Main

Strong-field light–matter interactions have revolutionized the ability to manipulate quantum systems on extremely short timescales. During the strong-field interaction, the basic properties of the medium can be substantially modified, altering the instantaneous quantum state of matter within less than one optical cycle1,2,3,4,5,6,7,8. Attosecond transient absorption spectroscopy has emerged to be one of the most potent metrology schemes in attosecond science. This scheme resolves the instantaneous response of a quantum system as it interacts with a laser field, and maps it into the absorption spectrum of attosecond pulses in the extreme-ultraviolet (XUV) regime. Transient absorption spectroscopy allows the simultaneous characterization of both fast dynamics (with attosecond precision) and narrow spectral features (with sub-electronvolt resolution9). Over the past decades, this scheme was applied in a large variety of systems, revealing fundamental attosecond-scale phenomena in atoms1,2,3,10,11,12,13,14,15,16,17,18,19,20, molecules21,22,23,24,25,26,27 and solids4,5,6,7,8,28,29,30.

Although attosecond transient absorption has been at the heart of attosecond science for more than a decade, it imposes fundamental challenges31. The primary challenge is set by the inevitable presence of multiple quantum paths, all of which are coherently mapped into the same absorption spectrum. Decoupling these different quantum pathways is instrumental to disentangling the complex dynamics that underlie the interaction. Transient absorption does not immediately offer a clear route to addressing this challenge. Here we present an approach to directly identify the dynamics of individual quantum paths by increasing the dimensionality of measurement.

As in many branches of physics, the complex properties of quantum phenomena can be revealed by retrieving the phase information, hidden in most experimental observables. Indeed, amplitude modulations of the transmitted attosecond pulses encode the transient absorption or gain. Phase modulations encode the transient change in the index of refraction, representing the transient phase, naturally lost in the intensity measurements. In the infrared (IR) range, the complex, multipath evolution of electronic wavefunctions in molecules was recovered by interfering the optical emission induced by the nonlinear interaction with an additional coherent reference field32,33,34. Pioneering studies in the XUV range have reconstructed the transient phase based on the Fano lineshape of the excitation35 or the Kramers–Kronig relations36, whereas a direct measurement resolved its evolution in free-induction decay37. Recently, complex attosecond transient absorption spectroscopy was demonstrated38, following the transient phase of XUV pulses on a femtosecond timescale, validating the Kramers–Kronig relations. However, retrieving the sub-cycle evolution of the transient phase in a broad range of phenomena—from sub-cycle band structure dynamics in solids and chemical shifts in molecules to interference of multiple quantum paths—remains a major challenge. Reconstructing the rich dynamics that underlie such phenomena requires the establishment of a direct scheme to resolve the full complex properties of the transient interaction with attosecond precision.

In this Article, we establish sub-cycle phase-resolved attosecond interferometry (SPRINT), integrating two fundamental schemes in attosecond science—attosecond transient absorption and XUV–XUV interferometry38,39,40,41,42,43,44,45. Transient interferometry enables us to recover the lost phase information, identify individual quantum paths induced in a light-driven system and isolate their coherent contribution. We first establish this scheme in helium atoms, demonstrating quantum channel separation and retrieving their individual temporal evolution. Next, we initiate a wavepacket composed of multiple excited states in neon and apply the SPRINT scheme to follow long-term electronic coherences. Finally, we apply a vectorial generalization of our scheme to topological materials. We theoretically demonstrate the ability to optically isolate the underlying anomalous current in light-driven topological materials, and resolve its temporal evolution with attosecond precision. Here transient interferometry provides a direct insight into the interplay of light-induced dynamics and topology, revealing substantial delays in the emission from the topological state, which are completely absent from the trivial one.

In transient absorption metrology, attosecond pulses are transmitted through a field-driven quantum system, mapping its instantaneous interaction with light into the transient amplitude and phase of the transmitted attosecond pulses. The nonlinear XUV–IR interaction modifies the transmitted attosecond pulses as a function of the two fields’ delay Δt, following E(ω, Δt) = A(ω, Δt)eiΔϕ(ω,Δt), where ω is the XUV frequency. XUV–XUV interferometry interferes these modified pulses with an additional, decoupled source of attosecond pulses, serving as a coherent reference, via ISPRINT(ω, Δt) = ∣A(ω, Δt)eiΔϕ(ω,Δt) + Eref(ω)∣2. This measurement provides direct access to the transient phase Δϕ(ω, Δt), allowing us to follow its evolution within the fundamental optical cycle with attosecond precision (Fig. 1a).

