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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.
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Keywords:
- weighted Gerchberg-Saxton algorithm /
- spatial light modulator /
- optical lattice /
- high-resolution imaging
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图 1 SLM的标量衍射理论图
Figure 1. Foundations of scalar diffraction theory of SLM.
图 2 迭代GSW算法的流程图
Figure 2. Flow chart of iterative GSW algorithm.
图 3 实验装置图 (a) SLM光路图; (b) 成像光路图; (c) 手风琴光晶格光路图(CCD, 电荷耦合器件; PBS, 偏振分束器, BD, 光挡; FM, 翻转镜片; DM, 双色分束器; PD, 光电二极管; AOD, 声光偏转器)
Figure 3. Experimental configuration: (a) SLM setup; (b) imaging setup; (c) accordion lattice setup (CCD, charge coupled device; PBS, polarizing beam splitter, BD, beam dump; FM, flip mirror; DM, dichroic mirror; PD, photodiode detectors; AOD, acousto-optic deflector).
图 4 相图合成(上)和实验结果(下) (a) GSW算法获得的光晶格相图, 零级光和目标晶格混合在一起; (b) 闪耀光栅相图; (c) 合成相图
Figure 4. Composition of the phase pattern (up) and the optical intensity distribution (bottom): (a) Optical lattice phase diagram obtained by GSW algorithm, zero-order light and target lattice mixed together; (b) blaze grating pattern; (c) final phase pattern.
图 5 算法的性能比较(第一行为相图, 第二行为实验结果) (a) SPL算法; (b) SR算法; (c) RM算法; (d) GSW算法
Figure 5. Performance comparison of different theoretical algorithms (Row 1, phase patterns; Row 2, optical intensity distribution): (a) SPL algorithm; (b) SR algorithm; (c) RM algorithm; (d) GSW algorithm.
图 6 双层扭转类石墨烯光晶格
Figure 6. Twisted-bilayer graphene-like optical lattice.
图 7 强度调控 (a) 非均匀光晶格; (b) 沿虚线路径的光强分布
Figure 7. Intensity control: (a) Inhomogeneous optical lattice; (b) optical intensity profiles along the dashed lines on panel (a)
图 8 具有不同相位模式的原子阵列 (a1), (a2)相图; (b1), (b2)原子阵列
Figure 8. Atomic arrays with different phase patterns: (a1), (a2) Phase patterns; (b1), (b2) atomic arrays.
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[1] Georgescu I M, Ashhab S, Nori F 2014 Rev. Mod. Phys. 86 153
Google Scholar
[2] Gross C, Bloch I 2017 Science 357 995
Google Scholar
[3] Das A, Chakrabarti B K 2008 Rev. Mod. Phys. 80 1061
Google Scholar
[4] Hofstetter W, Cirac J I, Zoller P, Demler E, Lukin M D 2002 Phys. Rev. Lett. 89 220407
Google Scholar
[5] Lee P A, Nagaosa N, Wen X G 2006 Rev. Mod. Phys. 78 17
Google Scholar
[6] Le Hur K, Rice T M 2009 Annals of Physics 324 1452
Google Scholar
[7] Polkovnikov A, Sengupta K, Silva A, Vengalattore M 2011 Rev. Mod. Phys. 83 863
Google Scholar
[8] Greiner M, Mandel O, Esslinger T, Hänsch T W, Bloch I 2002 Nature 415 39
Google Scholar
[9] Sherson J F, Weitenberg C, Endres M, Cheneau M, Bloch I, Kuhr S 2010 Nature 467 68
Google Scholar
[10] Bakr W S, Peng A, Tai M E, Ma R, Simon J, Gillen J I, Fölling S, Pollet L, Greiner M 2010 Science 329 547
Google Scholar
[11] Jördens R, Strohmaier N, Günter K, Moritz H, Esslinger T 2008 Nature 455 204
