A well-known shortcoming of High Harmonic Generation (HHG) is the strong dependence of the broadband HHG spectra (HGS) on the carrier envelope phase (CEP) of the driver. Here we numerically show that compared to the current well-established scalar (linearly polarized) schemes for generating broadband HGS, namely a short driver [Amplitude gating (AG)], Polarization-Gating (PG) or Time-Gating (TG), the vectorial driver of the Vectorial-Time-Polarization-Gating (VTPG) scheme renders the cutoff HGS much less sensitive to the CEP of the driver. The polarization state (helicity) of the emitted radiation is likewise CEP-resilient. Unlike scalar schemes, where the number of recollisions heavily depends on the CEP, in VTPG the CEP keeps this number almost unchanged, and only controls the partitioning of the recollisions between two orthogonal directions. This reduces the CEP-dependence of the HGS and decreases the spectral modulations. The CEP-resilience of the VTPG scheme holds promise for a variety of applications in attosecond science benefiting from quasicontinuous, helical HHG sources liberated from the necessity to stabilize the CEP of the laser.

The analysis of symmetries is extremely useful across science. In Physics, symmetries are used to derive conservation laws and selection rules for transitions in interacting systems. In the early days of nonlinear optics (NLO), symmetries were used to formulate a set of rules for photonic processes according to the medium's symmetries that are reflected in the NLO coefficient tensor. While this approach was believed to be complete and closed, the field has recently reignited as multi-color ultrashort laser pulses with tailored polarization and spatiotemporal structures become standard in NLO. A more complete theory has been recently emerging, which aims to incorporate all possible dynamical degrees of freedom of light: spin and orbital angular momentum, spatial structure, time-dependent polarizations, temporal envelopes, etc., in addition to the symmetries of the medium. This theoretical development is also accompanied by experimental advances that rely on tailored light beams that can now be generated with ever-increasing complexity, including topologies in real and a variety of synthetic dimensions, carrying poly-chromatic carrier waves, time-dependent varying angular momenta, local-chirality, and more. The nonlinear interactions between light fields with unique symmetries (or asymmetries) and matter is especially appealing, since that holds the key for developing new ultrafast spectroscopies with sub-femtosecond resolution, for exerting exact control over matter, and improving our fundamental understanding of how light and matter interact. We review these recent advances in this expanding field, focusing on the theory, its implications, and seminal experiments. We aim to establish a comprehensive database of symmetries and selection rules governing NLO light-matter interactions within the emerging new formalism, and invite the scientific community to contribute to this effort.

Photoelectron circular dichroism (PECD) is a method where randomly oriented chiral molecules are photoionized due to irradiation by circularly-polarized lasers, yielding large chiral signals in the photoelectron momentum distribution. Recently, PECD was explored with polarization-tailored light such as bi-chromatic and non-collinear drivers, which still produces significant chiral signals. Yet, all known PECD configurations to date exhibit non-zero time-local chirality. That is, they are driven by an intrinsically helical light source. Nonetheless, 'chiral' light can also be non-helical if its chirality manifests on longer timescales (e.g. an optical centrifuge). It remains unknown whether PECD can arise from non-helical coherent light. Here we predict that PECD indeed emerges from non-helical light by employing a train of linearly-polarized intense laser pulses with a rotating polarization axis, which are phase-coherent and time-delayed. We find strong PECD in the model chiral molecule CBrClFH under a wide parameter regime that can be optimized up to 8

Chiral (highly helical) extreme ultraviolet (XUV) sources are pivotal for investigating chiroptical phenomena on the ultrafast electronic timescale. Table-top, coherent High Harmonic Generation (HHG)-based sources are particularly well-suited for these studies. However, chiral materials, such as organic chiral molecules and solid-state magnetic materials, exhibit fine spectral features which necessitate broadband radiation for their complete interrogation. The generation of radiation that is both broadband and helical through HHG presents a seemingly paradoxical challenge: while chiral HHG emission requires at least two recollisions occurring along different directions in the polarization plane, the Floquet limit might already be reached with as few as three recollisions, resulting in a sparse spectrum characterized by pronounced discrete harmonic peaks. Here we propose a straightforward scheme that enables the interrogation of fine spectral features, in principle restricted only by the resolution of the XUV spectrometer, with chiral XUV light. Our method is based on using a vectorial two-color driver with close central-frequencies with slight symmetry breaking. It integrates the time-gating and polarization-gating techniques to generate a vectorial driver which induces well-controlled bursts of recollisions, occurring along different directions in the polarization plane. The method satisfies the dual requirements of an XUV source which is both broadband and helical. We perform polarization scan and demonstrate that the broadband XUV radiation exhibits rapid modulations in its spectral ellipticity, and fast alternation in its spectral helicities. The phase of modulations could be controlled by introducing a slight symmetry breaking. This allows us to control and modulate the XUV polarization state, which should enable the detection of chiroptical signals with enhanced sensitivity.

