-
本文主要研究铯原子Λ型三能级原子的部分PT对称和相变, 利用铯原子基态$\left| {6{{\mathrm{S}}_{1/2}}, F = 3} \right\rangle $、$| 6{{\mathrm{S}}_{1/2}}, $$ F = 4 \rangle $和激发态$\left| {6{{\mathrm{P}}_{3/2}}, F' = 4} \right\rangle $组成Λ型三能级原子系统, 由失谐Δ3 = 607 MHz的探测光与耦合光形成双光子拉曼吸收, 构成损耗通道. 增加了共振作用于能级$\left| {6{{\mathrm{S}}_{1/2}}, F = 3} \right\rangle $与$\left| {6{{\mathrm{P}}_{3/2}}, F' = 4} \right\rangle $跃迁的泵浦光改变两个基态能级的布居, 从而使Λ型三能级系统的吸收减小, 在一定条件下形成原子系统的增益通道, 从而构成部分PT对称的原子系统. 实验中通过改变耦合光和探测光的腰斑比σ, 观察到部分PT对称系统中由对称向破缺相的转变. 此外研究了探测光束强度分布的不对称程度Dasym, 精确地测量了部分PT对称的破缺点, 理论计算与实验测量结果相符. 本文所报道的部分PT对称性及其相变的结果, 为主动操纵非厄米系统中的多维激光束开辟了一条途径, 并在设计激光不同部分的光放大和衰减光学器件方面具有潜在的应用价值.
Parity-time (PT) in atomic systems is of great significance for exploring exotic phenomena in non-Hermitian physics and non-Hermitian systems. It has been found that if PT symmetry is satisfied only in a certain spatial direction, then the Hamiltonian of the system still has a spectrum with eigenvalues of real numbers, which is called partial PT symmetry. In this paper, we use a Λ-type three-level atomic system, which is composed of two ground states $\left| {6{{\mathrm{S}}_{1/2}}, F = 3} \right\rangle $,$\left| {6{{\mathrm{P}}_{3/2}}, F' = 4} \right\rangle $and an excited state $\left| {6{{\mathrm{P}}_{3/2}}, F' = 4} \right\rangle $of cesium atom, to investigate the partial PT symmetry. A probe laser with the detuning of Δ3 = 607 MHz and a coupling laser satisfy the condition of two-photon Raman absorption of cesium atom, forming a loss channel. In order to construct the gain channel, we add the repumping laser that resonates during the transition of $\left| {6{{\mathrm{S}}_{1/2}}, F = 3} \right\rangle $to $\left| {6{{\mathrm{P}}_{3/2}}, F' = 4} \right\rangle $, changing the population of the two ground state energy levels, thus reducing the absorption of the Λ level system and forming the gain channel of the atomic system under certain conditions. In order to obtain the equilibrium condition of the partial PT-symmetric system, firstly, the light spot of the repumping laser in the experiment is covered by the probe laser, and then the repumping laser is moved to overlap with half of the probe laser of the detection light. When the gain and loss are balanced, the partial PT-symmetric system is in equilibrium. By changing the beam-waist ratio σ of the coupling laser to the probe laser, the transition from symmetry to broken phase is observed in partial PT-symmetric systems. By measuring the asymmetry of the detection-beam intensity distribution Dasym, we can accurately determine the partial PT symmetry breaking point, and the breaking point is located at $\sigma = {\sigma _{{\mathrm{cr}}}} \approx 3.8$. The theoretical calculations are in good agreement with the experimental measurements. The results of partial PT symmetry and its phase transition, reported in this study, open up a way to actively manipulate multidimensional laser beams in non-Hermitian systems and have potential applications in the design of optical devices for laser amplification and attenuation in different parts of the laser. -
