# Full Characterization of a Molecular Cooper Minimum Using High-Harmonic Spectroscopy
## 1 Introduction  
Much of the focus of attosecond science involves the development and calibration of precise measurement techniques in atoms [1]. In recent years, many of these techniques were extended to small molecular systems in high-harmonic generation (HHG) [2] and high-harmonic spectroscopy (HHS) [3; 4]. As the field moves toward the investigation of dynamics in more complex targets, it becomes important to determine the applicability of techniques developed for atoms to the molecular case, and when found lacking, to update these methods to properly resolve dynamics. One example of such dynamics which garnered considerable attention in recent years is molecular charge migration [5], in which, following ionization, the electrons in a molecular ion undergo a coherent spatial oscillation, driven entirely by electron correlations. [PERSON] et al. identified high-harmonic spectroscopy as a promising tool for studying charge migration, with initial experiments in iodoacetylene [6]. There is not, however, a widely accepted paradigm for how dynamical processes, such as charge migration, manifest in attosecond measurement techniques such as HHS. One reasonable approach is to look for changes to known, calibrated structural features in high-harmonic spectra to infer additional information about dynamics. One such structure, well-known through photoionization, is the Cooper minimum [7] (CM). A CM is a local minimum in the photoionization cross-section at a specific photon energy, caused by a sign change in the bound-free transition dipole of a particular angular momentum channel. CMs were observed through photoionization in a variety of atoms [8] and small molecules [9; 10; 11] for many years. However, access to the phase behavior associated with the CM was only recently achieved [12] using HHS. In HHS, the recombination-dipole matrix element (RDME) probes the inverse process to single-photon ionization, and additionally preserves the phase of the transition dipole in the spectral phase of the emitted extreme ultraviolet (XUV) radiation. A CM manifests itself in an HHS measurement as both a minimum in the XUV spectral intensity, representing destructive interference between transition-dipole contributions from several angular momentum channels [13], and as a shift in the spectral phase versus energy near the local minimum [12]. Cooper minima in molecular HHG were previously detected in the spectral intensity [14], but not in the spectral phase. Because not all such features can be unambiguously assigned using spectral intensity alone, analysis of the spectral phase can be useful to probe such interactions. Here, we present the first molecular CM phase measurement, derived from measurements of the XUV group delay (GD), for the case of the highest occupied molecular orbital of methyl chloride (CH\({}_{3}\)Cl), which is analogous to the 3\(p\) orbital of argon. As we show, the CH\({}_{3}\)Cl CM was only clearly revealed through the combined analysis of XUV spectral intensity and phase. High harmonics generated by an intense laser-atom interaction are known to encode the frequency-dependent sub-cycle emission time in the GD of XUV light, in addition to the spectral-phase contribution from the RDME. In order to carefully remove the emission-time contribution from our measured XUV GD, we calculated the former using a strong-field approximation (SFA) [15], and subtracted the resulting SFA GD from the measured one. This approach was experimentally verified in the context of atomic HHG [16; 17; 18; 19; 20], but not for the present case of molecular HHG, and particularly not in the presence of a molecular CM. We studied its applicability to reveal target-specific information about the energy-dependent RDME in methyl chloride through a careful two-step calibration of the interaction intensity. We firstly characterized the intensity scaling of the SFA model in xenon, which is structureless in the relevant energetic region, by fitting the measured GD to the SFA prediction.