⇦Chinese Physics Letters, 2023, Vol. 40, No. 6, Article code 063201 Enhanced Extreme Ultraviolet Free Induction Decay Emission Assisted by Attosecond Pulses Wenkai Tao (陶文凯), Li Wang (王力), Pan Song (宋盼), Fan Xiao (肖凡), Jiacan Wang (王家灿), Zhigang Zheng (郑志刚), Jing Zhao (赵晶), Xiaowei Wang (王小伟)*, and Zengxiu Zhao (赵增秀)* Affiliations Department of Physics, National University of Defense Technology, Changsha 410073, China Received 25 March 2023; accepted manuscript online 25 April 2023; published online 16 May 2023 *Corresponding authors. Email: xiaowei.wang@nudt.edu.cn; zhaozengxiu@nudt.edu.cn Citation Text: Tao W K, Wang L, Song P et al. 2023 Chin. Phys. Lett. 40 063201    Abstract We demonstrate the extreme ultraviolet free induction decay emission that can be significantly enhanced by employing isolated attosecond pulses. The near infrared pulses are applied to excite the neon atoms into Rydberg states coherently, and isolated attosecond pulses are used to manipulate populations of the Rydberg states and the subsequent free induction decay process. The time resolved experimental measurement of dependence of the resonance emission yield would help to understand the buildup dynamics of population of excited states. The enhancement assisted by attosecond pulses can serve as a mechanism to develop high-flux extreme ultraviolet light sources.
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 DOI:10.1088/0256-307X/40/6/063201 © 2023 Chinese Physics Society Article Text The recombination of a liberated free electron to its ionic core in the presence of strong laser field radiates high-order harmonics (HHs), which have proven themselves as powerful extreme ultraviolet (XUV) light sources in terms of high photon energy up to water window,[1-3] ultrashort pulse duration down to attoseconds,[4-6] versatile spectroscopy in molecular orbital imaging,[7,8] and electron dynamics probing.[9,10] Different from HHs with large bandwidth, line emission known as XUV free induction decay (XFID),[11,12] which can be generated alongside HHs during the same strong-field process, has been drawing more and more attention due to its potential applications in research of Rydberg state excitation, EUV imaging, and lithography. When the electron revisits the ionic core after tunneling ionization in strong laser fields, it has a chance to reside in Rydberg orbitals instead of the ground state. The decay of the Rydberg states gives rise to coherent XFID emissions. Therefore, the key to improve the XFID yields is to increase the Rydberg state population by optimizing the laser parameters, since the subsequent decay is field free and hence unmanipulatable. Strong field Rydberg state excitation is initially considered as resonant transition from the ground state to the ac-Stark shifted Rydberg states[13,14] via multi-photon absorption. Efficient excitation of Rydberg states can only occur at specific laser intensity leading to channel closing[15-17] as observed in the above-threshold ionization.[18,19] It is found later that atomic potential is strongly distorted by the instantaneous strong laser field, resulting in unavoidable tunneling ionization and consequently the failure of the perturbative picture.[20] Part of the ground state wave function leaks into the continuum within subcycle time scale and can be subsequently recaptured into the excited states, namely frustrated tunneling ionization (FTI).[21] Since field ionization is involved, the principle quantum number and angular momentum distribution of Rydberg wavepacket are expected to depend crucially on the ground state orbital shape,[22] the pulse duration,[23] the laser ellipticity,[21,24] the carrier-envelope phase,[25] and trajectory interferences.[26] On the other hand, XFID can also be driven from atoms or molecules by XUV pulses with bandwidth covering the energy level of Rydberg states. A coherent superposition of the ground state and Rydberg states can be created by the input XUV pulses. The XFID generated from the decay of Rydberg states copropagates with the transmitted XUV pulses, and the destructive interference in the spectrum manifests as absorption. However, the XFID emission can be separated from the XUV pulses by introducing a non-uniform spatial phase with a near-infrared (NIR) laser pulse.[27] Moreover, perfect phase matching of XUV pulses is achievable in the vicinity of Rydberg energy levels, allowing for the generation of intense XFID emission.[28] The coherent Rydberg wavepackets established by strong field laser pulses and XUV pulses may interfere with each other, providing a way to manipulate the XFID emission. In this Letter, we experimentally study the XFID emission by populating Rydberg states with both intense NIR pulses and XUV attosecond pulses. It is found that if the Rydberg wavepacket is populated with strong laser fields in advance, the XFID emission is enhanced by 2–3 factors by the later attosecond XUV pulses. The time-resolved measurement of XFID yield versus NIR-XUV delay would help to understand the buildup dynamics of coherent excitation of Rydberg states. The enhancement assisted by XUV pulses can also serve as a mechanism to develop high-flux XUV light sources. The experiments were carried out with an attosecond transient absorption spectroscopy (ATAS) setup, as illustrated in Fig. 1. Intense few-cycle (6 fs) NIR pulses