1. Introduction

Over the past two decades, the investigation of intense lasers interacting with atoms and molecules has resulted in a comprehensive understanding of various strong-field phenomena such as multi-photon single ionization (for reviews see e.g. [1]), above threshold ionization [2] as well as high harmonic generation [3] and has significantly improved our knowledge on non-sequential double ionization [4]. Multiple-ionization of atoms and molecules by high intensity lasers instead is not well understood so far but has attracted significant recent interest especially addressing many-body correlation aspects in strong fields [5].

Strong-field physics tremendously benefits from the rapid development of ultra - short and-intense laser technology. Typically, high-power lasers equipped with traditional amplifier systems are used which are restricted, however, to repetition rates in the kHz range hampering e.g. the exploration of processes occurring with very low probability. On the other hand standard laser oscillators having MHz repetition rates are not able to produce sufficiently high intensities. Femtosecond lasers delivering pulses with output energies approaching the micro joule regime and peak intensities near PW/cm² at MHz repetition rates would be of paramount interest for several fields of research and technology, including micromachining, microstructuring, as well as ultra-fast pump-probe experiments. Thus, several techniques are presently developed in order to reach a reasonable compromise between single-pulse peak power and repetition rate. The traditional approach of increasing the pulse energy from femtosecond laser oscillators is cavity dumping [6, 7]. Another concept which has been pursued in the present work is based on increasing the laser cavity length using the Herriott-cell technology [8–11].

Non-sequential double ionization (NSDI) of atoms represents one striking example for the importance of correlated electron dynamics occurring in laser fields at not too high intensities. In this regime it is generally assumed that double ionization mainly proceeds by ejection of the second electron by a previously released electron colliding with its parent ion [12,13]. In a simple classical model, the maximum kinetic energy of the first electron amounts up to E≈3.17 U_p when it returns to the ion core depending on its release phase, where U_p =I/4ω ² denotes the ponderomotive energy in the laser field (I, ω: pulse intensity and frequency, respectively). Therefore, within the intuitive semi-classical recollision model a threshold should exist for NSDI expected to appear at an intensity when the energy of the rescattered electron approaches the ionization potential of the singly ionized atom modified by the presence of the laser electric field. Because the cross section rapidly drops with decreasing intensity, the low repetition rate of intense lasers so far has remained to be the main obstacle for experiments at sub-threshold intensities. One measurement near the threshold has been performed, but the fundamental question on the existence of a threshold as well as on possible mechanisms of non-sequential double ionization below this limit has not been solved [14]. This important issue in strong-field correlated electron quantum dynamics is expected to be tackled using high repetition-rate laser systems and is the main purpose of this work. Here, we report on the differential investigation of non-sequential double ionization of argon and neon in intense lasers fields studied with a femtosecond laser oscillator based on the Herriot-cell concept reaching 6.2 MHz with peak powers exceeding 10 MW. This femtosecond laser oscillator provides us, for the first time, with the possibility to investigate single and multi-electron transitions at low intensities for rare gases or molecules at extremely small ionization probabilities and, thus, ionization event rates.

2. Experimental techniques

The schematic experimental layout of the KLM Ti:sa laser oscillator used in our measurements is depicted in Fig.1. The oscillator is pumped by a continuous Verdi-V18 (Coherent INC) laser. In order to increase the stimulated lifetime and avoid detrimental intensities inside the laser crystal, the laser crystal is cooled down to-40°C. Here, we apply a Herriott-type multi-pass telescope to extend the cavity length to more than 24 m. The detailed design of the oscillator is described in reference [11]. A semiconductor saturable absorber mirror (SESAM) as an end mirror is used to stabilize the mode-locked pulse train. The laser system delivers single pulse energies of 0.6 µJ at an unprecedented repetition rate of 6.2 MHz. The wavelength of this laser is 795 nm. The net positive chirped pulses are compensated by a doublepass prism (SF10) compressor. In order to optimize the compression, the laser pulse is eventually focused into a 3 mm transparent sapphire plate, generating white light as shown in Fig. 1 at sufficiently high intensity, i.e. short pulse durations. In this test arm we additionally insert a fused silica plate with the same thickness as the window used to separate the high-vacuum chamber of the reaction microscope. By watching the white-light intensity we can now optimize the dispersion compensation of the pulse under identical conditions as shooting into the chamber by changing the distance between the two prisms of the compressor. For the experiment the test arm is removed, the output laser beam is expanded after compression with an off-axis telescope and then fed into the reaction-microscope vacuum chamber reaching a peak power of more than 10 MW corresponding to a maximum intensity beyond 10¹⁵W/cm²for a diffraction-limited focus area.

