2A20
Electron localization in laser-driven H2+3(RIKEN Center for Advanced Photonics)◯Erik Lötstedt, Katsumi Midorikawa[Introduction] It would be extremely useful if individual valence electrons could be
moved in a controllable way from one place to another in a molecule. In this way, chemicalbonds could be formed and/or broken at will. Intense, few-cycle laser pulses are a rather
new tool which has the possibility to achieve this ambitious aim. Intense is here usedto mean laser pulses with an intensity around 1014 W/cm2 (peak electric field around 10GV/m). At this high field strength, a large fraction of the valence electron density isinfluenced; it becomes possible to significantly displace (almost) the whole electron wavefunction. This is rather different compared to the situation when weak fields are used andonly a perturbatively small part of the wave function is affected. Few-cycle implies thatthe laser-molecule interaction is sensitive to the detailed shape of the electric field suchas the carrier-envelope phase (CEP).
In this contribution, we show theoretically that the intra-molecular motion of thebound electron in the molecular ion H2+
3 can be controlled by driving the dissociating
molecule with a few-cycle, CEP stable intense laser pulse of circular polarization. By
varying the value of the CEP, it is possible to select which one of the protons the electron++
finally binds to in the reaction H2+
3 → H + H + H. Our results extends direct electricfield control of electron localization within a molecule to triatomic systems. This kind ofcontrol scheme was previously applied to diatomic molecules only [1,2].
[Theoretical model] Before the interaction with the laser pulse, the H2+
3 molecular ion isassumed to be in the electronic ground state, with the nuclear wave function given by thelowest vibrational state of H+3 . This situation can be achieved by ejecting one electron fromthe stable H+3 by (for example) an attosecond pulse. The vertical ionization potential is
34 eV. In order to simplify the situation, we furthermore assume that the D3h (equilateraltriangle) symmetry of H+3 is conserved during the interaction with the laser field. Thismeans that the wave function depends on only one nuclear coordinate, R. Note that this++assumption restricts the possible dissociation channels to H2+
3 → H + H + H. At eachvalue of R, we include the three energetically lowest adiabatic electronic states ψn (r, R),
n = 1, 2, 3. Field ionization is not included in the model. The total wave function is thus
assumed to be written as3Ψ(r, R, t) = ∑ ψn (r, R)χn (R, t).

(1)

n=1

By taking an appropriate superposition of the adiabatic eigenstates ψn (r, R), we obtainelectronic states ψ̃n (r, R) that are localized at either one of the three protons in the limitof large R.
A summary of the theoretical model is shown in Fig. 1.
[Results and discussion] Since the three states ψn (r, R) are repulsive [see Fig. 1(b)],H2+
3 necessarily dissociates. During the dissociation, we drive the molecule with a circularly polarized laser pulse of the form
E(t) = E0 sin2 (πt/τ ) [x̂ cos(ωt + ϕ) + ŷ sin(ωt + ϕ)] ,(2)y [Å]−55x [Å]
0x [Å]5 −50x [Å]
5−50(b)ψ(r, R)
0.620R
1000.40.2−5Electronic eigenstates ψn (r, R)

05y [Å]1

50−5Localized electronic states ψen (r, R)

energy [eV]

(a)

R
R

23excited states H2+
3(two degenerate)

0−10−0.2−20−0.4−30

ground state H2+
3ground state H+
312

3

4

5R [Å]Figure 1: (a) Electronic states at R = 5.3 Å. The color scale refers to the value of the wave

function in units of Å−3/2 . (b) Potential energy curves of the adiabatic states ψn . Also shown isthe electronic ground state of H+3 . The vertical ionization potential H+3 → H2+
3 is indicated witha broken, vertical line.

where ϕ is the CEP. The laser pulse is thus assumed to be polarized in the same plane as
the orientation plane of the H2+
3 molecule. A laser wavelength of 800 nm and an intensity
14
2of around 10 W/cm are employed. The time-dependence of the wave function (1) iscalculated by solving the Schrödinger equation for the nuclear wave functions χn (R, t),including the laser-induced dipole couplings. In the talk, it will be shown that by varying
the value of ϕ, we can selectively populate the localized electronic states ψ̃n . This meansthat after the interaction with the laser pulse, the probability for the ejection of an H atomin the positive y direction is different from the probability of ejection in the negative y,negative x direction or negative y, positive x direction. In order to quantify the asymmetry
induced by the laser pulse, we introduce the asymmetry measure A, defined asA = P1 + ei2π/3 P2 + e−i2π/3 P3 ,(3)where Pn is the probability that the final electronic state is ψ̃n (the probability that theelectron binds to proton n). A = ∣A∣eiα is a complex number, where the amplitude ∣A∣
indicates the overall amount of localization: ∣A∣ = 0 signifies a completely delocalized
electron [such as the ground state ψ1 (r, R), see Fig. 1 (a)], while ∣A∣ = 1 means that theelectron is completely localized to one of the protons. The phase α tells us on which
proton the electron is localized: α = 0 indicates proton 1, α = 2π/3 proton 2, α = −2π/3
proton 3, and (for example) α = π/3 signifies an electron distributed equally on proton 1and 2.
As a main result of this investigation, we find that by changing the CEP, the asymmetry amplitude ∣A∣ can be made to vary periodically with ϕ (period 2π/3), with a maximum
value of ∼ 0.5. The phase α changes with ϕ in a stepwise manner between the values −2π/3,0 and 2π/3. This result can be interpreted with a simple model: The proton to which theelectron finally binds to is given by the direction of the laser force vector at a particular,
critical instant tc , when the coupling between the states ψn is most efficient.
[References][1] M. F. Kling, C. Siedschlag, A. J. Verhoef, J. I. Khan, M. Schultze, T. Uphues, Y. Ni,M. Uiberacker, M. Drescher, F. Krausz, and M. J. J. Vrakking, Science 312, 246 (2006).
[2] I. Znakovskaya, P. von den Hoff, S. Zherebtsov, A. Wirth, O. Herrwerth, M. J. J.
Vrakking, R. de Vivie-Riedle, and M. F. Kling, Phys. Rev. Lett. 103, 103002 (2009).