centered at 750 nm with energy of 1.8 mJ were produced via a helium-filled hollow-core fiber, which was fed with 4.2 mJ, 25 fs pulses by a 10-pass amplifier working at repetition rate of 1 kHz. The NIR pulses were then split into two arms with a $50\!:\!50$ beam splitter (BS). One of them is used to generate isolated attosecond pulses (IAPs) by going through polarization gating optics (PGO) and getting focused in a gas cell (GC1) filled with 70 mbar krypton. With proper laser intensity and gate width, continuous spectrum covering from below 17 eV to above 48 eV was generated, as shown in Fig. 2(a). In the wide continuum spectrum, only the spectral components around 20 eV is crucial for populating neon atoms. Then the isolated attosecond pulses were separated from the residual NIR laser pulses with a metal foil (MF), and were focused onto neon atoms (60 mbar) in the second gas cell (GC2). The other arm, after passing through a piezo-stage driven delay line (DL), was focused on the second cell by a fused-silica lens (FL), producing intense laser fields up to $2 \times 10^{15}$ W/cm$^2$. The two arms were combined with a hole-drilled mirror (HM). The transmitted IAPs along with the XFID emissions were detected by an XUV spectrometer,[29] which consists of a flat-field grating (FFG) and a microchannel plate (MCP) imaging detector. The delay between the IAP arm and XFID arm was actively stabilized by monitoring the interference fringes of a green continuous wave going through both arms of the Mach–Zehnder interferometer,[30] and the DL with sub-nanometer positioning accuracy allows for fine delay adjustment between the two arms with attosecond precision.
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Fig. 1. The experiments were performed with an attosecond transient absorption spectroscopy setup: The 1.8 mJ, 6 fs NIR driving pulses were first split by a $50\!:\!50$ beam splitter (BS). The IAPs were gated from a half-cycle linear-polarized window formed by polarization gating optics (PGO) with krypton atoms filled in the first gas cell (GC1). After being separated from the residual NIR pulses with an aluminum metal foil (MF), the IAPs were focused by a gold-coated toroidal mirror (TM) onto the second cell (GC2) filled with neon atoms. The NIR driving pulses were combined with IAPs by a hole-drilled mirror (HM) after going through a delay line (DL) and fused-silica lens (FL). The FID emission together with the transmitted IAPs was spectrally detected with an XUV spectrometer, which consists of a flat-field grating (FFG) and a microchannel plate (MCP) imaging detector.
Both the emitted XFID and IAP absorption spectra are recorded simultaneously by the spectrometer. Although they overlap with each other spectrally, they are none the less distinguishable, since the divergence angle of XFID emission is much larger than that of the IAP due to the large phase accumulated during the long-time excursion of the liberated electron before recapturing into Rydberg states, i.e. during the FTI process. To better visualize the emission (XFID) and absorption (IAP), we use the absorbance: \begin{align} \alpha \propto -\ln\frac{I_{\rm s}}{I_{\rm c}}, \tag {1} \end{align} where $I_{\rm c}$ is spectral intensity of IAP continuum, $I_{\rm s}$ is the spectral intensity of the signal, i.e., the total XUV intensity containing both XFID emission and transmitted IAP after the neon gas cell. The NIR laser intensity was set to be $6 \times 10^{14}$ W/cm$^2$ with an iris to produce observable XFID emissions. The absorbance was measured when the NIR pulses arrived earlier and later than the IAPs, as shown in Figs. 2(b) and 2(c), respectively. According to Eq. (1), the transmitted IAPs exhibit positive (blue) absorbance, while emitted XFID emissions exhibit negative (red) absorbance. It is clear to see that the IAPs are well collimated with 5 mrad divergence angle, within which absorption dominates. Narrow band XFID line emissions are observable only in large divergence angles. The observed XFID emission lines are identified as the decay of spin-orbit split Rydberg states $^2\!P_{1/2}ns/nd$ and $^2\!P_{3/2}ns/nd$, as labeled in the upper axis in Fig. 2(b). However, the bound state absorption lines in the IAP spectrum are barely perceptible due to their narrow spectral width. For the case that NIR pulses arrives later as shown in Fig. 2(c), the absorption lines in IAP spectra are more obvious due to spectral broadening by the following NIR pulses, which is consistent with the previous ATAS measurements.[31-33] The XFID spectra with NIR pulses only are almost identical to Fig. 2(c). More importantly, the XFID emissions are much weaker compared to the case shown in Fig. 2(b), which suggests interesting coherent interaction between the Rydberg wavepackets excited by NIR pulses and IAPs. To reveal the behind physics, the XFID emission spectra were acquired as a function of the delay between the NIR pulses and IAPs, as shown in Fig. 3(a). Negative delay indicates that the IAP arrives earlier than the NIR pulse. Each spectrum for a certain delay is integrated for 3000 laser shots to improve the signal-to-noise ratio. Since the XFID signals have complex spatial distribution as shown in Fig. 2(b), the spectra lineout is averaged within the deviation angle range from $-10$ to $-$7.5 mrad, where the XFID signal is most intense.
