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In the mid-1980s, chirped pulse amplification (Nobel Prize in Physics 2018) broke through previous limits to laser intensity, allowing intensities to exceed the atomic unit threshold (1 atomic unit of laser intensity corresponds to a power density of 3.5×1016 W/cm2). These strong laser fields can cause high-order nonlinear responses in atoms and molecules, resulting in a series of novel phenomena, among which high-order harmonic generation and attosecond pulse generation (Nobel Prize in Physics 2023) are particularly important. With the development of high-power laser technology, laser intensity has now reached the order of 1023 W/cm2 and is constantly increasing. Now, a fundamental question has been raised: can such a powerful laser field induce similar high-order nonlinear responses in atomic nuclei, potentially transitioning “strong-field atomic physics” into “strong-field nuclear physics”? To explore this, we investigate a dimensionless parameter that estimates the strength of light-matter interaction: $ \eta = D{E_0}/{{\Delta }}E $, where D is the transition moment (between two representative levels of the system), E0 is the laser field amplitude, DE0 quantifies the laser-matter interaction energy, and ΔE is the transition energy. If $ \eta \ll 1 $, the interaction is within the linear, perturbative regime. However, when $ \eta \sim 1 $, highly nonlinear responses are anticipated. For laser-atom interactions, D ~ 1 a.u. and ΔE = 1 a.u., so if E0 ~ 1 a.u., then $ \eta \sim 1 $ and highly nonlinear responses are initiated, leading to the above-mentioned strong-field phenomena. In the case of light-nucleus interaction, it is typical that $ \eta \ll 1 $. When considering nuclei instead of atoms, D becomes several (~5 to 7) orders of magnitude smaller, while ΔE becomes several (~5) orders of magnitude larger. Consequently, the laser field amplitude E0 will need to be 10 orders of magnitude higher, or the laser intensity needs to be 20 orders of magnitude higher (~ 1036 W/cm2), which is beyond existing technological limit and even exceeds the Schwinger limit, where vacuum breakdown occurs. However, there exist special nuclei with exceptional properties. For instance, the 229Th nucleus has a uniquely low-lying excited state with an energy value of only 8.4 eV, or 0.3 a.u. This unusually low transition energy significantly increases η. This transition has also been proposed for building nuclear clocks, which have potential advantages over existing atomic clocks. Another key factor is nuclear hyperfine mixing (NHM). An electron, particularly the one in an inner orbital, can generate a strong electromagnetic field at the position of the nucleus, leading to the mixing of nuclear eigenstates. For 229Th, this NHM effect is especially pronounced: the lifetime of the 8.4-eV nuclear isomeric state in a bare 229Th nucleus (229Th90+) is on the order of 103 s, while in the hydrogenlike ionic state (229Th89+) it decreases by five orders of magnitude to 10–2 s. This 1s electron greatly affects the properties of the 229Th nucleus, effectively changing the nuclear transition moment from D for the bare nucleus to $ D' = D + b{\mu _{\text{e}}} $ for the hydrogenlike ion, where D ~ 10–7 a.u., $ b \approx 0.03 $ is the mixing coefficient, $ {\mu _{\text{e}}} $ is the magnetic moment of the electron, and $ D'\approx b\mu_{\text{e}}\sim10^{-4}\ \text{a}\text{.u}. $ That is to say, the existence of the 1s electron increases the light-nucleus coupling matrix element by approximately three orders of magnitude, leading to the five-orders-of-magnitude reduction in the isomeric lifetime. With the minimized transition energy ΔE and the NHM-enhanced transition moment D', it is found that $ \eta \sim 1 $ for currently achievable laser intensities. Highly nonlinear responses are expected in the 229Th nucleus. This is confirmed by our numerical results. Highly efficient nuclear isomeric excitation can be achieved: an excitation probability of over 10% is achieved per nucleus per femtosecond laser pulse at a laser intensity of 1021 W/cm2. Correspondingly, the intense laser-driven 229Th89+ system emits secondary light in the form of high harmonics, which share similarities with those from laser-driven atoms but also have different features. In conclusion, it appears feasible to extend “strong-field atomic physics” to “strong-field nuclear physics”, at least in the case of 229Th. “Strong-field nuclear physics” is emerging as a new frontier in light-matter interaction and nuclear physics, providing opportunities for precisely exciting and controlling atomic nuclei with intense lasers and new avenues for coherent light emission based on nuclear transitions. -
Keywords:
- strong-field atomic physics /
- laser-nuclear physics /
- highly nonlinear responses /
- high harmonic generation
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图 1 (a)两能级原子示意图. $ {{\Delta }}E $是两能级之间能量差, $ \hbar \omega $是激光光子能量; (b)计算中所用激光脉冲示意图; (c)脉冲结束时刻原子激发概率随着激光场强的依赖关系, 黑色圆点是TDSE数值结果, 红色虚线是一阶含时微扰理论计算结果, $ \eta = D{E_0}/{{\Delta }}E $是相互作用能量与跃迁能量的比值
Figure 1. (a) Illustration of a two-level atom. $ {{\Delta }}E $ is the energy difference between the two levels and $ \hbar \omega $ is the energy of the laser photon; (b) illustration of the laser pulse used in the calculation; (c) end-of-pulse excitation probability versus laser intensity. Black dots are numerical results from TDSE, and the red dashed line is the result from first-order time-dependent perturbation theory, $ \eta = D{E_0}/{{\Delta }}E $ is the ratio between the interaction energy and the transition energy.
