangement at no cost in total time. Starting from an array of 256 sites loaded stochastically with 87^{87}87Rb atoms, we assemble a 100-atom array in under 20 ms with a rearrangement survival probability of 99.31(12)% per atom. This rearrangement increases the temperature of the atoms by 9(3) μμμK, which is small compared to the trap depth of 480 μμμK. Our method can also move individual atoms axially, enabling transport in different planes. We demonstrate this capability with a rearrangement protocol where one set of atoms leapfrogs over another.
High degree of adjustability enables the holographic tweezer array a versatile platform for creating an arbitrary geometrical atomic array. In holographic tweezer array experiments, an optical tweezer generated by a spatial light modulator (SLM) usually is used as a static tweezer array. However, the alternating current (AC) stark effect generally induces the intensity difference of traps in terms of different light shifts. So, intensity equalization is an essential prerequisite for preparing a many-body system with individually controlled atoms. Here, we report an intensity equalization algorithm. In particular, we observe the non-uniformity of the tweezer array is below 1.1% when the array size is larger than 1000. Our analysis shows that by optimizing the hardware performance of the optical system, this uniformity could be further improved. Our work offers the opportunities for large-scale quantum computation and simulation with reconfigurable atom arrays.