Conservation laws are some of the most generic and useful concepts in physics. In nonlinear optical parametric processes, conservation of photonic energy, momenta and parity often lead to selection rules, restricting the allowed polarization and frequencies of the emitted radiation. Here we present a scheme to derive conservation laws in optical parametric processes in which many photons are annihilated and a single photon is emitted. We first rederive with it the known nonlinear optical conservation laws, and then utilize it to predict and explore conservations of reflection parity and space-time parity. Conservation of reflection-parity arises from a generalized reflection symmetry of the polarization in a superspace, analogous to the superspace employed in the study of quasicrystals. Conservation of space-time parity similarly arises from space-time reversal symmetry in superspace. We explore these conservation laws numerically in the context of high-harmonic generation and outline experimental setups where they can be tested.

Photoionization is one of the most fundamental processes in light-matter interaction. Advanced attosecond photoelectron spectroscopy provides the possibility to characterize the ultrafast photoemission process in an extremely short attosecond time scale. Following scattering symmetry rules, residual ions encode ultrafast photoionization prints at the instant of electron removal forming an alternative electron emission chronoscope. Here, we experimentally illustrate the attosecond ion reconstruction of attosecond beating by interference of two-photon transition (RABBIT)-like interferometry through the development of high-resolution ion momentum detection in atomic photoionization processes. Our ion interferometry presents identical momentum- and time-dependent scattering phase shift, as we observed in photoelectron spectroscopy, and thus demonstrates that ion interferometry can be a possible alternative attosecond approach to resolve the photoionization process, without the electron homogeneity limitation.

We demonstrate a high harmonic-generation scheme that offers control over the bandwidth of the spectral peaks. The scheme uses a vectorial two-color driver with close central frequencies, generated by spectrally splitting a linearly polarized input femtosecond-duration laser pulse and subsequently recombining the two halves after their polarizations are made cross-elliptical and counter-rotating. This results in the generation of new emission channels that coalesce into broad odd-integer HHG peaks, the bandwidth of each being proportional to the frequency difference between the two colors, to the harmonic order and inversely proportional to the driver fields’ ellipticities. Peak broadening to the extent that a supercontinuum is formed is also demonstrated. This source will find use in HHG applications benefiting from high-flux broadband extreme ultraviolet radiation, such as attosecond transient absorption spectroscopy.

A High-Harmonic-Generation (HHG) scheme offering continuous control over the bandwidth of the spectral peaks is presented. The scheme uses a vectorial two-color driver with close frequencies, generated by spectrally splitting an input laser pulse and recombining the two halves after their polarizations are made cross-elliptical counter-rotating.

Conservation laws are one of the most generic and useful concepts in physics. In nonlinear optical parametric processes, conservation of photonic energy, momenta and parity often lead to selection rules, restricting the allowed polarization and frequencies of the emitted radiation. Here we present a new scheme to derive conservation laws in optical parametric processes in which many photons are annihilated and a single new photon is emitted. We then utilize it to derive two new such conservation laws. Conservation of reflection-parity (RP) arises from a generalized reflection symmetry of the polarization in a superspace, analogous to the superspace employed in the study of quasicrystals. Conservation of space-time-parity (STP) similarly arises from space-time reversal symmetry in superspace. We explore these new conservation laws numerically in the context of high harmonic generation and outline experimental set-ups where they can be tested.

We present an experimental study of time-refraction with propagating time-interfaces. We observe the special spectral signature of time-reflections generated by these interfaces, paving the way for their experimental demonstration in the optical regime.

Spectral splitting of high harmonic radiation is observed when a gas target is irradiated with a high-energy laser pulse, having an extreme amount of frequency chirp. The phenomenon, which may be observed only by using a multi-TW laser system, originates from the temporal evolution of the phase-matching conditions. We illustrate how these conditions are mapped to the spectral domain, and present experimental evidence which is validated by our model.

We present an experimental study of optical time-refraction in single-cycle time-interfaces. Specifically, we study the propagation of a probe pulse through a sample undergoing large refractive index changes induced by an intense ultra-short modulator pulse.

A new High Harmonic Generation (HHG) scheme, which doesn't rely on Tunnel-Ionization as the ionization mechanism but rather on Single-Photon Ionization, is theoretically proposed and numerically demonstrated. The scheme uses two driver fields: an extreme-ultraviolet driver which induces the ionization, and a circularly-polarized, co-rotating, two-color infrared driver carried at a fundamental frequency and its second harmonic which induces the recollision. Using Classical and time-dependent Schr\"odinger equation simulations of a model Argon atom, we show that in this scheme ionization is essentially decoupled from recollision. Releasing the process from being Tunneling-dependent reduces its degree of nonlinearity, which offers new capabilities in attosecond science, such as generation of High Harmonics from highly-charged ions, or from specific deep core electronic levels. It is shown that the emitted high harmonics involve the absorption of photons of one color of the infrared driver, and the emission of photons of the second color. This calls for future examination of the possible correlations between the emitted high harmonics.

