利用超高斯光模拟方势垒

doi:10.3969/j.issn.1000-5641.202022008

摘要/Abstract

摘要：

方势垒是一个研究量子力学中隧穿问题的理想模型. 提出了利用具有大蓝失谐的超高斯光和原子相互作用的偶极势能和超高斯光和电子的有质动力势能模拟方势垒. 通过比较超高斯势垒对入射平面波散射的数值解和方势垒对物质波散射的解析解, 发现当超高斯光场阶数大于20时能够有效地模拟方势垒对物质波的散射问题. 进一步研究了物质波入射到双超高斯势垒的共振隧穿现象. 研究结果为在实验上使用超高斯光束模拟方势垒量子隧穿现象提供了理论基础.

关键词: 超高斯光束, 方势垒, 散射, 透射系数

Abstract:

The square potential barrier is an ideal model for investigation of quantum tunneling. We simulate the square potential barrier by using the dipole potential for the interaction between an atom and a blue-detuned far-off-resonant super-Gaussian beam, as well as the ponderomotive potential for the interaction between an electron and a super-Gaussian beam. A comparison between the numerical results for scattering by the super-Gaussian potential barrier and the analytical results for scattering by a square potential barrier shows that a super-Gaussian beam with an order exceeding 20 could simulate a square potential barrier accurately. We also show that two super-Gaussian beams could be used to study the resonant quantum tunneling effect. In summary, our results could be applied to an experimental investigation of quantum tunneling through a square potential barrier.

Key words: super-Gaussian beam, square potential barrier, scattering, transmission coefficient

中图分类号:

O436.2

李佳欣, 董光炯. 利用超高斯光模拟方势垒[J]. 华东师范大学学报（自然科学版）, 2021, 2021(1): 129-136.

Jiaxin LI, Guangjiong DONG. Theoretical simulations of the square potential barrier with a super-Gaussian beam[J]. Journal of East China Normal University(Natural Science), 2021, 2021(1): 129-136.

