Carrier-envelope-phase-dependent above-threshold ionization of xenon observed with multi-cycle laser pulses

Carrier-envelope-phase (CEP)-dependent modulation was measured in above-threshold ionization of xenon driven with 30-fs laser pulses. We showed the dependence from the asymmetry map obtained using a velocity map imaging spectrometer, up to 17 eV in photoelectron energy. The dependence appeared to be linear with a slope of one photon energy increase per CEP change of 2π and did not rely on the sign or the amount of laser chirp. Our results indicated the existence of the quantum interference between different multiphoton ionization paths. © 2014 Optical Society of America OCIS codes: (020.4180) Multiphoton processes; (270.6620) Strong-field processes; (320.2250) Femtosecond phenomena. References and links 1. P. Agostini, F. Fabre, G. Mainfray, G. Petite, and N. K. Rahman, “Free-free transitions following 6-photon ionization of xenon atoms,” Phys. Rev. Lett. 42, 1127–1130 (1979). 2. W. Becker, F. Grasbon, R. Kopold, D. B. Milošević, G. G. Paulus, and H. 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Introduction
Since its discovery, above-threshold ionization (ATI) has been extensively investigated to reveal the photoionization dynamics of atoms under intense laser fields [1][2][3][4][5].Strong field ionization of atoms induces such interesting phenomena as high harmonic generation (HHG) [6,7], nonsequential double ionization (NSDI) [8][9][10], and ATI.While all three phenomena are results of photoionization of atoms in a strong laser field, HHG emits harmonic photons due to the recombination of the released electron with its parent ion, and NSDI happens when the returning electron kicks out another electron from the ion.ATI produces photoelectrons separated by incident photon energy in a photoelectron spectrum due to the absorption of photons in excess of the minimum required to overcome the ionization threshold of an atom.The measurements of ATI spectra have revealed structural information on atomic bound states and the rescatter-ing process of the freed electron [11,12].ATI is also useful in probing molecular structures from angle-resolved ATI spectra [13,14].In addition it has been known that the ATI process depends on the carrier-envelope phase (CEP) of few-cycle laser pulses [15,16].ATI is, thus, a fundamental process revealing the physics of strong field interaction in atoms and molecules.
As a sensitive measure of CEP, photoelectron emission has been investigated using few-cycle laser pulses.There exists an asymmetry in photoelectron yield along the polarization direction when a target atom is ionized by a linearly polarized few-cycle laser pulse, depending on CEP [16].This asymmetric emission in ionization has been the key to devise measurement instruments and develop detection techniques as well as the stabilization scheme for CEP.A stereographic imaging technique is introduced with linearly polarized few-cycle pulses to investigate the asymmetric emission along the polarization direction by using a velocity map imaging spectrometer [17,18].In addition the stereo-ATI technique has been widely used to determine the CEP of a laser pulse from a two-dimensional parametric plot of asymmetry [19], proving the usefulness of ATI in measuring the CEP of few-cycle laser pulses.
Even the CEP of few-cycle laser pulses can be determined by these methods, it is still a meaningful question to ask the maximum pulse duration to observe the CEP effect and how to extract the absolute phase from multi-cycle pulses.The CEP of a femtosecond pulse could be a control parameter in investigating electronic transition processes in molecules coupled with multi-cycle laser [20] or molecular dynamics [21].Photo-fragmentation, for example, was demonstrated for heavy molecules with CEP-controlled laser pulses [22].With the single-shot CEP meter the upper limit to detect CEP effects was shown to be a pulse duration of around 12.5 fs [23].Theoretical studies showed that the CEP effect could be observed even with multi-cycle laser pulses when quantum interference occurs between different ionization paths of an atom [24,25], and another study demonstrated the CEP effect experimentally with multi-cycle RF pulses [26].CEP dependence in HHG with multi-cycle laser pulses was shown by contribution of long electron trajectories [27].The demonstration of CEP-dependent ATI with multi-cycle laser pulses would, thus, be a challenging task to reveal new physical processes.
In this investigation we present the experimental observation of CEP-sensitive ATI of xenon atoms exposed to 30-fs laser pulses containing more than 10 optical cycles.Since the CEP effects in ATI have been observed only with few-cycle pulses, our results indicate that an ionization process, occurring over many optical periods, can still be sensitive to CEP.The observed features of the CEP dependence shown here should provide the clues for finding such a new process.

