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Acta Physica Sinica

Construction of two-dimensional arbitrary shape 87Rb atomic array based on spatial light modulator

Liang-Wei Wang, Fang-De Liu, Yun‐Da Li, Wei Han, Zengming Meng, Jing Zhang

Published Jan 1, 2023• 2 citations
Publisher

Abstract

The ultra-cold atomic system is a clean and highly controllable quantum system, which can be used for quantum simulation of important physical problems in many fields such as condensed matter physics, high-energy physics, astrophysics, and chemical reactions. The constructions of optical lattices with different configurations are an important prerequisite for simulating diverse complex quantum systems, especially solid materials. In this work, we use weighted Gerchberg-Saxton algorithm to generate holograms. By using liquid crystal spatial light modulator and high-resolution imaging system, holograms (in momentum space) are transformed into images in real space for constructing various two-dimensional (2D) optical trap arrays, such as simple triangular, hexagonal, square lattice and more complex honeycomb lattice. We load 87Rb ultra-cold atoms into the 2D optical trap arrays with a minimal spacing of 3 μm in between. This method is versatile and flexible, which is helpful in expanding the application scope of quantum simulation with optical lattices.

DOI
10.7498/aps.72.20222096

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The ultra-cold atomic system is a clean and highly controllable quantum system, which can be used for quantum simulation of important physical problems in many fields such as condensed matter physics, high-energy physics, astrophysics, and chemical reactions. The constructions of optical lattices with different configurations are an important prerequisite for simulating diverse complex quantum systems, especially solid materials. In this work, we use weighted Gerchberg-Saxton algorithm to generate holograms. By using liquid crystal spatial light modulator and high-resolution imaging system, holograms (in momentum space) are transformed into images in real space for constructing various two-dimensional (2D) optical trap arrays, such as simple triangular, hexagonal, square lattice and more complex honeycomb lattice. We load 87Rb ultra-cold atoms into the 2D optical trap arrays with a minimal spacing of 3 μm in between. This method is versatile and flexible, which is helpful in expanding the application scope of quantum simulation with optical lattices.
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.
Programmable arrays of ultracold atoms are a leading platform for quantum computation and simulation, enabling state-of-the-art implementations of quantum error correction, and analog simulations of Hubbard models that address open problems in condensed matter physics. In these systems, all local control is mediated through precisely shaped optical fields, and so the challenge of managing many-body quantum states becomes an exercise in optical design. In particular, one wishes for fast, flexible control with low disorder and heating, and access to large arrays with many atoms. An ideal optical system therefore must generate arbitrary patterns with high spatial resolution and low disorder, and alter these patterns on a timescale that is faster than the relevant atomic dynamics. Here, we present an optical system that is comparable to previous approaches in scale, while advancing all other axes. We demonstrate arbitrary pattern generation with 10−310^{-3}10−3 intensity resolution, a frame rate of >84>84>84 MFPS (megaframes per second), and a spatial resolution of 83×5283 \times 5283×52 beam waists (with 11×5211 \times 5211×52 waists accessible via a single 404040 GHz electro-optic modulator). These capabilities unlock a new class of experiments. We develop and numerically validate a scheme for fully programmable Hubbard models, with time-dependent control over local chemical potentials, tunneling amplitudes, on-site interactions, and patterns of artificial magnetic flux. The same architecture performs fast, arbitrary permutations of tweezers in 2D, decoupling optical constraints from the design of high-rate error-correcting codes.
Liquid crystal spatial light modulator (LC-SLM) can be readily used to fabricate the diffractive optical elements. However, a disadvantage of the finite resolution always exists in LC-SLM. In this paper, a new scheme of fabricating phase grating with LC-SLM is proposed to produce one-dimensional (1D) and two-dimensional (2D) array of optical traps. The advantage of the LC-SLM is fully utilized and the disadvantage is well avoided in our scheme. The phase distribution of the grating is optimized by using iterative Fourier series expansion. The grating is designed by simulation according to the LC-SLM technique parameters, and the corresponding light intensity distribution is calculated. The results show that the array has very high peak value intensity and big gradient of intensity by illuminating the grating with a large detuning and low power laser. The optical dipole potential of trapping cold atoms achieves the order of mK, and the interaction force between atom and optical field is much greater than the atom gravity.