图 2 (a)—(c)诱导电偶极矩Dind(t)及其(d)—(f)傅里叶变换得到的频谱; 激光强度分别为1011 W/cm2 (a), (d); 1014 W/cm2 (b), (e); 1016 W/cm2 (c), (f)
Figure 2. (a)–(c) Induced dipole moment Dind(t) and (d)–(f) the harmonic spectra from Fourier transform; the laser intensity is 1011 W/cm2 (a), (d); 1014 W/cm2 (b), (e); 1016 W/cm2 (c), (f).
图 3 (a)钍-229裸核(229Th90+)最低两个核能级相关参数; (b)类氢离子(229Th89+)的超精细劈裂与混合效应. 裸核的激发态寿命在103 s量级, 而类氢离子由于超精细混合效应, 激发态寿命大幅缩短为10–2 s量级
Figure 3. (a) The lowest two energy levels of the bare thorium-229 nucleus (229Th90+); (b) hyperfine splitting and state mixing in the hydrogen-like ionic state (229Th89+). Note that the lifetime of the nuclear excited state in the bare nucleus is on the order of 103 s, while the lifetime reduces dramatically to the order of 10–2 s due to hyperfine mixing effect.
图 4 (a) 光学谐振腔中的原子, 其中原子态可以与谐振腔中的光场态之间耦合形成缀饰态; (b)离子中的原子核, 其中原子核态可以与电子态之间耦合形成类似的耦合态
Figure 4. (a) Atom in a light cavity, where atomic states can couple with the light states, forming dressed states; (b) nucleus in an ion, where nuclear states can couple with the electronic states, forming coupled states.
图 5 (a)脉冲结束时刻钍-229核激发概率(Th89+与Th90+两种情况)与激光场强的依赖关系, 该图源自文献[21](已授权); (b) 4个不同激光场强下的Th89+高次谐波频谱, 该图源自文献[21](已授权)
Figure 5. (a) Nuclear isomeric excitation probability at the end of the laser pulse (for both Th89+ and Th90+) as a function of laser intensity, from Ref. [21] with permission; (b) harmonic spectra of Th89+ under four different laser intensities, from Ref. [21] with permission.
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[1] Strickland D, Mourou G 1985 Opt. Commun. 56 219
Google Scholar
[2] Voronov G S, Delone N B 1965 JETP Lett. 1 66
[3] Agostini P, Fabre F, Mainfray G, Petite G, Rahman N K 1979 Phys. Rev. Lett. 42 1127
Google Scholar
[4] Fittinghoff D N, Bolton P R, Chang B, Kulander K C 1992 Phys. Rev. Lett. 69 2642
Google Scholar
[5] Walker B, Sheehy B, DiMauro L F, Agostini P, Schafer K J, Kulander K C 1994 Phys. Rev. Lett. 73 1227
Google Scholar
[6] Larochelle S, Talebpour A, Chin S L 1998 J. Phys. B 31 1201
Google Scholar
[7] Ferray M, L’Huillier A, Li X F, Lompre L A, Mainfray G, Manus C 1988 J. Phys. B 21 L31
Google Scholar
[8] 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
[9] 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
[10] Yoon J W, Kim Y G, Choi I W, Sung J H, Lee H W, Lee S K, Nam C H 2021 Optica 8 630
Google Scholar
[11] Wang X L, Liu X Y, Lu X M, Chen J C, Long Y B, Li W K, Chen H D, Chen X, Bai P L, Li Y Y, Peng Y J, Liu Y Q, Wu F X, Wang C, Li Z Y, Xu Y, Liang X Y, Leng Y X, Li R X 2022 Ultrafast Sci. 2022 9894358
Google Scholar
[12] Qi J T, Li T, Xu R H, Fu L B, Wang X 2019 Phys. Rev. C 99 044610
Google Scholar
[13] Pálffy A, Popruzhenko S V 2020 Phys. Rev. Lett. 124 212505
Google Scholar
[14] Qi J T, Fu L B, Wang X 2020 Phys. Rev. C 102 064629
Google Scholar
[15] Wang X 2020 Phys. Rev. C 102 011601(R
Google Scholar
[16] Liu S W, Duan H, Ye D F, Liu J 2021 Phys. Rev. C 104 044614
Google Scholar
[17] Lindsey M L, Bekx J J, Schlesinger K G, Glenzer S H 2024 Phys. Rev. C 109 044605
Google Scholar
[18] Lan H Y, Wu D, Liu J X, Zhang J Y, Lu H G, Lv J F, Wu X Z, Luo W, Yan X Q 2023 Nucl. Sci. Tech. 34 74
Google Scholar
[19] Feng J, Wang W Z, Fu C B, Chen L M, Tan J H, Li Y J, Wang J G, Li Y F, Zhang G Q, Ma Y G, Zhang J 2022 Phys. Rev. Lett. 128 052501