The reaction microscope used in our experiments has been described in detail elsewhere [15,16]. The electrons and ions generated from atoms of a supersonic jet in the tightly focused laser field are guided towards two position-sensitive delay-line equipped multi-channel plate detectors (MCP) by applying weak homogenous electric (2V/cm) and magnetic (3 Gauss) fields along the laser polarization direction. Depending on the strength of the fields applied typically a 4π detection solid angle can be achieved for the ejected electrons and ions. The three dimensional momentum vectors of electrons and recoil ions can be recalculated from the measured respective impact positions and the times-of-flight (TOF). All analog signals from the MCPs and delay-lines are amplified and then digitized by an “Acqiris” transient recording system (Agilent Technoliges INC., temporal resolution: 1 ns). The gas jet density is about 1·10¹²/cm³. As indicated in Fig. 1 the laser is linearly polarized in parallel to the projection field vectors and, thus, along the spectrometer (longitudinal) symmetry axis i.e. along the time-of-flight directions of ions and electrons (||-axis). The atomic jet propagates perpendicular to this axis along the x-direction. Along the jet expansion the ion momentum resolution is limited by the internal jet temperature to 0.3 a.u.. Perpendicular to the jet expansion the jet is effectively collimated by the small laser focus thus reaching resolutions about 0.05 a.u. The transverse (with respect to the spectrometer symmetry axis) electron momentum resolution depends on the TOF. For flight times equal to an integer multiple of the cyclotron revolution time all electrons are focused onto the center of the detector thus imaging, under ideal conditions, the source area. Here, the momentum acceptance transverse to the extraction direction becomes infinite, only limited by geometrical restrictions and, accordingly, the momentum resolution is zero. For flight times half in between these focus points, electrons are on their maximum transverse distance from the origin, with optimum momentum resolution of about 0.1 a.u.. In the longitudinal direction along the extraction field the electron momentum resolution is 0.03 a.u..

 

Fig. 1. The experimental setup.

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As is indicated in Fig. 1, the on-axis parabolic mirror is especially designed to be directly integrated into the spectrometer, its surface forming several equipotential lines in order to avoid in-homogenous electric field distributions in the spectrometer. The coincident and momentum resolved detection of an electron and of the doubly ionized ion allows for a detailed exploration of the NSDI mechanisms, where the experiment particularly benefits from the large efficiency essentially covering 4π of the solid angle for both particles.

3. Experimental results

In order to optimize the laser focusing conditions, we first maximize the Ar⁺single ionization rate. In this case we observed an Ar⁺(Ne⁺) rate of about 20 kHz (1 kHz), i.e. less than 0.003 ions per laser shot ensuring the probability of false coincidences (the detection of an electron and an ion not emerging from the ionization of the same atom) to be negligibly small. The measured time-of-flight (TOF) spectrum for argon is shown in Fig. 2. The ratio of Ar2⁺to Ar⁺yields about 0.0056. The intensity of the laser pulse can be attenuated to the desired intensity using a half-wave plate.

 

Fig. 2. Time-of-flight (TOF) spectrum for Ar recoil ions at about 2.3×1014 W/cm2.