Ultracold atoms in optical lattices can be used to model condensed matter systems. They provide a clean, tuneable system which can be engineered to reach parameter regimes that are not accessible in condensed matter systems. Furthermore, they provide different techniques for probing the properties of these systems.This thesis presents an experimental and theoretical study of ultracold atoms in optical lattices for quantum simulation of two-dimensional systems.The first part of this thesis describes an experiment with a Bose-Einstein condensate of 87Rb loaded into a two-dimensional optical lattice. The beams that generate the optical lattice are controlled by acousto-optic deflection to provide a flexible optical lattice potential. The use of a dynamic ‘accordion’ lattice with ultracold atoms, where the spacing of the lattice is increased in both directions from 2.2 to 5.5 μm, is described. This technique allows an experiment such as quantum simulations to be performed with a lattice spacing smaller than the resolution limit of the imaging system, while allowing imaging of the atoms at individual lattice sites by subsequent expansion of the optical lattice. The optical lattice can also be rotated, generating an artificial magnetic field. Previous experiments with the rotating optical lattice are summarised, and steps to reaching the strongly correlated regime are discussed.The second part of this thesis details numerical techniques that can be used to describe strongly correlated two-dimensional systems. These systems are challenging to simulate numerically, as the exponential growth in the size of the Hilbert space with the number of particles means that they can only be solved exactly for very small systems. Recently proposed correlator product states [Phys. Rev. B 80, 245116 (2009)] provide a numerically efficient description which can be used to simulate large two-dimensional systems. In this thesis we apply this method to the two-dimensional quantum Ising model, and the Bose-Hubbard model subject to an artificial magnetic field in the regime where fractional quantum Hall states are predicted to occur.
The ability to assemble and reconfigure individual atoms is central to performing quantum science using optical tweezer arrays. Here, we demonstrate parallel omnidirectional atom transport and rearrangement using dynamic holograms generated by a single kilohertz-rate spatial light modulator. By carefully characterizing survival and heating, we show that atoms remain confined even when successive holograms are commanded before the liquid crystal has settled, enabling significantly faster transport. To generate holograms in real time, we develop and implement a warm-start, weighted Gerchberg-Saxton algorithm that achieves performance comparable to neural-network methods without requiring any training. Combining these techniques, we assemble ytterbium atoms into a 2078-site kagome lattice with 99.0% mean filling. In addition, we demonstrate parallel transport between array layers, combining axial and transverse motion to reconfigure atoms in three dimensions. Our approach is readily adaptable to existing tweezer platforms and provides a method for large-scale SLM-based atom assembly as well as programmable three-dimensional control.
Ultracold atoms in optical lattices can be used to model condensed matter systems. They provide a clean, tuneable system which can be engineered to reach parameter regimes that are not accessible in condensed matter systems. Furthermore, they provide different techniques for probing the properties of these systems.This thesis presents an experimental and theoretical study of ultracold atoms in optical lattices for quantum simulation of two-dimensional systems.The first part of this thesis describes an experiment with a Bose-Einstein condensate of 87Rb loaded into a two-dimensional optical lattice. The beams that generate the optical lattice are controlled by acousto-optic deflection to provide a flexible optical lattice potential. The use of a dynamic ‘accordion’ lattice with ultracold atoms, where the spacing of the lattice is increased in both directions from 2.2 to 5.5 μm, is described. This technique allows an experiment such as quantum simulations to be performed with a lattice spacing smaller than the resolution limit of the imaging system, while allowing imaging of the atoms at individual lattice sites by subsequent expansion of the optical lattice. The optical lattice can also be rotated, generating an artificial magnetic field. Previous experiments with the rotating optical lattice are summarised, and steps to reaching the strongly correlated regime are discussed.The second part of this thesis details numerical techniques that can be used to describe strongly correlated two-dimensional systems. These systems are challenging to simulate numerically, as the exponential growth in the size of the Hilbert space with the number of particles means that they can only be solved exactly for very small systems. Recently proposed correlator product states [Phys. Rev. B 80, 245116 (2009)] provide a numerically efficient description which can be used to simulate large two-dimensional systems. In this thesis we apply this method to the two-dimensional quantum Ising model, and the Bose-Hubbard model subject to an artificial magnetic field in the regime where fractional quantum Hall states are predicted to occur.