Experimental setup for CEP-sensitive ATI measurement
We performed an ATI experiment with a CEP-controlled femtosecond Ti:sapphire laser centered at 820 nm and a velocity map imaging spectrometer (VMIS).As shown in Fig. 1(a), linearly polarized, 1-mJ, 30-fs laser pulses, after focused by a spherical mirror, irradiate at a repetition rate of 1 kHz the effused xenon atoms having a backing pressure of 10 −7 Torr, and as a result free electrons are produced.These electrons are brought to the microchannel plate coupled with a phosphor screen by a set of the electrodes denoted by G, E, and R in Fig. 1(a).From the CCD image of the screen obtained after subtracting its background signal, the momentum distribution of electrons is reconstructed with the BASEX method [28], assuming cylindrical symmetry about the laser polarization axis.An example of the reconstructed momentum distribution is shown in Fig. 1(b).The CEP of the laser pulses was controlled by the direct locking method [29].As the oscillator, stabilized by the direct locking method, produces pulses with identical CEP, any pulse selection was not required for amplifying pulses with identical CEP.The CEP was stabilized to a level of jitter below 200 mrad (over 10 consecutive laser shots) for more than several hours without any adjustment.Scanning over CEP was carried out with a phase step of π/12.Laser energy fluctuation was maintained within 2%.The CEP dependence of ATI in xenon atoms could, thus, be measured reliably while scanning CEP at different experimental parameters.
To find the CEP dependence of ATI spectra, the difference between the spectra for positive momenta (p y > 0) and that for negative momenta (p y < 0) was considered.Here y refers to the laser polarization axis specified in Fig. 1(a).As a normalized measure of the difference, the asymmetry parameter [17], denoted by A(E, φ ), was used: where E is the electron energy, φ the CEP of the laser pulse, and P + (P − ) the electron spectrum with the azimuthal angle of the momentum within 15 • from the positive (negative) y-axis, respectively.Beyond this angle the asymmetry became weak with the increase of angle.Any variation of A(E, φ ) over φ indicates the CEP dependence of ATI.