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Fig. 2. (a) The continuum spectra of the IAPs used in the experiments. Although the spectrum covers from below 17 eV to above 48 eV, only the spectral components around 20 eV are crucial for populating neon atoms. (b) The measured absorbance when the NIR pulses arrived earlier than the IAPs. (c) The measured absorbance when the NIR pulses arrived later than the IAPs. The positive absorbance indicates absorption, while negative absorbance indicates emission.
The delay step size is 141 as with rms time jitter of 40 as. However, the zero delay position cannot be determined experimentally. To determine the time zero, the spectra of transmitted IAPs, i.e., the ATAS measurements, are also extracted from the delay-dependent spectra, since attosecond transient absorption spectrums (ATASs) of neon atoms have been well studied before.[34,35] By averaging the spectra within the divergence angle from $-5$ to 5 mrad, the ATASs of the neon atoms are obtained, as shown in Fig. 3(b). The strong energy level modulation around zero delay is evident, and the precise position of delay zero can be determined by comparing our measurement with time-dependent Schrödinger equation calculation in Fig. 2(d) of Ref. [34]. Note that the experimental neon ATAS in Fig. 3(b) is quite different from the previous experiments, since the NIR laser intensity in this work is much stronger than before to populate Rydberg states via FTI. In conventional ATAS experiments, the NIR pulses, which introduce weak couplings between excited states, should be kept at moderate intensity far below the level for ionization. However, the time zero is still recognizable, thanks to the giant AC-stark shift. Although there are rich electronic dynamics in Fig. 3(b), it is difficult to extract Rydberg state population from the ATAS spectra since the NIR pulses introduce lots of coupling between excited states and the continuum states, which results in energy level broadening, shifting and splitting.
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Fig. 3. (a) The measured XFID emission spectra as a function of the delay between the NIR pulses and IAPs with delay step size of 141 as and time jitter of 40 as. Negative delay indicates that the IAP arrives earlier than the NIR pulse. The FID emission is distinctly enhanced when the IAP arrives after the NIR pulse, and the onset of the enhancement starts at the delay time of about 10 fs. (b) The ATAS of neon atoms extracted from the delay-dependent measurements by averaging the spectra within the divergence angle from $-5$ to 5 mrad.
After calibrating the delay axis of Fig. 3(a), it can be seen that the FID emission is distinctly enhanced by adding an IAP after the NIR pulse. The onset of the enhancement starts at the delay time of about 10 fs for almost all the FID emission lines. As addressed earlier, the observed FID emission signals with large divergence angle are caused by the decay of Rydberg states populated in FTI process under the driven of NIR laser fields. Therefore, the earlier arrival of the IAPs has almost no influence on FID yield, which was generated later by the NIR pulses. Furthermore, the Rydberg electrons excited with IAPs would be ionized by the following NIR pulses, so no enhancement is expected for negative delay. Nevertheless, when NIR pulses are imposed on neon atoms earlier, Rydberg wavepackets are created and their decay lasts for more than hundreds of femtoseconds. When IAPs arrive later, resonant transitions occur to coherently increase amplitude of the Rydberg wavepackets, and hence increase the FID emission. According to the FTI picture, the electron is captured to the Rydberg orbitals at the end of the laser pulses, i.e., about 10 fs away after the peak for the used 6 fs pulses. This is consistent with the onset moment of the enhancement. The enhancement factors are different for different emission lines according to Fig. 3(a). The delay-dependent XFID yields are illustrated in Fig. 4 for the decay of Rydberg states $^2\!P_{3/2}4s$ (circle), $^2\!P_{1/2}4s$ (square), $^2\!P_{3/2}5s$ (upward triangle), $^2\!P_{1/2}5s$ (downward triangle), and summation of $^2\!P_{3/2}6s$–$8s$ (plus). The two 4 s FID lines have similar increment behavior, and the other three are almost identical. Thus, two S-shape increasing curves with form $f(x)=a/(1+e^{-x})+b$ are fitted to demonstrate the increment of $4s$ (blue) and $5s$–$8s$ (green) states, which suggest an enhancement factor of 2 for $4s$ states and 3 for $5s$–$8s$ states.