Keywords:
- partial PT symmetry /
- gain and loss /
- PT symmetry broken
[1] Bender C M, Boettcher S 1998 Phys. Rev. Lett. 80 5243
Google Scholar
[2] Bender C M 2005 Contemp. Phys. 46 277
Google Scholar
[3] Klaiman S, Cederbaum L S 2008 Phys. Rev. A 78 062113
Google Scholar
[4] El-Ganainy R, Makris K G, Khajavikhan M, Musslimani Z H, Rotter S Christodoulides D N 2018 Nat. Phys. 14 11
Google Scholar
[5] Ashida Y, Gong Z, Ueda M 2020 Adv. Phys. 69 249
Google Scholar
[6] Konotop V V, Shchesnovich V S, Zezyulin D A 2012 Phys. Lett. A 376 2750
Google Scholar
[7] Szameit A, Rechtsman M C, Bahat-Treidel O, Segev M 2011 Phys. Rev. A 84 021806(R
Google Scholar
[8] Feng L, Ayache M, Huang J, Xu Y L, Lu M H, Chen Y F, Fainman Y, Scherer A 2011 Science 333 729
Google Scholar
[9] Regensburger A, Bersch C, Miri M, Onishchukov G, Christodoulides D N, Peschel U 2012 Nat. Phys. 488 167
Google Scholar
[10] Peng B, Özdemir S K, Lei F, Monifi F, Gianfreda M, Long G L, Fan S, Nori F, Bender C M, Yang L 2014 Nat. Phys. 10 394
Google Scholar
[11] Wen J M, Jiang X, Jiang L, Xiao M 2018 J. Phys. B: At. Mol. Opt. Phys. 51 222001
Google Scholar
[12] Hang C, Huang G X, Konotop V V 2013 Phys. Rev. Lett. 110 083604
Google Scholar
[13] Peng P, Cao W C, Shen C, Qu W Z, Wen J M, Jiang L, Xiao Y H 2016 Nat. Phys. 12 1139
Google Scholar
[14] Jiang Y, Mei Y F, Zuo Y, Zhai Y H, Li J S, Wen J M, Du S W 2019 Phys. Rev. Lett. 123 193604
Google Scholar
[15] Zhang Z Y, Zhang Y Q, Sheng J T, Yang L, Miri M A, Christodoulides D N, He B, Zhang Y P, Xiao M 2016 Phys. Rev. Lett. 117 123601
Google Scholar
[16] Zhang Z Y, Feng Y, Ning S H, Malpuech G, Solnyshkov D D, Xu Z F, Zhang Y P, Xiao M 2022 Photonics Res. 10 958
Google Scholar
[17] Feng Y, Liu Z Z, Liu F, Yu J W, Liang S, Li F, Zhang Y P, Xiao M, Zhang Z Y 2023 Phys. Rev. Lett. 131 013802
Google Scholar
[18] Zhang Z Y, Liang S, Septembre I, Yu J W, Huang Y P, Liu M C, Zhang Y P, Xiao M, Malpuech G, Solnyshkov D 2024 Phys. Rev. Lett. 132 263801
Google Scholar
[19] Miri M A, Alù A 2019 Science 363 7709
Google Scholar
[20] Chong Y D, Ge L, Stone A D 2011 Phys. Rev. Lett. 106 093902
Google Scholar
[21] Xiao L, Zhan X, Bian Z H, Wang K K, Zhang X, Wang X P, Li J, Mochizuki K, Kim D, Kawakami N, Yi W, Obuse H, Sanders B C, Xue P 2017 Nat. Phys. 13 1117
Google Scholar
[22] Zhang J, Peng B, Özdemir S K, Pichler K, Krimer D O, Zhao G M, Nori F, Liu Y X, Rotter S, Yang L 2018 Nat. Photonics 12 479
Google Scholar
