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The rescattering scenario that the ionized photoelectron is guided back to the vicinity of the atomic core under an oscillating laser field is the key to understanding strong field processes. Strong field photoelectron holography, which stems from the interference of direct and rescattering waves, has great potential applications in studying strong field physics and detecting ultrafast electron dynamics. The article develops the underlying quantum orbits interference picture. By including Coulomb potential, the uniform glory rescattering theory is introduced, which gives reasonably quantitative results in accord with time-dependent Schrödinger equation and experimental results. And reconstructing the ultrashort light pulses in the time domain with the Coulomb glory temporal gate is also studied. Deepening the understanding of strong field photoelectron holography will lead to further enlightening in ultrafast physics and contribute to future applications.
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Keywords:
- tunneling ionization /
- strong field holography /
- Coulomb glory effect /
- two-color laser field
[1] Agostini P, Fabre F, Mainfray G, Petite G, Rahman N K 1979 Phys. Rev. Lett. 42 1127
Google Scholar
[2] Paulus G G, Nicklich W, Xu H, Lambropoulos P, Walther H 1994 Phys. Rev. Lett. 72 2851
Google Scholar
[3] Krause J L, Schafer K J, Kulander K C 1992 Phys. Rev. Lett. 68 3535
Google Scholar
[4] Walker B, Sheehy B, DiMauro L F, Agostini P, Schafer K J, Kulander K C 1994 Phys. Rev. Lett. 73 1227
Google Scholar
[5] Krausz F 2009 Rev. Mod. Phys. 81 163
Google Scholar
[6] Paul P M, Toma E S, Breger P, Mullot G, Auge F, Balcou Ph, Muller H G, Agostini P 2001 Science 292 1689
Google Scholar
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Google Scholar
[11] Krausz F, Stockman M I 2014 Nature Photonics 8 205
Google Scholar
[12] Corkum P B 1993 Phys. Rev. Lett. 71 1994
Google Scholar
[13] Huismans Y, Rouzee A, Gijsbertsen A, Jungmann J H, Smolkowska A S, Logman P S W M, Lepine F, Cauchy C, Zamith S, Marchenko T, Bakker J M, Berden G, Redlich B, van der Meer A F G, Muller H G, Vermin W, Schafer K J, Spanner M, Ivanov M Yu, Smirnova O, Bauer D, Popruzhenko S V, Vrakking M J J 2011 Science 331 61
Google Scholar
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Google Scholar
[15] Bian X B, Huismans Y, Smirnova O, Yuan K J, Vrakking M J J, Bandrauk A D 2011 Phys. Rev. A 84 043420
Google Scholar
[16] Du H C, Wu H M, Wang H Q, Yue S J, Hu B T 2016 Opt. Lett. 41 697
Google Scholar
[17] Meckel M, Staudte A, Patchkovskii S, Villeneuve D M, Corkum P B, Dorner R, Spanner M 2014 Nat. Phys. 10 594
Google Scholar
[18] Wiese J, Onvlee J, Trippel S, Küpper J 2021 Phys. Rev. Res. 3 013089
Google Scholar
[19] He M, Li Y, Zhou Y M, Li M, Cao W, Lu P X 2018 Phys. Rev. Lett. 120 133204
Google Scholar
[20] Kang H P, Maxwell A S, Trabert D, Lai X Y, Eckart S, Kunitski M, Schoffler M, Jahnke T, Bian X B, Dorner R, de Morisson Faria C F 2020 Phys. Rev. A 102 013109
Google Scholar
[21] Tan J, Zhou Y M, He M R, Chen Y B, Ke Q H, Liang J T, Zhu X S, Li M, Lu P X 2018 Phys. Rev. Lett. 121 253203
Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
[26] Ford K W, Wheeler J A 1959 Ann. Phys. 7 259
Google Scholar
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Google Scholar
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Google Scholar
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图 1 正交双色场中极化平面内强场光电子全息动量谱(
$p_z = 0$ ) (a)含时薛定谔方程计算结果; (b)强场近似计算结果, 黑线表示强场近似计算的干涉极大位置[23]Figure 1. Strong field photoelectron holography in laser polarization plane (
$p_z = 0$ ) with an OTC field calculated by TDSE (a) and SFA (b). Black solid line in panel (b) is the interference maxima estimated by SFA[23]
图 2 (a) glory轨迹示意图; (b)对应同一个末态动量的初始轨迹横向动量分布; (c)离核距离
$z_0$ 的高斯波包散射, glory轨迹最终与z轴距离为$b_{\rm{g}}$ [32]Figure 2. (a) Glory trajectories; (b) initial transverse momentum distribution corresponding to the same final photoelectron momentum; (c) scattering of a Gaussian wavepacket with a
$z_0$ distance from the center, the distance of the glory orbit to the z axis is$b_{\rm{g}}$ [32]
图 4 (a)坐标空间以及(b)动量空间中对应同一个动量末态
$\boldsymbol{p}_{\rm{f}} = (0.12, 0, 0.66)$ 的8条光电子轨迹. 对应同一个动量末态$\boldsymbol{p}_{\rm{f}}$ 的初始(c)横向坐标以及(b)动量分布[27]Figure 4. The photoelectron trajectories in (a) coordinate and (b) momentum spaces corresponding to the same final momentum
$\boldsymbol{p}_{\rm{f}} = (0.12, 0, 0.66)$ . The initial (c) transverse coordinates and (d) momenta distribution corresponding to the same final momentum$\boldsymbol{p}_{\rm{f}}$ [27]
图 5 中红外激光电离氙原子亚稳态光电子动量分布[13](a)红色实线为UGRT给出的干涉极小, 黑色虚线为GRT给出的干涉极小; (b)黑色方块为UGRT给出的干涉极大[27]
Figure 5. The momentum distribution of metastable Xe ionized by mid-IR laser field[13]: (a) Red solid line is the interference minima given by UGRT. black dashed line the minima given by GRT; (b) black squares are the interference maxima given by UGRT[27]
图 6 对应不同的
$p_x$ 动量最终沿y方向的横向动量分布, 时间延迟为零.$p_z$ 方向的TDSE结果已经积分掉了. 蓝色点线表示TDSE计算结果, 红色实线是零阶贝塞尔函数结果Figure 6. Transversal momentum distribution for different
$p_x$ with time delay$\Delta \tau = 0$ . Momentum$p_z$ direction for the TDSE results has been integrated. Blue dotted lines represent the TDSE results, red lines are fitted squared zero Bessel function
图 7 (a)通过glory再散射时间快门对待测场进行时间采样示意图, 蓝色虚线表示隧穿电子的亚周期运动; (b)不同时间延迟下TDSE理论模拟的光电子动量谱[23].
Figure 7. (a) Illustration of the sampling of a test laser field with the Coulomb glory rescattering process. Blue dashed arrows indicate the subcycle excursion of the tunneled electrons. (b) Integrated photoelectron momentum distribution simulated using the TDSE with different time delays[23]
图 8 (a), (b)待测光为椭偏率随时间变化的复杂光脉冲下的y与z方向动量分布与时间延迟的关系图; (c)提取出的电场形状的三维展示(蓝色球体), 结果与精确的合成波形进行了对比(黑色球体)[23]
Figure 8. (a), (b) Streaking photoelectron momentum spectra for two independent polarization directions of the synthesized test laser light with time-varying ellipticity (
$p_x = 0.8$ ); (c) three dimensional representation of the extracted electric field (blue spheres). The result is compared to the synthesized waveform(black spheres)[23] -
[1] Agostini P, Fabre F, Mainfray G, Petite G, Rahman N K 1979 Phys. Rev. Lett. 42 1127
Google Scholar
[2] Paulus G G, Nicklich W, Xu H, Lambropoulos P, Walther H 1994 Phys. Rev. Lett. 72 2851
Google Scholar
[3] Krause J L, Schafer K J, Kulander K C 1992 Phys. Rev. Lett. 68 3535