Fig. 1: SPRINT.
figure 1

a, Integrating attosecond transient absorption with XUV–XUV interferometry. A phase-locked XUV–IR (XUV 1 + IR) beam, with a relative delay Δt is focused into helium atoms, inducing a nonlinear interaction. The underlying dynamics are encoded in the transient amplitude and phase of the transmitted light, characterized by 2ωIR oscillations. Interfering the transmitted XUV field (black) with a reference XUV source (magenta) provides access to the transient phase Δϕ (Δt). Manipulating Δt encodes the transient amplitude and phase, mapped into the instantaneous amplitude and phase of the interferogram. b, Illustration of the nonlinear XUV–IR interaction. Harmonic 13 (magenta) is modified by multipath interference. These paths couple adjacent odd harmonics (harmonic 11 and harmonic 15 in orange and purple, respectively) via four-wave-mixing processes, involving two additional IR photons. Harmonic 15 is resonant with the 1s4p excited state. c, In an absorption-only measurement, the dynamics of all the three quantum paths are mapped into the 2ωIR Fourier peak, preventing access to their individual coherent contribution. In contrast, within SPRINT, the reference source interferes with each individual path, mapping its individual contribution onto a distinct Fourier peak. This peak identifies the absorbed XUV photon energy that initiates each path, simultaneously resolving its amplitude and phase evolution.

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Recovering the phase information enables us to directly decouple the various quantum paths induced by the nonlinear interaction, isolating their coherent contribution. We start with absorption-only measurements, emphasizing the fundamental limitation imposed by the lack of phase information. In the frequency domain, transient absorption is viewed as an internal quantum path interferometer46, each being characterized by a nonlinear process, converting an absorbed XUV frequency Ω to an emitted frequency ω. In the leading perturbative order, for centrally symmetric systems, each arm is composed of a single XUV photon and two IR photons, coupling neighbouring harmonic orders into the absorption spectrum (Fig. 1b). Scanning the XUV–IR delay controls the relative phase between the paths, leading to oscillations in the absorption spectrum with 2ωIR frequency, where ωIR is the angular frequency of the fundamental field. Although transient absorption induces an internal interferometer, it imposes a fundamental limitation—one cannot access the complex contribution of each individual quantum path.

Adding an external coherent source enables us to lift the degeneracy and isolate the coherent contribution of each path. Each quantum path accumulates a linear phase of eiΩΔt, which is dictated by the absorbed frequency Ω. The SPRINT signal at harmonic 13, for example, follows

$${I}_{{\rm{SPRINT}}}\left(H13,\Delta t\right)={\left\vert {\varepsilon }_{15}{{\rm{e}}}^{15{\rm{i}}{\omega }_{{\rm{IR}}}\Delta t}+{\varepsilon }_{13}{{\rm{e}}}^{13{\rm{i}}{\omega }_{{\rm{IR}}}\Delta t}+{\varepsilon }_{11}{{\rm{e}}}^{11{\rm{i}}{\omega }_{{\rm{IR}}}\Delta t}+{E}_{{\rm{ref}}}\right\vert }^{2},$$
(1)

where εi is the complex amplitude of each quantum path. Performing a Fourier analysis with respect to Δt allows us to map each path onto an isolated Fourier peak, identifying its complex contribution (Fig. 1c).

We demonstrate the SPRINT scheme via a one-dimensional approach, controlling a single delay line. This scheme allows for an attosecond-scale time-resolved measurement over a large temporal range. It consists of three primary stages (Methods). In the first stage, we prepare an attosecond pulse train (APT) via high-harmonic generation47, by focusing an intense IR laser field into a gas target. The IR and APT co-propagate and are refocused by a two-segment mirror that controls their relative delay Δt with attosecond resolution. In the second stage, the combined XUV–IR field is transmitted within a second gas cell, inducing a perturbative nonlinear XUV–IR interaction. Finally, the IR field is focused into a third gas jet, generating a secondary source of high-harmonic generation, serving as the reference field.