[23] Shui T, Yang W X, Liu S P, Li L, Zhu Z H 2018 Phys. Rev. A 97 033819
Google Scholar
[24] Li J M, Harter A K, Liu J, de Melo L, Joglekar Y N, Luo L 2019 Nat. Commun. 10 855
Google Scholar
[25] Xiao L, Deng T S, Wang K K, Zhu G Y, Wang Z, Yi W, Xue P 2020 Nat. Phys. 16 761
Google Scholar
[26] Xiao L, Deng T S, Wang K K, Wang Z, Yi W, Xue P 2021 Phys. Rev. Lett. 126 230402
Google Scholar
[27] 唐原江, 梁超, 刘永椿 2022 物理学报 71 171101
Google Scholar
Tang Y J, Liang C, Liu Y C 2022 Acta Phys. Sin. 71 171101
Google Scholar
[28] Yang J 2014 Opt. Lett. 39 1133
Google Scholar
[29] Kartashov Y V, Konotop V V, Torner L 2015 Phys. Rev. Lett. 115 193902
Google Scholar
[30] Wang H, Huang J, Ren X, Weng Y, Mihalache D, He Y 2018 Rom. J. Phys. 63 205
[31] Ge L, Stone A D 2014 Phys. Rev. X 4 031011
Google Scholar
[32] Xue Y M, Hang C, He Y H, Bai Z Y, Jiao Y C, Huang G X, Zhao J M, Jia S T 2022 Phys. Rev. A 105 053516
Google Scholar
-
图 1 (a) 实验装置示意图. (b)铯原子气室中探测光、耦合光和泵浦光横截面. 探测光和耦合光为圆形高斯光斑, 泵浦光设计为椭圆形高斯光斑, 与探测光和耦合光的一半重合, 形成二维部分PT对称的损耗和增益通道. (c)铯原子基态和激发态三能级构成部分PT系统中损耗(左)与增益通道(右)的能级示意图, Ωp, Ωc和 Ωr为Rabi频率, Δ2和Δ3分别为激光束的频率失谐
Fig. 1. (a) Sketch of the experimental setup. (b) The probe and coupling laser are circular Gaussian, and the repumping laser is designed as elliptical Gaussian, the coupling laser covers the whole probe beam, whereas the repumping laser covers the right-half region of the probe beam, which creates a 2D partially PT-symmetric potential for the probe laser. (c) Energy level diagram of loss and gain channels in the three-level component PT system of cesium atoms, the left and right panels show the loss and gain configurations, respectively; Ωp, Ωc and Ωr are Rabi frequencies and Δ2 and Δ3 are frequency detuning of laser beam.
图 2 (a) Λ型三能级原子系统中的损耗p + c (紫色)与增益p + c + r (红色)的光谱; (b)测量增益和损耗对应的PD 信号, p代表频率远离失谐的情况; p + c对应探测光与耦合光共同作用的结果; p + c + r对应的是3束光同时存在的情况. 此时泵浦光与探测光的光斑完全重叠; (c) 部分PT系统处于平衡位置时探测光增益和损耗分别对应的电平信号, 移动泵浦光的光斑与探测光光斑的一半重合, 此时对应的信号p + c + r与p 完全重合
Fig. 2. (a) Spectra of loss p + c (purple) and gain p + c + r (red) in a Λ-type three-level atomic system; (b) the measurements of PD signals for the gain and loss of the probe laser, the signal p corresponds to that the probe laser with the frequency far detuning from the resonance; p + c corresponds to that the probe laser propagates in the atoms driven only by the coupling laser; p + c + r corresponds to that the probe laser propagates in the atoms driven by both coupling and repumping lasers, repumping laser is fully overlapped with the probe beam, which the signals p + c + r and p + c are located symmetrically about the signal p; (c) the repumping laser is then moved to behalf overlapped with the probe beam, in which the signal p + c + r coincides with the signal p.