Symmetries and their associated selection rules are extremely useful in many fields of science. For systems of electromagnetic (EM) fields interacting with matter, the symmetries of matter and the EM fields' time-dependent polarization determine the properties of the nonlinear responses, and they can be facilitated for controlling light emission and enabling ultrafast symmetry breaking spectroscopy of various properties. Here, we formulate a general theory that describes the macroscopic and microscopic dynamical symmetries (including quasicrystal-like symmetries) of EM vector fields, revealing many previously unidentified symmetries and selection rules in light-matter interactions. We demonstrate an example of multiscale selection rules experimentally in the framework of high harmonic generation. This work paves the way for novel spectroscopic techniques in multiscale systems and for imprinting complex structures in extreme ultraviolet-x-ray beams, attosecond pulses, or the interacting medium itself.

Attosecond chronoscopy is central to the understanding of ultrafast electron dynamics in matter from gas to the condensed phase with attosecond temporal resolution. It has, however, not yet been possible to determine the timing of individual partial waves, and steering their contribution has been a substantial challenge. Here, we develop a polarization-skewed attosecond chronoscopy serving as a partial wave meter to reveal the role of each partial wave from the angle-resolved photoionization phase shifts in rare gas atoms. We steer the relative ratio between different partial waves and realize a magnetic-sublevel-resolved atomic phase shift measurement. Our experimental observations are well supported by time-dependent R-matrix numerical simulations and analytical soft-photon approximation analysis. The symmetry-resolved, partial-wave analysis identifies the transition rate and phase shift property in the attosecond photoelectron emission dynamics. Our findings provide critical insights into the ubiquitous attosecond optical timer and the underlying attosecond photoionization dynamics.

Data for the article "Selection rules in symmetry-broken systems by symmetries in synthetic dimensions" by Matan Even Tzur, Ofer Neufeld, Eliyahu Bordo, Avner Fleischer, and Oren Cohen.

Selection rules are often considered a hallmark of symmetry. Here, we employ symmetry-breaking degrees of freedom as synthetic dimensions to demonstrate that symmetry-broken systems systematically exhibit a specific class of symmetries and selection rules. These selection rules constrain the scaling of a system's observables (non-perturbatively) as it transitions from symmetric to symmetry-broken. Specifically, we drive bi-elliptical high harmonic generation (HHG), and observe that the scaling of the HHG spectrum with the pump's ellipticities is constrained by selection rules corresponding to symmetries in synthetic dimensions. We then show the generality of this phenomenon by analyzing periodically-driven (Floquet) systems subject to two driving fields, tabulating the resulting synthetic symmetries for (2 + 1)D Floquet groups, and deriving the corresponding selection rules for high harmonic generation (HHG) and other phenomena. The presented class of symmetries and selection rules opens routes for ultrafast spectroscopy of phonon-polarization, spin-orbit coupling, symmetry-protected dark bands, and more.

Attosecond chronoscopy is central to the understanding of ultrafast electron dynamics from gas to condensed phase with attosecond temporal resolution. It has, however, not yet been able to determine the timing of individual partial waves, and steering their contribution has been a substantial challenge. Here, we develop a polarization-skewed attosecond chronoscopy to reveal their roles from the angle-resolved photoionization phase shifts in rare gas atoms. By scanning the relative polarization angle between an extreme-ultraviolet attosecond pulse train and a phase-locked near-infrared laser field serving as a partial wave meter, we break the cylindrical symmetry and observe an emission direction dependent phase shift in the photoionized electron momenta. The experimental observations are well supported by numerical simulations using the R-matrix with time-dependence method, and by analytical analysis using the soft-photon approximation. Our symmetry-resolved, partial-wave analysis identifies the transition rate and phase shifts of each individual ionization pathway in the attosecond photoelectron emission dynamics. Our findings provide critical insights into the ubiquitous attosecond optical timer and the underlying attosecond photoionization dynamics, thereby offer new perspectives for the control, manipulation, and exploration of ultrafast electron dynamics in complex systems.

Floquet systems often exhibit dynamical symmetries (DS) that govern the time-dependent dynamics and result in selection rules. When a DS is broken, selection rule deviations are expected. Typically, information about the symmetry-breaking perturbation/phase and the time-dependent dynamics can be extracted from these deviations, hence they are regarded as a background free gauge of symmetry breaking. However, to date, DS breaking & selection rule deviations are not described by a general approach, thus there is no universal insight about the interplay between selection rule deviations, the symmetry breaking perturbation, and the broken DS. Here we consider DS breaking in Floquet systems from a general standpoint, formulating a general theory that analytically connects the symmetry-broken and fully symmetric systems. Using an external laser (of arbitrary frequency and polarization), as a model DS breaking perturbation, we discover that the broken symmetry systematically imposes selection rules on the symmetry-broken system, which physically manifest as scaling laws of selection rule deviations. We term these rules ‘selection rules for breaking selection rules’—a new concept in physics. We numerically validate the analytical theory in the context of high harmonic generation. Our discovery is a general feature of nonlinear wave-mixing phenomena, and we expect it to apply to any Floquet system (classical & quantum) and to any DS breaking mechanism (either by intrinsic or extrinsic elements of the system).