Figure 2 describes experimentally resolved transient interferometry in helium, focusing on harmonic 13. First, we perform the well-established transient absorption measurement by switching off the reference beam. Scanning Δt reproduces the expected 2ωIR oscillations1,3, having an ~1.3 fs period (Fig. 2a, d). Next, we perform XUV–XUV interferometry by removing the interaction cell. Figure 2b,e confirms that the signal is dominated by 13ωIR oscillations, corresponding to an ~200 as period. The weak Fourier peaks observed at (13 ± 1)ωIR are associated with a minute leak of IR intensity through the aluminium filter, being fully isolated in our Fourier analysis (Methods). Finally, we integrate both components of the interaction—transient absorption and XUV–XUV interferometry—via the triple-source interaction. Scanning Δt leads to 13ωIR oscillations that beat with 2ωIR periodicity (Fig. 2c). The Fourier analysis (Fig. 2f) reveals that the beating of the 2ωIR and 13ωIR oscillations forms two new background-free (13 ± 2)ωIR sidebands. The asymmetry of the (13 ± 2)ωIR sidebands reflects the transient amplitude and phase, being coupled in the frequency domain, as well as the symmetry breaking between the nonlinear mechanisms influencing harmonic 13. We can extract the transient phase by returning to the time domain. Applying the analytic signal analysis48 enables us to isolate the transient phase and follow its evolution within the IR optical cycle (Supplementary Section 3). The retrieved transient phase is presented in Fig. 2g, showing a clear sub-cycle evolution, dominated by the expected 2ωIR oscillation.

Fig. 2: Resolving the sub-cycle transient phase in helium.
figure 2

a, Attosecond transient absorption. Intensity of harmonic 13 in the absence of the reference source. Negative delays correspond to the XUV preceding the IR. The 1.3 fs periodicity corresponds to the 2ωIR oscillations. For visibility, we focus on several oscillation periods where the XUV precedes the IR by ~20 fs. b, Attosecond interferometry. Interferometric signal of harmonic 13 in the absence of nonlinear interaction with helium atoms. The 200 as periodicity corresponds to the optical period of harmonic 13. c, Attosecond transient interferometry, obtained with all three gas sources. The beating pattern between the 1.3 fs and 200 as periodicities encodes the transient phase information. d–f, Fourier analysis of a–c (d–f, respectively) focusing on the low- and high-oscillation frequencies. g, Retrieved transient phase of harmonic 13, presenting a pronounced sub-cycle phase oscillation at 2ωIR. h, Experimentally retrieved temporal evolution of the envelope of the resonant sideband 15 in harmonic 13. i, Reconstructed oscillating waveform of the generated field at several representative values of the delay, as highlighted in h. The waveforms are vertically shifted for visibility.

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As described by equation (1), the dynamics are determined by the coherent summation of quantum paths, each being characterized by a frequency pair (Ω, ω), converting an absorbed XUV frequency Ω into an emitted frequency ω. The SPRINT scheme reveals the amplitude and phase of each frequency component in this plane, allowing the identification of individual quantum paths. In the following, we focus on the (13 ± 2)ωIR sidebands. Here sideband 11 follows the same diagonal slope as the linear signal, shifted by 2ωIR, revealing the dominant role of the off-resonant nonlinear mechanism. In contrast, sideband 15 of harmonic 13 shows a rich spectral pattern, indicating the role of multiple interfering paths. Such response reflects the resonant excitation by harmonic 15, profoundly modifying the nonlinear interaction.

The ability to recover the complex information associated with each quantum path allows direct access to its temporal evolution. Fourier filtering each sideband and performing a two-dimensional inverse Fourier transform projects this path into the time domain, reconstructing its temporal waveform. Focusing on the resonant excitation mapped to sideband 15, we present its reconstructed slowly varying amplitude envelope in Fig. 2h, whereas Fig. 2i presents the reconstructed field itself at several representative values of the delay. As in spectral interferometry with an external reference field49, this reconstruction is performed up to a one-dimensional convolution with the reference field, which represents the temporal analogue of the well-known point spread function of an optical microscope.

Figure 2h reveals the role of the resonant dynamics. Its evolution in the time and delay plane (t, Δt) follows a diagonal path, peaking at Δt ≈ −20 fs (negative delays correspond to the XUV arriving before the IR), followed by an additional extended horizontal feature at Δt < −40 fs. Solving the time-dependent Schrödinger equation, in a restrictive excitation model50 (Supplementary Section 4), reveals the origin of this response. At the peak of the laser pulse, the resonant 1s4p level is strongly Stark shifted to higher energy3, being effectively off-resonant with respect to harmonic 15. However, after ~20 fs, the Stark shift subsides and this level once again lies within the bandwidth of harmonic 15. Such resonant dynamics have been observed in XUV free-induction decay and high-harmonic generation metrology, inducing the so-called Stückelberg oscillations51,52. Our analysis time resolves the formation of these oscillations in an XUV excitation. Finally, the horizontal feature occurs when the XUV–IR overlap is negligible, corresponding to the perturbed free-induction decay regime9.