图 3 实验测量初始损耗间隔分别为SL = 7.7, 13.7, 27.0, 37.1和40.4 mV时, 增益SGL与原子密度ρ的关系, 灰色虚线左边代表的是部分PT对称区域, 右边是部分PT对称破坏区域, 误差棒是两次测量的标准偏差
Fig. 3. (a) Relationship between the gain SGL and the atomic density when the initial loss interval is SL = 7.7, 13.7, 27.0, 37.1 and 40.4 mV, respectively, the gray dotted line on the left represents a partial PT symmetry region, and on the right is a non-partial PT-symmetry region, error bars denote standard error of two measurements.
图 4 (a) 耦合光与探测光的腰斑比$ \sigma = 2.14 $, 系统处于部分PT对称区域时对应的探测光的光斑是均匀分布, 对应的理论模拟结果(a1); (b) 耦合光与探测光的腰斑比$ \sigma = $$ 4.55 $时, 探测光光斑分布呈现不均匀的分布, 且左半边暗右半边亮, 此时系统处于PT破缺, 对应的理论模拟(b1)
Fig. 4. (a) Measured result for $ \sigma = 2.14 $ of the probe intensity distribution, which is uniform, and the numerical results corresponding to panel (a1). (b) Measured result for $\sigma = 4.55$ of the partial PT symmetry broken, and the numerical results corresponding to panel (b1).
图 5 探测光的光斑不对称度Dasym与耦合光和探测光的腰斑比σ的依赖关系, 可以看到部分PT破缺点的位置是σ = σcr ≈ 3.8, 玫红色圆圈是实验测量结果, 蓝色虚线是理论计算结果, 红色虚线左边代表的是部分PT对称区域, 右边是部分PT对称破缺区域, 误差棒是5次测量的标准偏差
Fig. 5. Experimental measurements (magenta circle) and calculations (blue line) of Dasym as a function of beam-waist ratio σ, where the EP locates at σ = σcr ≈ 3.8, the red dotted line represents the partial PT symmetry region on the left and the partial PT symmetry broken region on the right, error bars denote standard error of five measurements.
-
[1] Bender C M, Boettcher S 1998 Phys. Rev. Lett. 80 5243
Google Scholar
[2] Bender C M 2005 Contemp. Phys. 46 277
Google Scholar
[3] Klaiman S, Cederbaum L S 2008 Phys. Rev. A 78 062113
Google Scholar
[4] El-Ganainy R, Makris K G, Khajavikhan M, Musslimani Z H, Rotter S Christodoulides D N 2018 Nat. Phys. 14 11
Google Scholar
[5] Ashida Y, Gong Z, Ueda M 2020 Adv. Phys. 69 249
Google Scholar
[6] Konotop V V, Shchesnovich V S, Zezyulin D A 2012 Phys. Lett. A 376 2750
Google Scholar
[7] Szameit A, Rechtsman M C, Bahat-Treidel O, Segev M 2011 Phys. Rev. A 84 021806(R
Google Scholar
[8] Feng L, Ayache M, Huang J, Xu Y L, Lu M H, Chen Y F, Fainman Y, Scherer A 2011 Science 333 729
Google Scholar
[9] Regensburger A, Bersch C, Miri M, Onishchukov G, Christodoulides D N, Peschel U 2012 Nat. Phys. 488 167
Google Scholar
