EXPLORING HIGH ATOMIC EXCITATION WITH INTENSE SHORT-

WAVELENGTH RADIATION

P. Lambropoulos

IESL- FORTH and University of Crete, Heraklion, Crete, Greece

ITAMP June 19-21 2006

Based on work performed in collaboration with

Lambros Nikolopoulos, Mihalis Makris,Spyros Themelis as well as Michael Meyer, Francois

Wuilleumier and Bernard Piraux.

Introduction

Forty four years ago, when the laser had just appeared, with only the CW He-Ne and the pulsed Ruby lasers in existence , at

fixed wavelengths in the red, Abella (PRL 9, 453 (1962))observed the first two-photon absorption in an atomic vapor,namely Cesium, exploiting the possibility of thermally tuning slightly the wavelength of the Ruby laser. He was thus able

to observe the excitation of the 9D(3/2) state via two-photon absorption from the ground 6S(1/2) state. At around the same

period, second harmonic generation was observed,and for a few years, those remained the only observations of

non-linear laser-atom or matter interactions. Then followed the “dark ages”, so to speak, of multiphoton

processes, or more precisely, what was to eventually emergeas multiphoton physics. These attempts were well motivated,

as it was reasonable to expect that further technologicaldevelopments will bring new laser sources, with higher intensity

and more tunability.Thus not much happened, until the late 1960’s when,

on the one hand, the Nd-glass laser (at λ =0.53 μm) with muchhigher intensity and, on the other hand, the dye-laser(flash-lamp pumped) with broader tunability appeared.

By the dawn of the 1970’s, the renaissance of laser-atominteractions was well under way.

In anticipation of the discussion of few-photon processesExpected to be studied with XUV and beyond coherent,

intense sources, this is a good place to note that what was proven and studied in considerable detail through the

mid 80’s, is that the rate of N-photon ionization is proportional, not to the Nth power of the intensity, as is

often stated, but the Nth order correlation function. For a purely coherent state, the Nth order correlation

function is indeed the Nth power of the intensity, but for a source with strong intensity fluctuations (chaotic), this

correlation function is larger by a factor of N ! .This means, and has been studied and demonstrated experimentally since the mid 70’s , that the N-photon ionization yield, under a source with strong intensity

fluctuations, is larger by a factor of N ! , assuming the same average intensity.

Perhaps the most dramatic experimental demonstration came from Saclay (PRL 32, 265) in 1974 in 11-photon

ionization.

In view of upcoming coherent and fairly intense sources from the XUV through hard X-rays, with pulse durations of the order of tens of fs, it is natural to ask whether we are

where the infrared to optical multiphoton physics was in the mid 60’s and to speculate about possible developments as

the sources continue their development.

A few remarks on typical parameters of intense, short duration sources in the infrared and optical are useful at this point. A brief summary of such parameters is given below. Let us keep in mind that the most intense source with which most of the non-perturbative phenomena have become accessible is the Titanium-Safire laser of wavelength 780 nm i.e. photon energy about 1.59 eV. Since the term intense is also used in the context of the XUV sources, let us examine its meaning in comparison to the parameters below.

The quantity that is most meaningful as a criterion of the onset of non-perturbative behaviour, leading to the presence of significant ATI and HOHG, is the ponderomotive potential, representing the cycle-averaged quiver energy of a free electron in the AC field. As a point of calibration, note that at 1064 nm and intensity 1013 W/cm2, the ponderomotive energy is about 1 eV, which is very close to the photon energy of 1.16 eV. Thus at intensities 1015 W/cm2 and wavelength 780 nm (photon energy ~ 1.5 eV), the ponderomotive potential is of the order of about 60 photons.

Now, let us observe that the ponderomotive potential scales proportionally to the intensity and inversely proportionally to the square of the frequency, while the ratio of the ponderomotive potential to the photon frequency is inversely proportional to the cube of the frequency.Thus, for example, for photons of energy of 100 eV and intensity 1015 W/cm2, the ponderomotive potential is about 0.01 eV, which is four orders of magnitude smaller than the photon energy. As a result, tunneling, etc. will be of no importance at this combination of intensity and frequency, and that holds true even if the intensity becomes two orders of magnitude larger.