图/表 6

图1

图2

图3

图4

图5

图6

参考文献 47

1	HUND F. Zeitschrift für Physik, On the interpretation of molecular spectra. 1927, 43, 805- 811.
2	NORDHEIM L. Zeitschrift für Physik, Zur theorie der thermischen emission und der reflexion von elektronen an metallen. 1928, 46, 833- 855.
3	OPPENHEIMER J R. Physical Review, Three notes on the quantum theory of aperiodic effects. 1928, 31, 66- 81.
4	GAMOW G. Zeitschrift für Physik, Zur quantentheorie des atomkernes. 1928, 51 (3/4): 204- 212.
5	GURNEY R W, CONDON E U. Nature, Wave mechanics and radioactive disintegration. 1928, 122 (3073): 439- 439.
6	GURNEY R W, CONDON E U. Physical Review, Quantum mechanics and radioactive disintegration. 1929, 33 (2): 127- 140.
7	MILLIKAN R A, EYRING C F. Physical Review, Laws governing the pulling of electrons out of metals by intense electrical fields. 1926, 27 (1): 51- 67.
8	BÜTTIKER M, IMRY Y, LANDAUER R, et al. Physical Review B, Generalized many-channel conductance formula with application to small rings. 1985, 31 (10): 6207- 6215.
9	BARDEEN J. Physical Review Letters, Tunnelling from a many-particle point of view. 1961, 6 (2): 57- 59.
10	ESAKI L. Physical Review, New phenomenon in narrow germanium P-N junctions. 1958, 109 (2): 603- 604.
11	BINNIG G, ROHRER H, GERBER C, et al. Physical Review Letters, Surface studies by scanning tunneling microscopy. 1982, 49 (1): 57- 61.
12	TERSOFF J, HAMANN D R. Physical Review Letters, Theory and application for the scanning tunneling microscope. 1983, 50 (25): 1998- 2001.
13	曾谨言. 量子力学(卷1) [M]. 2版. 北京: 北京大学出版社, 1998: 63-68.
14	OLKHOVSKY V S, RECAMI E. Physics Reports, Developments in the time analysis of tunneling processes. 1992, 214 (6): 339- 357.
15	OLKHOVSKY V S, RECAMI E, JAKIEL J. Physics Reports, Unified time analysis of photon and particle tunnelling. 2004, 398 (3): 133- 178.
16	SHAFIR D, SOIFER H, BRUNER B D, et al. Nature, Resolving the time when an electron exits a tunnelling barrier. 2012, 485 (7398): 343- 346.
17	LANDSMAN A S, KELLER U. Physics Reports, Attosecond science and the tunnelling time problem. 2015, 547 (5): 1- 24.
18	KWIAT P, STEINBERG A, CHIAO R. Physical Review Letters, Measurement of the single-photon tunneling time. 1993, 71 (5): 708- 711.
19	LANDAUER R, MARTIN T. Reviews of Modern Physics, Barrier interaction time in tunneling. 1994, 66 (1): 217- 228.
20	SPIELMANN C, SZIPÖCS R, STINGL A, et al. Physical Review Letters, Tunneling of optical pulses through photonic band gaps. 1994, 73 (17): 2309- 2311.
21	TSU R, ESAKI L. Applied Physics Letters, Tunneling in a finite superlattice. 1973, 22 (11): 562- 565.
22	CHANG L L, ESAKI L, TSU R. Applied Physics Letters, Resonant tunneling in semiconductor double barriers. 1974, 24 (12): 593- 595.
23	SHEALY D L, HOFFNAGLE J A. Beam shaping profiles and propagation [C]// Proceedings SPIE 5876, Laser Beam Shaping VI. 2005: 58760D. DOI: 10.1117/12.619305.
24	DICKEY F M, WEICHMAN L S, SHAGAM R N. Laser beam shaping techniques [C]// Proceedings of the SPIE, Volume 4065 : High-Power Laser Ablation III. SPIE, 2000: 338-348.
25	CHEN H X, SUI Z, CHEN Z P, et al. Acta Optica Sinica, Laser beam shaping using liquid crystal spatial light modulator. 2001, 21 (9): 1107- 1111.
26	LIU J S, CHENG Q Y, YUE D G, et al. Laser Physics, Dynamical analysis of the effect of super-Gaussian laser pulses on molecular orientation. 2018, 28 (12): 1- 7.
27	SCHIFFER M, RAUNER M, KUPPENS S, et al. Applied Physics B, Guiding, focusing and cooling of atoms in a strong dipole potential. 1998, 67 (6): 705- 708.
28	KUPPENS S, RAUNER M, SCHIFFER M, et al. Physical Review A, Polarization-gradient cooling in a strong doughnut-mode dipole potential. 1998, 58 (4): 3068- 3079.
29	SILVESTRI S D, LAPORTA P, MAGNI V, et al. Optics Letters, Unstable laser resonators with super-Gaussian mirrors. 1988, 13 (3): 201- 203.
30	LIU J S, TAGHIZADEH M R. Optics Letters, Iterative algorithm for the design of diffractive phase elements for laser beam shaping. 2002, 27 (16): 1463- 1465.
31	LIU J S, CALEY A J, TAGHIZADEH M R. Optics Communications, Symmetrical iterative Fourier-transform algorithm using both phase and amplitude freedoms. 2006, 267 (2): 347- 355.
32	LIU J S, THOMSON M J, TAGHIZADEH M R. Journal of Modern Optics, Automatic symmetrical iterative Fourier-transform algorithm for the design of diffractive optical elements for highly precise laser beam shaping. 2006, 53 (4): 461- 471.
33	ZHAO Y, LI Y P, ZHOU Q G. Optics Letters, Vector iterative algorithm for the design of diffractive optical elements applied to uniform illumination. 2004, 29 (7): 664- 666.
34	林勇, 胡家升, 吴克难. 光学学报, 一种用于光束整形的衍射光学元件设计算法. 2007, 27 (9): 1682- 1686.
35	BÉLANGER P A, LACHANCE R L, PARÉ C. Optics Letters, Super-Gaussian output from a CO₂ laser by using a graded-phase mirror resonator . 1992, 17 (10): 739- 741.
36	DONG G J, EDVADSSON S, LU W, et al. Physical Review A, Super-Gaussian mirror for high-field-seeking molecules. 2005, 72 (3): 031605.
37	DUAN Z, FAN B, YUAN C H, et al. Physical Review A, Quantum tunneling time of a Bose-Einstein condensate traversing through a laser-induced potential barrier. 2010, 81 (5): 055602.
38	ZHOU L, ZHENG R F, ZHANG W. Physical Review A, Spin-sensitive atom mirror via spin-orbit interaction. 2016, 94 (5): 053630.
39	HARTEMANN F V, VAN METER J R, TROHA A L, et al. Physical Review E, Three-dimensional relativistic electron scattering in an ultrahigh-intensity laser focus. 1998, 58 (4): 5001- 5012.
40	STUPAKOV G V, ZOLOTOREV M S. Physical Review Letters, Ponderomotive laser acceleration and focusing in vacuum for generation of attosecond electron bunches. 2001, 86 (23): 5274- 5277.
41	FRIEDRICH B, HERSCHBACH D. Physical Review Letters, Alignment and trapping of molecules in intense laser fields. 1995, 74 (23): 4623- 4626.
42	刘盛纲. 强激光与粒子束, 自由电子激光的空间电荷波理论. 1990, (2): 131- 147.
43	张永德. 量子力学 [M]. 2版. 北京: 科学出版社, 2008: 55-59.
44	MATHEWS J H, FINK K K. Numerical methods using matlab: International edition [M]. [S.l]: Prentice-Hall Inc, 2004: 339.
45	LAI H M, CHAN S W. Optics Letters, Large and negative Goos–Hänchen shift near the Brewster dip on reflection from weakly absorbing media. 2002, 27 (9): 680- 682.
46	SHEN N H, CHEN J, WU Q Y, et al. Optics Express, Large lateral shift near pseudo-Brewster angle on reflection from a weakly absorbing double negative medium. 2006, 14 (22): 10574- 10579.
47	KAMIŃSKI P, DROŻDŻ S, PLOSZAJCZAK M, et al. Physical Review C, Even-odd anomalous tunneling effect. 1993, 47 (4): 1548- 1552.