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Fig. 4. The delay-dependent XFID yields for the decay of Rydberg states $^2\!P_{3/2}4s$ (circle), $^2\!P_{1/2}4s$ (square), $^2\!P_{3/2}5s$ (upward triangle), $^2\!P_{1/2}5s$ (downward triangle), and summation of $^2\!P_{3/2}6s$–$8s$ (plus). Two S-shape increasing curves are fitted to demonstrate increment of $4s$ (blue) and $5s$–$8s$ (green) states, which suggest an enhancement factor of 2 for $4s$ states and 3 for $5s$–$8s$ states.
The enhancement of FID emission in strong laser fields with the help of IAPs is of great importance to generation of narrow band XUV emissions. Although an XUV monochromator[36,37] is designed to select specific spectral components with high resolution, it decreases the energy with efficiency lower than 10%. The proposed scheme in this work, together with the previously revealed phase matching mechanism,[28] is promising to improve the photon flux of XUV line emissions. However, further investigations, e.g., the coherent interference between the Rydberg wavepackets created by NIR and IAP, the dependence of enhancement factor on IAP/NIR intensity, the IAP introduced phase modulation of NIR populated Rydberg states, and the physics behind the different behaviors for different Rydberg states and so on, are needed to fully understand the enhancement mechanism. In conclusion, we have demonstrated the enhancement of FID emission using an IAP in addition to the NIR driving pulse. When the IAP arrives at the neon atoms later than the NIR driving pulse, the FID emissions are enhanced by 2–3 factors. The dependence of the FID emission yield on the NIR-XUV delay would help to understand the buildup dynamics of population of excited states. The enhancement assisted by XUV pulses can also serve as a mechanism to develop high-flux vacuum ultraviolet light sources. Acknowledgments. This work was supported by the National Key Research and Development Program of China (Grant No. 2019YFA0307703), and the National Natural Science Foundation of China (Grant Nos. 11974426 and 12234020). References Generation of Coherent Soft X Rays at 2.7 nm Using High HarmonicsCoherent Water Window X Ray by Phase-Matched High-Order Harmonic Generation in Neutral MediaHigh efficiency ultrafast water-window harmonic generation for single-shot soft X-ray spectroscopy53-attosecond X-ray pulses reach the carbon K-edgeStreaking of 43-attosecond soft-X-ray pulses generated by a passively CEP-stable mid-infrared driverGeneration of 88 as Isolated Attosecond Pulses with Double Optical Gating*Tomographic imaging of molecular orbitalsGeneralized molecular orbital tomographyReal-time observation of valence electron motionAttosecond spectroscopy of size-resolved water clustersPhase-resolved two-dimensional spectroscopy of electronic wave packets by laser-induced XUV free induction decayStrong-field-approximation model for coherent extreme-ultraviolet emission generated through frustrated tunneling ionizationExcitation of Rydberg wavepackets by short laser pulsesAbove-threshold ionization with subpicosecond laser pulsesRydberg states in the strong field ionization of hydrogen by 800, 1200 and 1600 nm lasersFine structures in the intensity dependence of excitation and ionization probabilities of hydrogen atoms in intense 800-nm laser pulsesObservation of dynamic Stark resonances in strong-field excitationDetailed comparison of above-threshold-ionization spectra from accurate numerical integrations and high-resolution measurementsObservation of large populations in excited states after short-pulse multiphoton ionizationCoulomb Potential Recapture Effect in Above-Barrier Ionization in Laser PulsesStrong-Field Tunneling without IonizationOrbital effects in strong-field Rydberg state excitation of N2 , Ar, O2 and XeControlling quantum numbers and light emission of Rydberg states via the laser pulse durationEllipticity dependence of neutral Rydberg excitation of atoms in strong laser fieldsCoherent extreme-ultraviolet emission generated through frustrated tunnelling ionizationElectron dynamics in laser-driven atoms near the continuum thresholdSpace–time control of free induction decay in the extreme ultravioletCoherent phase-matched VUV generation by field-controlled bound statesIn situ calibration of an extreme ultraviolet spectrometer for attosecond transient absorption experimentsDelay control in attosecond pump-probe experimentsSub-cycle Oscillations in Virtual States Brought to LightTime-domain perspective on Autler-Townes splitting in attosecond transient absorption of laser-dressed helium atomsResonance effects and quantum beats in attosecond transient absorption of heliumSubcycle laser control and quantum interferences in attosecond photoabsorption of neonAttosecond transient absorption probing of electronic superpositions of bound states in neon: detection of quantum beatsTime-delay compensated monochromator for the spectral selection of extreme-ultraviolet high-order laser harmonicsDesign Study of Time-Preserving Grating Monochromators for Ultrashort Pulses in the Extreme-Ultraviolet and Soft X-Rays
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