In the next step, we apply SPRINT to resolve electronic coherences in neon53, demonstrating the ability of this scheme to probe more complex dynamics that are extremely challenging to retrieve by standard transient absorption measurements12. We resonantly excite a wavepacket composed of several electronic states in the energy range of 20.5–20.8 eV, lying within the bandwidth of harmonic 13. A delayed IR field maps their coherence into the emission of harmonic 15 via the four-wave-mixing mechanism. Finally, the coherent superposition of the multistate excitation is resolved via the SPRINT scheme (Fig. 3a,b). A Fourier analysis with respect to the delay reveals the underlying electronic coherences (Fig. 3c), focusing on sideband 13 of harmonic 15. In contrast to the helium results, in neon, the sideband is characterized by several sharp features along the horizontal axis (excitation frequency), each contributing to emission in the range of ~24.2–24.4 eV. The main features are centred at 20.57 eV and 20.66 eV, corresponding to the spin–orbit split (2p1/2)5s and (2p3/2)5s excited states, respectively, and at 20.71 eV ((2p3/2)4d/f) and 20.76 eV ((2p3/2)5p). Indeed, all of these states are coherently mapped into the same emitted frequencies in harmonic 15.

Fig. 3: Resolving electronic coherences in neon.
figure 3

a, Illustration of the pulse sequence in SPRINT, focusing on large delays Δt. Transient absorption relies on resolving the interference between the excitation pulse (magenta) and the nonlinear generated field (purple). Their large temporal separation reduces their interference signal, hindering its detection. In contrast, SPRINT resolves the interference of the generated field with the external reference, both being synchronized to the IR pulse, enhancing the detection of coherences at large delays. b, Harmonic 13 of an APT resonantly excites a wavepacket, composed of several spin–orbit split excited states in neon in the range of 20.5–20.8 eV. A delayed IR pulse maps its coherent evolution onto harmonic 15 via four-wave mixing. c, Fourier analysis of the SPRINT result, focusing on this four-wave-mixing process, revealing the coherent contribution of multiple electronic resonances. The inset presents a broader view of the horizontal axis, also showing the linear interferometric signal. d, Reconstruction of the evolution of electronic coherences with delay across multiple timescales. The measurement reflects quantum beats over tens of femtoseconds, 2ωIR oscillations corresponding to the four-wave-mixing timescale and attosecond beating at the XUV frequency itself (inset).

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The SPRINT measurement enables us to reconstruct the temporal evolution of this process (Fig. 3d). This result is obtained by applying a Fourier filter around the resonant features and around the linear Fourier peak. For simplicity, we integrate over the optical frequency in the range of 24.25–24.35 eV, focusing on the evolution with delay. The reconstructed dynamics are dominated by three distinct timescales, simultaneously captured by our measurement. The longest of these reflects the electronic coherences, dictated by the spectral separation between the resonances, evolving during tens of femtoseconds. These so-called quantum beats46 are highly visible in our measurement, reflected as periodic revivals in the interferometric coherence. Next, we observe the 1.3 fs timescale, corresponding to the 2ωIR oscillations associated with the four-wave-mixing process. Finally, the inset in Fig. 3d shows the attosecond timescale, corresponding to the optical period of harmonic 15 itself.

Despite these coherences being well resolved by SPRINT, they are not visible in the transient absorption signal, represented by a 2ωIR Fourier peak. What is the fundamental difference between SPRINT and transient absorption that limits their detection? An intuitive answer can be obtained in the time domain (Fig. 3a). Electronic coherences are commonly resolved at large time delays Δt. Transient absorption resolves them by interfering the generated signal with the excitation field, separated by Δt. However, performing a high-contrast interferometric measurement between two signals separated by large delays is challenging. SPRINT overcomes this limitation by interfering the generated signal with the external reference, which is synchronized with the generated field, for all delays. Therefore, SPRINT is ideally suited to resolve lasting coherences, allowing their high-contrast interferometric measurement, over a large temporal dynamic range.

In the final stage, we theoretically demonstrate a vectorial generalization of the SPRINT scheme, and apply it to probe ultrafast dynamics in topological systems. The discovery of topological states of matter is at the heart of a large variety of fundamental condensed-matter phenomena54. Integrating topology with attosecond metrology raises a fundamental question: what is the link between the topological state of matter and the dynamical properties of its response? Pioneering studies have revealed the origin of ultrafast dynamics in topological systems55,56,57,58,59. In these systems, the Berry curvature generates an anomalous electronic current, induced orthogonally to the driving field. Establishing an all-optical measurement of this current would reveal its temporal evolution on ultrafast timescales.