What about the pulse duration ? Well, even a duration of 5 fs, contains many cycles of radiation with photon energy even 50 eV. And one thing that has become clear is that, surprisingly, if the pulse has duration, say, 10 cycles or more, and insignificant ponderomotive potential (in the sense discussed above) LOPT (Lowest Order Perturbation Theory) is perfectly valid for the treatment of multiphoton transitions. What is not valid, however, is that XUV photons and beyond interact mainly with electrons below the valence shell of atoms. As a consequence, the SAE (Single Active Electron) model that has been so successful in strong- field interactions, in the infrared, is no longer valid. We have to deal with a multielectron problem which makes theory more demanding, with the reward that a new landscape of phenomena is now unveiled. Let us examine some of those.

Single

Single-photon double ionization of Helium

Single photon double ionization cross section of

Helium

Typical semiquantitative cross section obtained with a goodground state and Coulomb functions (Z=2) final states.

High-order, strong field ionization and double ionization of He

Demonstration of non-sequential double ionization of Heliumunder a strong infrared laser of 780 nm.

What about 2-photon double ionization of He ?

• Required photon energies between 25 and 80 eV.

• Intensities?

• Pulse durations?

• Sequential, Non-sequential and all that ?

Coming back to that, after a discussion of possible pump-probe processes.

Pump - probe

If it were possible to combine an FEL pulse with a pulsed optical laser, another exciting possibility emerges. Excitation of an autoionizing (AI) state, in the presence of an optical laser coupling it to another, higher AI state, makes it possible to study the coupling between such states, through the measurement of the resulting AC Stark splitting, as the intensity of the optical laser becomes stronger, and the probing FEL frequency is scanned, across the resonance profile.

Turning this problem around, one could combine these two pulses, introducing a delay between the two, and by probing the signal of ionization from the upper resonance, extract information about the duration and even the temporal shape of the FEL pulse, as discussed most recently in JPB 37,4281 (2004).

Doubly excited states is not the only context in which the coupling of highly excited states can be studied in this fashion. Along identical lines, one can consider the coupling of triply excited states (see PRA 62, 062719 (2000)), or core excited Auger resonances, as illustrated by the predictions in the sequence of figures below.

Ionization dynamics in double resonance involving autoionizing states in helium: the effect of pulse shapes

J. Phys. B: At. Mol. Opt. Phys. 37 4281-4293 (2004)

S.I. Themelis, P. Lambropoulos and M. Meyer

Measurement of the AC Stark splitting, due to the coupling of the two autoionizting states by an optical laser of known

intensity, provides direct information on the value of the dipole matrix element between the two AI states.

Prediction of the ac-Stark splitting of coupled core-excited Auger states of Sodium

Laser-induced transitions between core excited states of Na

J. Phys. B: At. Mol. Opt. Phys. 38 2119-2132 (2005)

S.I. Themelis, P. Lambropoulos and F.J. Wuilleumier

Laser-induced transitions between triply excited hollow states

PHYS REV LETT 85, 42-45 (2000) ; PRA 62, 062719 (2000).

L.B. Madsen, P. Schlagheck and P. Lambropoulos

Two-photon double ionization of Helium

Channels of single and double ionization

Two-photon PES of Helium under the irradiation with a Gaussian pulse of photon energy 45 eV, peak intensity 1011 W/cm2 and 50 fs duration.