[10] Peng B, Özdemir S K, Lei F, Monifi F, Gianfreda M, Long G L, Fan S, Nori F, Bender C M, Yang L 2014 Nat. Phys. 10 394
Google Scholar
[11] Wen J M, Jiang X, Jiang L, Xiao M 2018 J. Phys. B: At. Mol. Opt. Phys. 51 222001
Google Scholar
[12] Hang C, Huang G X, Konotop V V 2013 Phys. Rev. Lett. 110 083604
Google Scholar
[13] Peng P, Cao W C, Shen C, Qu W Z, Wen J M, Jiang L, Xiao Y H 2016 Nat. Phys. 12 1139
Google Scholar
[14] Jiang Y, Mei Y F, Zuo Y, Zhai Y H, Li J S, Wen J M, Du S W 2019 Phys. Rev. Lett. 123 193604
Google Scholar
[15] Zhang Z Y, Zhang Y Q, Sheng J T, Yang L, Miri M A, Christodoulides D N, He B, Zhang Y P, Xiao M 2016 Phys. Rev. Lett. 117 123601
Google Scholar
[16] Zhang Z Y, Feng Y, Ning S H, Malpuech G, Solnyshkov D D, Xu Z F, Zhang Y P, Xiao M 2022 Photonics Res. 10 958
Google Scholar
[17] Feng Y, Liu Z Z, Liu F, Yu J W, Liang S, Li F, Zhang Y P, Xiao M, Zhang Z Y 2023 Phys. Rev. Lett. 131 013802
Google Scholar
[18] Zhang Z Y, Liang S, Septembre I, Yu J W, Huang Y P, Liu M C, Zhang Y P, Xiao M, Malpuech G, Solnyshkov D 2024 Phys. Rev. Lett. 132 263801
Google Scholar
[19] Miri M A, Alù A 2019 Science 363 7709
Google Scholar
[20] Chong Y D, Ge L, Stone A D 2011 Phys. Rev. Lett. 106 093902
Google Scholar
[21] Xiao L, Zhan X, Bian Z H, Wang K K, Zhang X, Wang X P, Li J, Mochizuki K, Kim D, Kawakami N, Yi W, Obuse H, Sanders B C, Xue P 2017 Nat. Phys. 13 1117
Google Scholar
[22] Zhang J, Peng B, Özdemir S K, Pichler K, Krimer D O, Zhao G M, Nori F, Liu Y X, Rotter S, Yang L 2018 Nat. Photonics 12 479
Google Scholar
[23] Shui T, Yang W X, Liu S P, Li L, Zhu Z H 2018 Phys. Rev. A 97 033819
Google Scholar
[24] Li J M, Harter A K, Liu J, de Melo L, Joglekar Y N, Luo L 2019 Nat. Commun. 10 855
Google Scholar
[25] Xiao L, Deng T S, Wang K K, Zhu G Y, Wang Z, Yi W, Xue P 2020 Nat. Phys. 16 761
Google Scholar
[26] Xiao L, Deng T S, Wang K K, Wang Z, Yi W, Xue P 2021 Phys. Rev. Lett. 126 230402
Google Scholar
[27] 唐原江, 梁超, 刘永椿 2022 物理学报 71 171101
Google Scholar
Tang Y J, Liang C, Liu Y C 2022 Acta Phys. Sin. 71 171101
Google Scholar
[28] Yang J 2014 Opt. Lett. 39 1133
Google Scholar
[29] Kartashov Y V, Konotop V V, Torner L 2015 Phys. Rev. Lett. 115 193902
Google Scholar
[30] Wang H, Huang J, Ren X, Weng Y, Mihalache D, He Y 2018 Rom. J. Phys. 63 205
