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超冷原子系统是一个纯净的、高度可控的量子体系, 可对凝聚态物理、高能物理、天体物理和化学反应等领域的重要物理问题进行量子模拟. 构造不同构型的光晶格是模拟多样化的复杂量子系统的一个重要前提. 本文采用权重Gerchberg-Saxton算法生成多种形状的光晶格全息图, 利用液晶型空间光调制器和高分辨率光学系统, 把全息图(动量空间)变换到实空间构造出多种形状的二维晶格阵列, 包括简单的三角、六角、正方晶格和更为复杂的蜂巢晶格等, 并实现对87Rb超冷原子二维晶格阵列的装载, 晶格的最小间距为3 μm. 这种方法具有通用性强、操控灵活的优势, 将有助于拓展光晶格中超冷原子量子模拟的应用.
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关键词:
- 权重Gerchberg-Saxton算法 /
- 空间光调制器 /
- 光晶格 /
- 高分辨率成像
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.-
Keywords:
- weighted Gerchberg-Saxton algorithm /
- spatial light modulator /
- optical lattice /
- high-resolution imaging
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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)
Fig. 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
Fig. 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
Fig. 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 7 强度调控 (a) 非均匀光晶格; (b) 沿虚线路径的光强分布
Fig. 7. Intensity control: (a) Inhomogeneous optical lattice; (b) optical intensity profiles along the dashed lines on panel (a)
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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
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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
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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[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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