Vectorial SPRINT resolves the complex optical emission—both phase and amplitude—induced by the anomalous currents via the interference of the optical emission with an orthogonally polarized external reference field. This scheme can be directly realized by a simple 90° rotation of the IR polarization between the sources60. The interference signal provides two important advantages. First, it serves as a heterodyne detector of the weak orthogonal polarization component generated by the system, allowing the identification and isolation of the anomalous current’s contribution. Second, as in scalar SPRINT, it identifies and decouples the multiple quantum paths that contribute to this anomalous emission, enabling their temporal reconstruction.

The vectorial SPRINT signal follows

$${I}^{\,{\rm{SPRINT}}}(\omega,\Delta t)={\Big\vert}\mathop{E}\nolimits_{{\rm{in}}}^{\,(x)}(\omega,\Delta t)+{E}_{{\rm{gen}}}^{\,(x)}(\omega,\Delta t){\Big\vert}{\scriptstyle{2}\atop}+{\Big\vert}{E}_{{\rm{gen}}}^{\,(y)}(\omega,\Delta t)+{E}_{{\rm{ref}}}^{\,(y)}(\omega){\Big\vert}{\scriptstyle{2}\atop},$$
(2)

where we have decomposed the transmitted field as \(\overrightarrow{E}=\left({E}_{{\rm{in}}}^{\,(x)}\right.\)\(+\left.{E}_{{\rm{gen}}}^{\,(x)}\right)\hat{x}+{E}_{{\rm{gen}}}^{\,(y)}\,\hat{y}\), \({\overrightarrow{E}}_{{\rm{in}}}\) is the incident excitation field and \({\overrightarrow{E}}_{{\rm{gen}}}\) is the emission due to the induced current. In the frequency domain, \({\overrightarrow{E}}_{{\rm{gen}}}\) is directly proportional to the induced current, encoding the anomalous transient current, dictated by the topological state of the system. Note that the x-polarized term in equation (2) is equivalent to a transient absorption measurement, whereas transient interferometry is directly performed along the \(\hat{y}\) direction, leading to oscillations in the XUV frequency range. Therefore, a Fourier analysis with respect to Δt allows us to separate these two terms. The x-polarized term is mapped into the low-frequency regime and the y-polarized term is mapped into the high-frequency regime, allowing its isolation without an XUV polarizer.

We simulate ultrafast dynamics in topological systems using the prototypical example of the Haldane model61, with an additional deeply bound band (Supplementary Section 5 provides a complete description). The transient currents are induced by an x-polarized attosecond pulse train and a y-polarized ~800 nm few-cycle pulse, whereas the transmitted radiation interferes with the y-polarized external reference (Fig. 4a). We calculate the induced emission \({\overrightarrow{E}}_{{\rm{gen}}}\) as a function of the XUV–IR delay Δt. We focus on the comparison between a topological state (topological parameter, λ = 0.95; Supplementary Section 5) and a trivial state (λ = 1.05), in the vicinity of the topological phase transition (λ = 1).

Fig. 4: Probing topological material via vectorial SPRINT.
figure 4

a, An x-polarized attosecond pulse train in the XUV range (black) and a y-polarized IR pulse (red) interact with a Haldane solid in its topological or trivial phase. The nonlinear interaction induces coherent XUV emission in both polarization components (black and orange). The y-polarized component is heterodyned by its interference with an external reference XUV pulse (magenta). b, Fourier analysis of the orthogonal SPRINT signal, revealing the individual spectral contributions of distinct wave-mixing processes. FWM±, four-wave-mixing processes. c, Reconstructed waveform of the y component of the oscillating electric field, comparing between the topological and trivial cases for the FWM− process. A few cycles of the IR central frequency are plotted as a guide to the eye. d, Same data as c, for the x-polarized component. After ~6 fs, the y component of the two waveforms is shifted by ~π. Such a shift is completely absent in the x-polarized components.

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Figure 4b presents the Fourier transform of the vectorial SPRINT scheme with respect to Δt. As in the scalar case, this representation maps the different quantum paths that contribute to the interaction. The generated field \({\overrightarrow{E}}_{{\rm{gen}}}\) is composed of different nonlinear mechanisms associated with upconversion, downconversion or intraharmonic four-wave-mixing processes. The various nonlinear processes map into different sidebands in the two-dimensional frequency plane (Fig. 4b). The bright central diagonal line follows ω = Ω and is therefore dominated by the linear response, slightly broadened by intraharmonic four-wave-mixing processes. The two neighbouring diagonal sidebands, following ω = Ω ± 2ωIR, represent four-wave-mixing processes (FWM±, respectively).

