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 3.5×10
16W/cm
2). 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 10
23W/cm
2and 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
Dis the transition moment (between two representative levels of the system),
E
0is the laser field amplitude,
DE
0quantifies the laser-matter interaction energy, and Δ
Eis 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 Δ
E= 1 a.u., so if
E
0~ 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,
Dbecomes several (~5 to 7) orders of magnitude smaller, while Δ
Ebecomes several (~5) orders of magnitude larger. Consequently, the laser field amplitude
E
0will need to be 10 orders of magnitude higher, or the laser intensity needs to be 20 orders of magnitude higher (~ 10
36W/cm
2), 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 (
229Th
90+) is on the order of 10
3s, while in the hydrogenlike ionic state (
229Th
89+) it decreases by five orders of magnitude to 10
–2s. This 1s electron greatly affects the properties of the
229Th nucleus, effectively changing the nuclear transition moment from
Dfor the bare nucleus to $ D' = D + b{\mu _{\text{e}}} $ for the hydrogenlike ion, where
D~ 10
–7a.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 Δ
Eand 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 10
21W/cm
2. Correspondingly, the intense laser-driven
229Th
89+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.
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