Google Scholar
[4] Walker B, Sheehy B, DiMauro L F, Agostini P, Schafer K J, Kulander K C 1994 Phys. Rev. Lett. 73 1227
Google Scholar
[5] Krausz F 2009 Rev. Mod. Phys. 81 163
Google Scholar
[6] Paul P M, Toma E S, Breger P, Mullot G, Auge F, Balcou Ph, Muller H G, Agostini P 2001 Science 292 1689
Google Scholar
[7] Hentschel M, Kienberger R, Spielmann Ch, Reider G. A, Milosevic N, Brabec T, Corkum P, Heinzmann U, Drescher M, Krausz F 2001 Nature 414 509
Google Scholar
[8] Gaumnitz T, Jain A, Pertot Y, Huppert M, Jordan I, Ardana-Lamas F, Worner H J 2017 Opt. Express 25 27506
Google Scholar
[9] Kruer W 2019 The Physics Of Laser Plasma Interactions (Boca Raton: CRC Press) pp11,12
[10] Goulielmakis E, Yakovlev V. S, Cavalieri A. L, Uiberacker M, Pervak V, Apolonski A, Kienberger R, Kleineberg U, Krausz F 2007 Science 317 769
Google Scholar
[11] Krausz F, Stockman M I 2014 Nature Photonics 8 205
Google Scholar
[12] Corkum P B 1993 Phys. Rev. Lett. 71 1994
Google Scholar
[13] Huismans Y, Rouzee A, Gijsbertsen A, Jungmann J H, Smolkowska A S, Logman P S W M, Lepine F, Cauchy C, Zamith S, Marchenko T, Bakker J M, Berden G, Redlich B, van der Meer A F G, Muller H G, Vermin W, Schafer K J, Spanner M, Ivanov M Yu, Smirnova O, Bauer D, Popruzhenko S V, Vrakking M J J 2011 Science 331 61
Google Scholar
[14] Haertelt M, Bian X B, Spanner M, Staudte A, Corkum P B 2016 Phys. Rev. Lett. 116 133001
Google Scholar
[15] Bian X B, Huismans Y, Smirnova O, Yuan K J, Vrakking M J J, Bandrauk A D 2011 Phys. Rev. A 84 043420
Google Scholar
[16] Du H C, Wu H M, Wang H Q, Yue S J, Hu B T 2016 Opt. Lett. 41 697
Google Scholar
[17] Meckel M, Staudte A, Patchkovskii S, Villeneuve D M, Corkum P B, Dorner R, Spanner M 2014 Nat. Phys. 10 594
Google Scholar
[18] Wiese J, Onvlee J, Trippel S, Küpper J 2021 Phys. Rev. Res. 3 013089
Google Scholar
[19] He M, Li Y, Zhou Y M, Li M, Cao W, Lu P X 2018 Phys. Rev. Lett. 120 133204
Google Scholar
[20] Kang H P, Maxwell A S, Trabert D, Lai X Y, Eckart S, Kunitski M, Schoffler M, Jahnke T, Bian X B, Dorner R, de Morisson Faria C F 2020 Phys. Rev. A 102 013109
Google Scholar
[21] Tan J, Zhou Y M, He M R, Chen Y B, Ke Q H, Liang J T, Zhu X S, Li M, Lu P X 2018 Phys. Rev. Lett. 121 253203
Google Scholar
[22] Li M, Xie H, Cao W, Luo S Q, Tan J, Feng Y D, Du B J, Zhang W Y, Li Y, Zhang Q B, Lan P F, Zhou Y M, Lu P X 2019 Phys. Rev. Lett. 122 183202
Google Scholar
[23] Tao J F, Cai J, Xia Q Z, Liu J 2020 Phys. Rev. A 101 043416
Google Scholar
[24] Willenberg B, Maurer J, Mayer B W, Keller U 2019 Nat. Commun. 10 5548
Google Scholar
[25] Tao J F, Xia Q Z, Cai J, Fu L B, Liu J 2017 Phys. Rev. A 95 011402
Google Scholar
[26] Ford K W, Wheeler J A 1959 Ann. Phys. 7 259
Google Scholar
[27] Liao L G, Xia Q Z, Cai J, Liu J 2022 Phys. Rev. A 105 053115
Google Scholar
[28] Milosevic D B 2017 Phys. Rev. A 96 023413
Google Scholar
[29] Gutzwiller M C 1967 J. Math. Phys. 8 1979
Google Scholar
[30] Berry M V 1969 Sci. Prog. 57 43
[31] Berry M V 1969 J. Phys. B: At. Mol. Phys. 2 381
Google Scholar
[32] Xia Q Z, Tao J F, Cai J, Fu L B, Liu J 2018 Phys. Rev. Lett. 121 143201
Google Scholar
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