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Ionization by high-intensity lasers is considered to proceed either via multi-photon absorption or via tunneling ionization depending on the value of the so-called Keldysh, or adiabaticity parameter. The Keldysh Parameter is given by $\gamma =\sqrt{I_p⁄2U_p}$, where I_p is the ionization potential and U_p is the ponderomotive potential. As is well-known, in the tunneling region the maximum drift momentum of a released electron (and of the created ion as well) can be calculated from classical considerations to be $2\sqrt{U_p}$ along the laser polarization (longitudinal) direction. At electron energies beyond 2U_p, elastic backscattering of the electron off the ion core contributes to a long, high-energy plateau extending up to 10U_p, which is the largest drift energy an electron can gain from the field in the backscattering process. As has been described in detail in [17], a clear kink in the measured longitudinal momentum distributions of photoelectrons or ions from single ionization of neon and argon occurring at $2\sqrt{U_p}$ has been used for the absolute calibration of the laser peak intensity to be 2.3·10¹⁴ W/cm². Longitudinal electron momentum spectra up to $2\sqrt{U_p}$ can be easily explained in the tunneling regime. Most likely electrons tunnel at phases where the field is maximum yielding a maximum in the distribution at zero momentum. With increasing p|| up to the maximum drift momentum the spectrum smoothly but strongly falls off, reflecting the fact that the tunnel probability dramatically drops with decreasing laser field strength.

The measured momentum spectra for single as well as double ionization of argon and neon are presented in Figs. 3a-d, respectively at the above laser intensity. The Keldysh parameters for argon (I_p=15.76 eV) is γ≈0.74 and for neon is γ≈0.87 (I_p=21.56 eV) at the given intensity. The Keldysh parameters for those species are lower than 1. That is to say our laser intensity is in the tunneling region. But distinct above-threshold ionization (ATI) peaks for single ionization are still observed. This indicate that multi-photon ionization can be at work at this intensity.

 

Fig. 3. Momentum distributions for singly and doubly charged argon (a,b) and neon (c,d) along the laser polarization direction at an intensity of 2.3·10¹⁴W/cm².

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For Ar⁺, the momentum distribution exhibits a characteristic maximum at zero momentum and the positions of above-threshold peaks do not significantly change compared to measurements at the high intensities [18,19].We interpret this as being due to the fact that single ionization of argon is directly established through the a resonant absorption channel at those intensities (Freeman resonance). In contrast to argon, the momentum distribution for single ionization of neon has a pronounced dip structure at zero momentum. In reference [18] it was speculated that the ATI-like feature observed there at significantly higher intensities resulted from resonant ionization. More recent experimental work [19] attributed the dip structure as well to a resonant mechanism but, in both cases, the exact pathway for resonant enhancement was not specified.

Since the laser electric field at present intensities is quite strong, all intermediate states are ac-Stark shifted and a specific one of them might be brought into resonance with the N-photon dressed ground state at a certain intensity. Then, multi-photon ionization through this resonant state is strongly enhanced giving rise to a peak in the photo-electron spectrum at an energy of hν-E_int, where E_int is the ionization potential of a field-free state. If the laser pulse would exhibit a sharp intensity profile, temporally as well as spatially, this peak would only appear at one specific intensity, i.e. exactly when, and only when the respective state is ac-Stark shifted into resonance. Under real experimental conditions however, the spatio-temporal intensity profile of the laser pulse guarantees that once the resonance condition has been reached for the peak intensity increasing the intensity further always keeps the resonance condition for some spatial or/and temporal part of the pulse, such that the resonance peak does not disappear at all but simply stays at its position independent of the intensity. For neon, we attribute the first ATI-like peak for single ionization in this intensity region to the 2p⁵6p or 2p⁵5d intermediatestate with Freeman resonance.

Exploiting the advantage of the high repetition rate, we can decrease the intensity to values as low as 0.9·10¹⁴W/cm² when a spike of electrons emerges with near zero momentum for single ionization of neon, shown in Fig. 4a. The appearance of a sharp electron energy peak which is intensity-dependent identifies this spike to be due to a non-resonant channel in contrast to resonant ionization, where the electron energy is expected to be independent of the intensity assuming that the magnitude of the ac-Stark shift is similar to the ponderomotive shift. Non-resonant absorption occurs at the lowest intensities where we can measure. The energies of those electrons can in principle span the range from the zero-intensity value, 18hν-U_p-21.56eV down to 0eV. It is worth mentioning that we do not observe any indication of doubly charged neon at this intensity. As to single ionization of argon, we can decrease the laser intensity down to 0.3·10¹⁴ W/cm². The electron momentum distribution along the laser polarization is given in Fig. 4b. It has a pronounced dip structure compared with its momentum distribution at the high intensities. This might be a result of the channel switching effect [20]. At the lower intensity, the dominant ionization path proceeds with 11-photon via an ftype Rydberg state and while the laser intensity increasing the dominant ionization path will switch to a 12-photon ionization channel via g-type Rydberg states.