P. Lambropoulos, L.A.A. Nikolopoulos and M. MakrisPRA 72, 013410 (2005)

Two-photon double ionization cross sections

TDSE

TD

( TDSE –FC calculation by B. Piraux (2006) )

Two-photon double-ionization cross section of Helium. Final states uncorrelated, B-splines basis (L.A.A. Nikolopoulos and P. Lambropoulos (unpublished))

Ionization yield as a function of peak laser power for photon energy 41.85 eV (27th harmonic) and two

different pulse durations(Experiment by Nabekawa et al. PRL 94, 043001 (05))

(See also L.A.A. Nikolopoulos and P. lambropoulos J. Phys. B. 39, 883 (2006) )

Ionization yield as a function of peak power for photon energy 44.95 eV (29th harmonic)(J. Phys. B 39, 883 (2006)

Single- and two-photon ionization cross sections(J. Phys. B 39, 883 (2006))

Laser intensity dependences, including effects of the spatial distribution of the radiation ( PRA 72, 013410 (2006))

Europhysics Lett. 54, 722 (2001)

Europhysics Lett

Europhysics Lett. 54, 722 (2001)

Let us push our speculation a bit further. If, as expected from the next phase of the FEL sources, photons in the energy range of about 70 to 80 eV and intensities - with some guessing involved here - above 1013

W/cm2, one could consider the direct generalization of the two-photon, double

ionization of He, to the three-photon triple ionization of Li, depicted schematically in

the figure that follows. This would indeed be an exciting possibility, as one could probe the behavior of the triple continuum, about

which very little is known, with unprecedented flexibility. The theoretical

task here is daunting, but it may be time to start .

CONCLUDING REMARKS

If indeed, as anticipated, FEL sources in the XUV and beyond do deliver intensities of around 1015 W/cm2, or a couple of orders of magnitude more, in the photon energy range up to 200 eV, for the moment, we can look forward to a new phase of multiphoton physics, involving multiple electron excitations, probing of highly excited states, coupled to multiple continua, opening thus new vistas of atomic and molecular processes. Synchronization with optical or UV lasers, or combination of FEL wavelengths, could open even more avenues, that require another discussion and elaboration. And…remember, intensity fluctuations, from the perspective of few-photon ionization (multiple or not) enhance the process, which should also be kept in mind in assessing intensity from such measurements.Finally, although the specific discussion has focused on photon energies in the XUV and soft X-rays, clearly its extension to shorter wave-lengths and deeper shells would be considerably richer in the type of physics it can probe.

Although

Some relevant papers

Multichannel theory of two-photon single and double ionization of heliumJ. Phys. B: At. Mol. Opt. Phys. 34, 545-564 (2001) L. A. A. Nikolopoulos and P. Lambropoulos

Double-electron above threshold ionization of heliumJ. Phys. B: At. Mol. Opt. Phys. 34 L69-L78 (2001)J S Parker, L R Moore, K J Meharg, D Dundas and K T Taylor

Correlation effects in two-photon single and double ionization of heliumPhys. Rev. A 68, 013409 (2003)S. Laulan and H. Bachau

Core-Excited Resonance Enhancement in the Two-Photon CompleteFragmentation of HeliumPhys. Rev. Lett. 88, 173002 (2002)J. Colgan and M. S. Pindzola

Two-photon double ionization of HeJ. Phys. B: At. Mol. Opt. Phys. 36 L1-L7 (2003)Liang Feng and Hugo W van der Hart

Electron angular distributions in two-photon double ionization of heliumEUROPHYS LETT 54 (6): 722-728 (2001) M. G. Makris, L. A. A. Nikolopoulos and P. Lambropoulos

Ionization dynamics in double resonance involving autoionizing states in helium: The effect of pulse shapesJ. Phys. B 37 (21), 4281-4393 (2004).  S.I. Themelis, P. Lambropoulos and M. Meyer

Laser-induced transitions between core excited states of NaJ. Phys. B 38, 2119 (2005)S.I. Themelis, P. Lambropoulos and F.J. Wuilleumier

Signatures of direct double ionization under xuv radiation, PRA 72, 013410 (2005)P. Lambropoulos, L. A. A. Nikolopoulos, and M. G. Makris

L.A.A. Nikolopoulos and P.L., J. Phys. B 39,883 (2006)

Recent and the only experimental paper:

Production of Doubly Charged Helium Ions by Two-Photon Absorption of anIntense Sub-10-fs Soft X-Ray Pulse at 41.85 eV Photon EnergyPhys. Rev. Lett. 94, 043001 (2005). Y. Nabekawa, H. Hasegawa, E.J. Takahasi and K. Midorikawa