The ability to separate the different processes enables us to retrieve their individual dynamics. By taking cuts in this plane, along the diagonal lines, and performing an inverse Fourier transform, we can retrieve their temporal evolution. In the following, we focus on the FWM− channel (Fig. 4b), having a remarkable dynamical response to the topological phase transition. Figure 4c presents the inverse Fourier transform of this diagonal cut, comparing between the trivial (red line) and topological (blue line) states. The temporal evolution of the two states shows a striking difference. After approximately 6 fs, the topological and trivial states begin to oscillate out of phase, and remain out of phase for the duration of the signal. For comparison, we plot the emission along the parallel direction (Fig. 4d). As can be clearly observed, the temporal evolution—both amplitude and phase—are almost identical as we switch from the trivial to the topological states.

A frequency analysis of the FWM− process reveals the origin of these dynamics. The orthogonal emission undergoes an ~π phase shift of the Fourier peak associated with resonant XUV absorption into the K valley (19ωIR), dominated by a strong Berry curvature that flips its sign across the topological phase transition55,61. In contrast, this phase shift is absent in the parallel component (Supplementary Section 5). This result can be understood by its analogy to transport measurements. In such experiments, the anomalous orthogonal current reveals the topological state of the material, corresponding to the so-called anomalous Hall currents. Indeed, our measurement represents an ultrafast optical version of this scheme. The orthogonally polarized IR field acts with or against the anomalous velocity of the electrons, amplifying its signature in the experimental results. The resultant orthogonal current is then heterodyned by the interference with the orthogonal reference and enables us to reveal its dynamical properties.

To conclude, in this study, we have established attosecond transient interferometry, integrating attosecond transient absorption with XUV–XUV interferometry. This scheme follows the sub-cycle evolution of the transient phase, enabling us to decouple the underlying quantum paths and reconstruct their individual temporal evolution. Attosecond transient interferometry is ideally suited to resolve sub-cycle dynamics as well as long-term electronic coherences with attosecond precision. Applying it to topological systems establishes a new and exciting approach to isolate the anomalous current and resolve the interplay of its dynamics with the system’s topology.

Attosecond transient interferometry holds the potential to considerably extend the scope of attosecond metrology, uncovering new phenomena, so far hidden in absorption-only measurements. The unmediated access to the underlying dynamics will identify deviations from theoretical approximations, resolving the influence of multielectron interactions62, electronic coherences20 or non-adiabatic transitions27. This scheme can be directly applied to laser-driven solids in which the band structure can be transiently modified63,64 within the optical cycle, disentangling the multiple quantum paths and resolving their coherent properties and coupling mechanisms. Probing the vectorial dynamics of electronic currents will reveal the dynamical symmetry properties of a large range of light-driven quantum systems65,66.

Methods

Supplementary Fig. 1 presents a schematic of the experimental setup for SPRINT. An amplified Ti:sapphire laser system operated at a 1 kHz repetition rate delivers approximately 30 fs pulses at a central wavelength of 792 nm, generating the IR field. The laser beam is focused into a continuous-flow gas cell, generating the first APT. We spatially separate the co-propagating laser field and APT beams with a thin aluminium filter (200 nm thickness). Both beams are then refocused and recombined by a curved two-segment mirror (75 cm focal length) into the interaction gas cell, inducing the nonlinear XUV–IR interaction. This cell is placed upstream from the focal plane of the IR beam to reduce its intensity, thereby suppressing XUV emission by the IR alone. The third gas source (continuous-flow glass nozzle, orifice of approximately 10 µm), is placed approximately two times the IR Rayleigh length downstream. The higher intensity enables the generation of the reference APT. Following the cutoff of the harmonics in the second APT source, together with the geometry of the beam, we calibrate the IR intensity at the interaction cell as 10 TW cm–2. In the helium (neon) experiments, both APT sources are generated in krypton (argon). The inner part of the focusing mirror reflects the APT in the spectral range of 17–51 eV. A piezo-stage controls the temporal delay Δt with a step size of 6.7 as and an accuracy of about 1 as, over a range of 200 fs. The co-propagating APT beams are spectrally resolved by a flat-field aberration-corrected concave grating and recorded by a microchannel plate detector, imaged by a charge-coupled device camera.