Two-dimensional electron momentum spectra for single ionization at even lower intensity have been investigated before using the velocity imaging technique along with low repetition rate lasers [20–22]. There, thick targets were used to compensate for the low ionization probabilities at the expense of detecting only two momentum components of the electron retrieving the third one by the “onion peeling” technique and, more importantly, being not able to perform coincidence experiments. In our experiments, the gas density is very low in order to avoid false coincidence signal. By applying the low repetition rate amplified laser, it is very hard to enter into the intensity region of the above measurements.

 

Fig. 4. (a): Electron momentum distribution for single ionization of neon along the laser polarization direction at an intensity of 0.9·10¹⁴ W/cm². (b): Electron momentum distribution for single ionization of argon along the laser polarization direction at an intensity of 0.3·10¹⁴W/cm².

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It is well-known from a series of recent investigations [23–25] that the characteristic double hump structure observed for Ne2⁺momentum distributions along the laser polarization axis can be attributed to the rescattering mechanism within the tunneling ionization regime concerning the first electron. In the present experiment the laser intensity was about 2.3·10¹⁴ W/cm² which is well in the regions of non-sequential double ionization for some noble gases as well as molecules and the pondermotive potential is about 13.7eV at this intensity. Thus, the maximum recollision energy that an electron can obtain from the laser field without additional interaction with the nucleus is about 43.4eV which is close to the impact ionization threshold of Ne⁺(I_p=41eV). As has been discussed in detail before, the occurrence of a sharp double hump structure indicating that the Ne²⁺ions are created at a well defined phase in the oscillating laser field close to a zero crossing can be explained by “rescattering” model [24]. Upon inelastic scattering at the return of the tunnel ionized first electron to the core a second electron can be removed from Ne⁺by electron impact ionization. With the recollision energy being close to the threshold for non-sequential double ionization, the influence of the time dependent laser field on the instantaneous ionization potential of the parent ion has to be taken into account [14].

In contrast to neon, double ionization of argon at this laser intensity shows a pronounced difference pointing to a different dominating double ionization mechanism. This “filling of the valley” has been observed in numerous measurements before, mostly at higher intensities though and was attributed to recollision-excitation plus subsequent ionization (RESI) [17,26]. Here, a second bound electron is excited upon recollision with a cross section σ_exc and then can tunnel in one of the subsequent field maxima leading to smaller ion momenta since the second electron is most likely released close to a field maximum. Differences between different targets concerning the dominating ionization mechanism have been attributed within this model to different ratios σ_ion/σ_exc where σion denotes the cross section for direct recollisioninduced ionization. In the present experiment, the ratios of σ_ion/σ_exc are 0.32 and 0.45 for argon and neon, respectively. Even thought the ionization-to-excitation ratio is very similar, the targets behave very differently as is obvious from the momentum distributions. We find that close to the threshold intensity the dominating mechanism for non-sequential double ionization of argon is due to recollision-excitation plus subsequent field ionization (RESI).

4. Conclusion

In conlcusion, we have investigated single and non-sequential strong-field double ionization of neon and argon close to the classical recollision double ionization threshold using a longcavity femtosecond oscillator. For the lowest intensity, a spike of electrons is observed at zero longitudinal momentum for singly charged neon and is attributed to non-resonant ionization. As to single ionization of argon at lowest intensity, a pronounced dip structure results from the channel-switching effect. Using this laser sytem, the features of non-sequential double ionization of Argon and Neon can be investigated. To our knowledge, this work is the first successful attempt to study single and double ionization of atoms using a high repetition-rate femtosecond oscillator. In the near future, we aim to explore non-sequential double ionization at even lower intensities close to the double ionization threshold, significantly below the recollision impact-ionization threshold.