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[20] Qi J T, Zhang H X, Wang X 2023 Phys. Rev. Lett. 130 112501
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[21] Zhang H X, Li T, Wang X 2024 Phys. Rev. Lett. 133 152503
Google Scholar
[22] Kroger L, Reich C 1976 Nucl. Phys. A 259 29
Google Scholar
[23] Seiferle B, von der Wense L, Bilous P V, Amersdorffer I, Lemell C, Libisch F, Stellmer S, Schumm T, Düllmann C E, Pálffy A, Thirolf P G 2019 Nature 573 243
Google Scholar
[24] Shabaev V M, Glazov D A, Ryzhkov A M, Brandau C, Plunien G, Quint W, Volchkova A M, Zinenko D V 2022 Phys. Rev. Lett. 128 043001
Google Scholar
[25] Lewenstein M, Balcou Ph, Ivanov M Yu, L’Huillier A, Corkum P B 1994 Phys. Rev. A 49 2117
Google Scholar
[26] Walker P, Podolyák Z 2021 Phys. World 34 29
Google Scholar
[27] Peik E, Tamm C 2003 Europhys. Lett. 61 181
Google Scholar
[28] Thielking J, Okhapkin M V, Głowacki P, Meier D M, von der Wense L, Seiferle B, Düllmann C E, Thirolf P G, Peik E 2018 Nature 556 321
Google Scholar
[29] Masuda T, Yoshimi A, Fujieda A, Fujimoto H, Haba H, Hara H, Hiraki T, Kaino H, Kasamatsu Y, Kitao S, Konashi K, Miyamoto Y, Okai K, Okubo S, Sasao N, Seto M, Schumm T, Shigekawa Y, Suzuki K, Stellmer S, Tamasaku K, Uetake S, atanabe M, Watanabe T, Yasuda Y, Yamaguchi A, Yoda Y, Yokokita T, Yoshimura M, Yoshimura K 2019 Nature 573 238
Google Scholar
[30] Kraemer S, Moens J, Athanasakis-Kaklamanakis M, Bara S, Beeks K, Chhetri P, Chrysalidis K, Claessens A, Cocolios T E, Correia João G M, Witte H D, Ferrer R, Geldhof S, Heinke R, Hosseini N, Huyse M, Köster U, Kudryavtsev Y, Laatiaoui M, Lica R, Magchiels G, Manea V, Merckling C, Pereira Lino M C, Raeder S, Schumm T, Sels S, Thirolf Peter G, Tunhuma S M, Van Den Bergh P, Van Duppen P, Vantomme A, Verlinde M, Villarreal R, Wahl U 2023 Nature 617 706
Google Scholar
[31] Tiedau J, Okhapkin M V, Zhang K, Thielking J, Zitzer G, Peik E, Schaden F, Pronebner T, Morawetz I, De Col L Toscani, Schneider F, Leitner A, Pressler M, Kazakov G A, Beeks K, Sikorsky T, Schumm T 2024 Phys. Rev. Lett. 132 182501
Google Scholar
[32] Elwell R, Schneider C, Jeet J, Terhune J, Morgan H, Alexandrova A N, Tran Tan H B, Derevianko A, Hudson E R 2024 Phys. Rev. Lett. 133 013201
Google Scholar
[33] Zhang C, Ooi T, Higgins J S, Doyle J F, von der Wense L, Beeks K, Leitner A, Kazakov G A, Li P, Thirolf P G, Schumm T, Ye J 2024 Nature 633 63
Google Scholar
[34] Lyuboshitz V L, Onishchuk V A, Podgoretskij M I 1966 Sov. J. Nucl. Phys. 3 420
[35] Szerypo J, Barden R, Kalinowski Ł, Kirchner R, Klepper O, Płochocki A, Roeckl E, Rykaczewski K, Schardt D, Żylicz J 1990 Nucl. Phys. A 507 357
Google Scholar
[36] Wang W, Wang X 2024 Phys. Rev. Lett. 133 032501
Google Scholar
[37] Purcell E M 1946 Phys. Rev. 69 681
[38] Haroche S 2013 Rev. Mod. Phys. 85 1083
Google Scholar
[39] Wineland D J, 2013 Rev. Mod. Phys. 85 1103
Google Scholar
[40] Baldwin G C, Solem J C 1997 Rev. Mod. Phys. 69 1085
Google Scholar
[41] Izquierdo M 2022 Technical Design Report: Scientific Instrument Soft X-Ray Port (SXP): Part A-Science Cases (Schenefeld, European X-Ray Free-Electron Laser Facility GmbH) Report Number: XFEL. EU TR-2022-001A
[42] Liu T, Huang N S, Yang H X, Qi Z, Zhang K Q, Gao Z F, Chen S, Feng C, Zhang W, Luo H, Fu X X, Liu H, Faatz B, Deng H X, Liu B, Wang D, Zhao Z T 2023 Front. Phys. 11 1172368
Google Scholar
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