[1]	徐颖, 范红豪, 沙依甫加马力·达吾来提. ATLAS 2.76 TeV单喷注实验数据对CT18NNLO部分子分布函数的影响[J]. 华东师范大学学报（自然科学版）, 2024, 2024(4): 30-39.
[2]	卢晨, 于志飞, 焦高锋, 陈丽清, 袁春华. 受激拉曼散射系统的时间模式特性研究[J]. 华东师范大学学报（自然科学版）, 2023, 2023(4): 109-118.
[3]	方波, 于志飞, 陈丽清. 光-原子混合干涉实现加速度测量[J]. 华东师范大学学报（自然科学版）, 2022, 2022(4): 139-146.
[4]	王倩婧, 杜骏杰. 二维电磁亥姆霍兹腔中回音壁模式研究[J]. 华东师范大学学报（自然科学版）, 2021, 2021(1): 119-128.
[5]	李帆, 杨继锋. 核子核子散射一圈图的手征有效场论分析[J]. 华东师范大学学报(自然科学版), 2016, 2016(3): 67-75.
[6]	田英，全军. 含单势垒量子隧穿结构电子稳恒输运中的接点效应[J]. 华东师范大学学报(自然科学版), 2013, 2013(3): 186-193.
[7]	洪官林，沈芳，沈宏. 长江口及邻近海域水体反射率的模拟[J]. 华东师范大学学报(自然科学版), 2012, 2012(1): 37-46.
[8]	李可舟;秦怡;江红;朱守正. 适用于特定介质电磁散射的单等效流积分方程[J]. 华东师范大学学报(自然科学版), 2010, 2010(1): 135-141.
[9]	石岩, 李相美, 何为凡, 徐学诚. PS/CNTs复合材料中CNTs作用的研究[J]. 华东师范大学学报(自然科学版), 2006, 2006(5): 116-120.
[10]	石岩;李相美;何为凡;徐学诚. PS/CNTs复合材料中CNTs作用的研究[J]. 华东师范大学学报(自然科学版), 2006, 2006(5): 116-120.
[11]	黄勇;安同一;钱鉴;樊明捷. 微波心动图仪的设计和研制[J]. 华东师范大学学报(自然科学版), 2004, 2004(4): 40-47.