Google Scholar
[12] Qi X L, Zhang S C 2011 Rev. Mod. Phys. 83 1057
Google Scholar
[13] Hasan M Z, Kane C L 2010 Rev. Mod. Phys. 82 3045
Google Scholar
[14] Semeghini G, Levine H, Keesling A, Ebadi S, Wang T T, Bluvstein D, Verresen R, Pichler H, Kalinowski M, Samajdar R, Omran A, Sachdev S, Vishwanath A, Greiner M, Vuletić V, Lukin M D 2021 Science 374 1242
Google Scholar
[15] Li C H, Yan Y, Feng S W, Choudhury S, Blasing D B, Zhou Q, Chen Y P 2022 PRX Quantum 3 010316
Google Scholar
[16] Struck J, Ölschläger C, Le Targat R, Soltan-Panahi P, Eckardt A, Lewenstein M, Windpassinger P, Sengstock K 2011 Science 333 996
Google Scholar
[17] Jotzu G, Messer M, Desbuquois R, Lebrat M, Uehlinger T, Greif D, Esslinger T 2014 Nature 515 237
Google Scholar
[18] Uehlinger T, Jotzu G, Messer M, Greif D, Hofstetter W, Bissbort U, Esslinger T 2013 Phys. Rev. Lett. 111 185307
Google Scholar
[19] González-Tudela A, Cirac J I 2019 Phys. Rev. A 100 053604
Google Scholar
[20] Meng Z M, Wang L W, Han W, Liu F D, Wen K, Gao C, Wang P J, Chin C, Zhang J 2023 Nature 615 231
[21] Dai H N, Yang B, Reingruber A, Xu X F, Jiang X, Chen Y A, Yuan Z S, Pan J W 2016 Nat. Phys. 12 783
Google Scholar
[22] Mandel O, Greiner M, Widera A, Rom T, Hänsch T W, Bloch I 2003 Phys. Rev. Lett. 91 010407
Google Scholar
[23] Choi J Y, Hild S, Zeiher J, Schauß P, Rubio-Abadal A, Yefsah T, Khemani V, Huse D A, Bloch I, Gross C 2016 Science 352 1547
Google Scholar
[24] White D H, Haase T A, Brown D J, Hoogerland M D, Najafabadi M S, Helm J L, Gies C, Schumayer D, Hutchinson D A W 2020 Nat. Commun. 11 4942
Google Scholar
[25] Zhang Z D, Chen L C, Yao K X, Chin C 2021 Nature 592 708
Google Scholar
[26] Mazurenko A, Chiu C S, Ji G, Parsons M F, Kanász-Nagy M, Schmidt R, Grusdt F, Demler E, Greif D, Greiner M 2017 Nature 545 462
Google Scholar
[27] Endres M, Bernien H, Keesling A, Levine H, Anschuetz E R, Krajenbrink A, Senko C, Vuletic V, Greiner M, Lukin M D 2016 Science 354 1024
Google Scholar
[28] Henderson K, Ryu C, MacCormick C, Boshier M G 2009 New J. Phys. 11 043030
Google Scholar
[29] Fatemi F K, Bashkansky M, Dutton Z 2007 Opt. Express 15 3589
Google Scholar
[30] Zhang D F, Gao T Y, Zou P, Kong L R, Li R Z, Shen X, Chen X L, Peng S G, Zhan M S, Pu H, Jiang K J 2019 Phys. Rev. Lett. 122 110402
Google Scholar
[31] Chen P K, Liu L R, Tsai M J, Chiu N C, Kawaguchi Y, Yip S K, Chang M S, Lin Y J 2018 Phys. Rev. Lett. 121 250401
Google Scholar
[32] Goodman J W 2005 Introduction to Fourier Optics (Greenwood Village: Roberts and Company Publishers) p63
[33] Di Leonardo R, Ianni F, Ruocco G 2007 Opt. Express 15 1913
Google Scholar
[34] Bengtsson J 1994 Appl. Opt. 33 6879
Google Scholar
[35] Turtaev S, Leite I T, Mitchell K J, Padgett M J, Phillips D B, Čižmár T 2017 Opt. Express 25 29874
Google Scholar
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