# What will happen if a ground state hydrogen atom is placed in a low frequency, but high intensity laser field?

Similar questions have been asked before, but this one extends the scope of interpretation and applications.

Let us ask the question: What will happen if we have a laser gun that produces a high intensity laser beam, of the order $10^{15} Wm^{-2}$ say, and frequency about $4\times 10^{14}Hz$, and shoot a hydrogen atom in its ground state? The duration of the laser pulse is sufficiently long. Answers in terms of physical arguments will be appreciated.

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@Emilio Pisanty Thank you for all this valuable information. Much appreciated. –  JKL Feb 13 '13 at 17:36
@VladimirKalitvianski Thank you for your answer and the information you have posted. Appreciated. –  JKL Feb 13 '13 at 19:16

For low-frequency, high-intensity laser fields, atomic and molecular targets can be ionized by multi-photon ionization (which is a nonlinear process and thus requires high intensity, but is nevertheless possible) as well as tunnel ionization (which can also happen in a sufficiently strong DC, or quasi-DC, field).

If you turn on the intensity further, above-threshold ionization can happen, in which the atomic potential barrier is pushed low enough that the ground state can escape. By this time the laser electric field comparable or stronger than the atomic one, which means that perturbation-theoretic concepts like photon absorption no longer mean much.

Apart from that, one very interesting phenomenon that can happen is the generation of very high order harmonics of the laser field. This is caused by the ionized electron being reaccelerated by the laser field towards the parent ion and colliding with it. The electron can then recombine and emit all of its considerable energy as a remarkably short (sub-femtosecond) pulse of light. This means that harmonics of order up to ~130 have been detected. A good reference for this is

M. Lewenstein, Ph. Balcou, M. Yu. Ivanov, Anne L’Huillier, and P. B. Corkum. Theory of high-harmonic generation by low-frequency laser fields. Phys. Rev. A 49 no.3, pp. 2117–2132 (1994).

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As I mention in the post, both mechanisms are possible. Which one will dominate depends on the intensity, frequency, and duration of the laser pulse. Typically tunnel ionization only beats multiphoton ionization for short pulses of low frequency. –  Emilio Pisanty Feb 13 '13 at 11:42
I think the duration is not important here, only the frequency and intensity. The Keldysh parameter is a very simple way of predicting whether multiphoton or tunneling ionization will occur. –  perplexity Feb 13 '13 at 11:59
There isn't a clear divide between the two mechanisms, which are simply limiting behaviours of full nonlinear treatments. While small $\gamma\propto\omega/E_0$ does strongly favour tunnel-type ionization, I understand from speaking with experimentalists that this signal can get obscured by multiphoton events for long pulses; this is because tunnel ionization is essentially a single-cycle event while multiphoton mechanisms require 10+ cycles to become effective. I'll check and post further details. –  Emilio Pisanty Feb 13 '13 at 13:21
OK, I've checked. It's not a fundamental dependence on pulse duration, but rather a technological one, for two reasons. First, it is hard to get pulses strong enough to show tunnelling ionization without compressing the energy into a rather short pulse. More importantly, though, for pulses longer than ~1ps, there is a long turn-on time before the intensity reaches tunnel-ionization strengths, and during this turn-on time multiphoton ionization can act, (i) creating a lot of "noise" electrons and even (ii) depleting the sample. –  Emilio Pisanty Feb 13 '13 at 13:48
Thus, while tunnel ionization does occur, it was hard to prove experimentally that it was happening. The first reference, as far as I'm aware, is S. Augst, D. Strickland, D. D. Meyerhofer, S. L. Chin, and J. H. Eberly. Tunneling ionization of noble gases in a high-intensity laser field. Phys. Rev. Lett. 63, 2212–2215 (1989). doi:10.1103/PhysRevLett.63.2212‌​. –  Emilio Pisanty Feb 13 '13 at 13:51

Even in an "insufficient frequency" wave an atom can get excited and ionized due to multi-photon absorption. Many years ago I read an article of Keldysh about the corresponding cross sections.

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The reference is Keldysh, L. V. Ionization in the field of a strong electromagnetic wave. Sov. Phys. JETP 20 no. 5, pp. 1307-1314 (1965). [Zh. Eksp. Teor. Fiz. 47, pp. 1945-1957 (1964).] –  Emilio Pisanty Feb 13 '13 at 11:35
Another classic reference is Perelomov, A M, Popov, V S and Terent'ev, M V. Ionization of atoms in an alternating electric field. Sov. Phys. JETP 23 no. 5, pp. 924-934 (1966). [Zh. Eksp. Teor. Fiz. 50, pp. 1393-1409 (1966).] –  Emilio Pisanty Feb 13 '13 at 11:38
(Both are, unfortunately, rather hard to obtain, though.) –  Emilio Pisanty Feb 13 '13 at 11:38
Hard to obtain (and hard to read in Russian), but maybe not for Vladimir;-) –  perplexity Feb 13 '13 at 20:09