[31] Ge L, Stone A D 2014 Phys. Rev. X 4 031011
Google Scholar
[32] Xue Y M, Hang C, He Y H, Bai Z Y, Jiao Y C, Huang G X, Zhao J M, Jia S T 2022 Phys. Rev. A 105 053516
Google Scholar
-
[1] 邵凯花, 席忠红, 席保龙, 涂朴, 王青青, 马金萍, 赵茜, 石玉仁. 双组分玻色-爱因斯坦凝聚体中PT对称势下的异步量子Kármán涡街. 物理学报, 2024, 73(11): 110501. doi: 10.7498/aps.73.20232003 [2] 曾超, 毛一屹, 吴骥宙, 苑涛, 戴汉宁, 陈宇翱. 一维超冷原子动量光晶格中的手征对称性破缺拓扑相. 物理学报, 2024, 73(4): 040301. doi: 10.7498/aps.73.20231566 [3] 杨硕颖, 殷嘉鑫. 时间反演对称性破缺的笼目超导输运现象. 物理学报, 2024, 73(15): 150301. doi: 10.7498/aps.73.20240917 [4] 陈礼元, 高超, 林机, 李慧军. $ {\cal{PT}}$ 对称极化子凝聚体系统中的稳定孤子及其调控. 物理学报, 2022, 71(18): 181101. doi: 10.7498/aps.71.20220475[5] 王恩权, 陈浩, 杨毅, 隆正文, HassanabadiHassan. 洛伦兹对称破缺框架下的广义克莱因-戈尔登谐振子. 物理学报, 2022, 71(6): 060301. doi: 10.7498/aps.71.20211733 [6] 杨树政, 林恺. 洛仑兹破缺标量场的霍金隧穿辐射. 物理学报, 2019, 68(6): 060401. doi: 10.7498/aps.68.20182050 [7] 蒲瑾, 杨树政, 林恺. 洛伦兹破缺理论与Vaidya黑洞弯曲时空中的Dirac粒子隧穿辐射特征. 物理学报, 2019, 68(19): 190401. doi: 10.7498/aps.68.20190437 [8] 张卫锋, 李春艳, 陈险峰, 黄长明, 叶芳伟. 时间反演对称性破缺系统中的拓扑零能模. 物理学报, 2017, 66(22): 220201. doi: 10.7498/aps.66.220201 [9] 耿虎, 计青山, 张存喜, 王瑞. 缀饰格子中时间反演对称破缺的量子自旋霍尔效应. 物理学报, 2017, 66(12): 127303. doi: 10.7498/aps.66.127303 [10] 张莹, 雷佑铭, 方同. 混沌吸引子的对称破缺激变. 物理学报, 2009, 58(6): 3799-3805. doi: 10.7498/aps.58.3799 [11] 鲁公儒, 李 祥, 李培英. R-宇称破缺的相互作用研究. 物理学报, 2008, 57(2): 778-783. doi: 10.7498/aps.57.778 [12] 张 艳, 文 侨, 张 彬. 部分相干平顶光束在线性增益(损耗)介质中的光谱特性. 物理学报, 2006, 55(9): 4962-4967. doi: 10.7498/aps.55.4962 [13] 张超, 吕海峰, 张庆瑜. 低能Pt原子与Pt(111)表面相互作用的分子动力学模拟. 物理学报, 2002, 51(10): 2329-2334. doi: 10.7498/aps.51.2329 [14] 董正超. d波超导体NIS结中的时间反演对称态的破缺与准粒子寿命效应. 物理学报, 2000, 49(2): 339-343. doi: 10.7498/aps.49.339 [15] 王 海, 周云松, 王艾玲, 郑 鹉, 陈金昌. Pt/Co/Pt/Ni多层膜的磁光特性. 物理学报, 1999, 48(13): 151-158. doi: 10.7498/aps.48.151 [16] 易林, 姚凯伦. 三维量子自旋玻璃理论(Ⅲ)──replica对称破缺解. 物理学报, 1996, 45(1): 133-139. doi: 10.7498/aps.45.133 [17] 余扬政, 陈熊熊. 二维超对称模型的超对称破缺和Witten指数. 物理学报, 1993, 42(2): 214-222. doi: 10.7498/aps.42.214 [18] 孙宗琦. 振动弯结与点缺陷交互作用时间平均场的对称破缺及自组织现象. 物理学报, 1992, 41(12): 1987-1992. doi: 10.7498/aps.41.1987 [19] 周洁, 李树英, 谭飞. Si中Pt的复合行为. 物理学报, 1983, 32(4): 497-506. doi: 10.7498/aps.32.497 [20] 赵保恒. 自发破缺规范理论中的光子-光子散射. 物理学报, 1976, 25(1): 53-57. doi: 10.7498/aps.25.53
下载:
计量
- 文章访问数: 760
- PDF下载量: 44
- 被引次数: 0