Experimental results and discussion
From the ATI spectra acquired with the VMIS an asymmetry map was obtained while changing CEP, as shown in Figs.2(a) and 2(b).For the electron energy below 11hω, where hω=1.51 eV is the laser photon energy, the asymmetry map shows linear dependence on CEP with slopes of about hω/2π.Even when other parameters such as laser chirp, intensity, and focusing position were varied, the slope did not change as far as the dependence was observed.The asymmetry was clearly observed in the intensity range from 3.5 × 10 13 W/cm 2 to 5.5 × 10 13 W/cm 2 , while the maximum asymmetry value was 0.03 as shown in Fig. 2(a).For the electron energy above 11hω, the CEP dependence was not observed while a modulation along the vertical axis was present.Such CEP-independent modulation might be attributed to the uneven gain of the spectrometer for the positive and negative directions or to some physical process.In contrast to the common understanding that CEP dependence appears only with few-cycle laser pulses, the ATI of xenon atoms clearly exhibited the dependence even with multi-cycle (30 fs) pulses.
The effect of laser chirp on the CEP dependence was also examined, as shown in Fig. 3, with different amount of chirp as well as its sign.The shortest pulse had a temporal width  3(a), the modulation became weaker than the case in Fig. 3(b), while the case for the negatively chirped 31-fs pulses still revealed the dependence in linear slopes as shown in Fig. 3(c).In Fig. 3(d), obtained with negatively chirped 35-fs pulses, the dependence became very weak at the low electron energy below 8hω and disappeared at higher energy.From the comparison between Figs. 3(a) and 3(c), it was found that the slope in the asymmetry map was hω/2π, maintaining the same value regardless of the amount of laser chirp and the slope did not change signs with chirp sign.It is contrary to the theoretical prediction by Abel et al. [18] based on the dispersion up to the second-order spectral phase.
To explain these results, we need to clarify the ionization regime by which the CEP dependence observed with multi-cycle laser pulses is governed.Because the laser intensity used in the experiment corresponds to the Keldysh parameter slightly larger than unity, the results could be affected by both tunneling ionization (TI) and multi-photon ionization (MPI).It has been known that, in the TI regime, the asymmetry in CEP-dependent events diminishes with the number of optical cycles contained in a laser pulse in theory [3,30] and experiment [16,23].Although we can expect from Yudin et al. [31] that the relative contribution from TI could be slightly more than that of MPI in our intensity range, the sub-cycle nature of the electron emission through TI would have the CEP dependence averaged out for laser pulses longer than a few cycles.Especially rescattered electrons generated through TI might form the CEP-insensitive photoelectron spectra in high-energy part in Fig. 2(a).On the other hand, the low-energy part of ATI spectra might have contribution from MPI process.As a consequence, the CEP-dependent feature  observed with multi-cycle laser pulses should be an event in the MPI regime.
For the description of the CEP dependence appearing in ATI with multi-cycle laser pulses of xenon, a multiphoton model, used by Abel et al. [18], was examined.This model is based on the interference between different quantum paths set by low and high frequency components of a driving laser.They reach the same final states with the number of absorbed photons differed by one, producing electron wave packets with opposite parities.This generates the asymmetry in ATI spectra as a result of the quantum interference between the two electron wave packets with different parities.The spectral phase of adjacent peaks in the photoelectron spectra contains a phase offset by the amount of the CEP of the pulse.Since the adjacent peaks in the asymmetry map can appear with the CEP shift of 2π, the slope hω/2π can be formed.This concept might account for the CEP-dependent ATI observed up to 17 eV with the multi-cycle laser pulses.
The quantum interference between different ionization paths, giving the asymmetry of ATI spectra, can be conveniently described in the frequency domain.Several different ionization pathways are possible, as an atom can absorb excessive photons to produce ATI electrons at different frequencies.The laser spectrum used in our experiments extended from 0.94hω to 1.07hω, where ω is the central frequency of the laser pulse.For example, the components of 0.95hω and 1.05hω meet the interference condition at 0 th -order in the ATI spectrum after absorbing 11 and 10 photons, respectively.Another example would be the components at 0.97hω and 1.02hω which have the same kinetic energy at 10 th -order peak in the ATI spectrum with 21and 20-photon absorption, respectively.Actual contributions are continuous around this transi-tion, so the eventual asymmetry map is the sum of all possible sets of combinations.Within the laser intensity aforementioned the CEP dependence due to the interference can occur for the kinetic energy below 11hω in the spectrum whenever the conditions are satisfied.Specifically for Figs.3(b) and 3(c) where the asymmetry is prominent for the photoelectron energy between 3hω and 9hω, the conditions are met with considerable spectral intensities.Because the asymmetry parameter contains the term, e iφ , where φ is the CEP, the change in CEP also follows the periodicity of 2π.Therefore, the CEP dependence observed using multi-cycle laser pulses originate from the quantum interference between electron wave packets produced with opposite parities.
A feature of the chirp dependence in our results, however, requires different approach from the one by Abel et al.In their model, with consideration of the quadratic spectral phase of a fewcycle pulse, the change in CEP caused an offset of peaks in the asymmetry map.On the other hand, in our experiments with multi-cycle pulses the slopes did not change in the asymmetry map when the amount or even the sign of the chirp changes as shown in Fig. 3.The chirpdependence of the CEP effect appeared in a simple pattern of linear slopes.For comparison, we analyzed the pulse by the FROG technique to estimate the group delay dispersion (GDD).Two asymmetry maps with GDD of about (+)230 fs 2 , (-)150 fs 2 , respectively, in Figs.3(a) and 3(c), are shown to have no major difference regardless of the sign and the amount of the chirp of the laser pulse.This discrepancy might come from the existence of higher-order spectral phase terms.A new theoretical model is, thus, needed to rigorously explain our experimental results carried out with multi-cycle laser pulses.

Conclusion
We experimentally demonstrated the CEP-dependent ATI of atoms with multi-cycle laser pulses.In contrast to the substantial evidences obtained by others that CEP dependence should involve sub-cycle processes using few-cycle laser pulses, our results showed that the CEP of a laser pulse could clearly affect multi-cycle processes.The ATI spectra of xenon atoms exhibited CEP dependence even for 30-fs laser pulses.The CEP-dependent asymmetry, examined for laser intensity and chirp, could be qualitatively explained using the quantum interference occurring between the two electron wave packets formed from different multiphoton ionization paths with opposite parities.The observation that the slope of the asymmetry map did not change its sign with the change of laser chirp sign indicated that the multiphoton model by Abel et al. could not explain the experimental results; such effects would be clarified in successive investigations.Our results will push the investigation of CEP-dependent ATI phenomena one step forward by instigating a new theoretical development.

Fig. 2 .
Fig. 2. (a) Asymmetry map as a function of CEP and electron energy and (b) electron spectra at the two directions along the laser polarization for the CEP, φ = π.The shortest 30-fs laser pulses with intensity of 5 × 10 13 W/cm 2 were applied.