Valleytronics in bulk MoS2 with a topologic optical field.

The valley degree of freedom1-4 of electrons in materials promises routes towards energy-efficient information storage with enticing prospects for quantum information processing5-7. Current challenges in utilizing valley polarization are symmetry conditions that require monolayer structures8,9 or specific material engineering10-13, non-resonant optical control to avoid energy dissipation and the ability to switch valley polarization at optical speed. We demonstrate all-optical and non-resonant control over valley polarization using bulk MoS2, a centrosymmetric material without Berry curvature at the valleys. Our universal method utilizes spin angular momentum-shaped trefoil optical control pulses14,15 to switch the material's electronic topology and induce valley polarization by transiently breaking time and space inversion symmetry16 through a simple phase rotation. We confirm valley polarization through the transient generation of the second harmonic of a non-collinear optical probe pulse, depending on the trefoil phase rotation. The investigation shows that direct optical control over the valley degree of freedom is not limited to monolayer structures. Indeed, such control is possible for systems with an arbitrary number of layers and for bulk materials. Non-resonant valley control is universal and, at optical speeds, unlocks the possibility of engineering efficient multimaterial valleytronic devices operating on quantum coherent timescales.

Observation of interband Berry phase in laser-driven crystals.

Ever since its discovery1, the notion of the Berry phase has permeated all branches of physics and plays an important part in a variety of quantum phenomena2. However, so far all its realizations have been based on a continuous evolution of the quantum state, following a cyclic path. Here we introduce and demonstrate a conceptually new manifestation of the Berry phase in light-driven crystals, in which the electronic wavefunction accumulates a geometric phase during a discrete evolution between different bands, while preserving the coherence of the process. We experimentally reveal this phase by using a strong laser field to engineer an internal interferometer, induced during less than one cycle of the driving field, which maps the phase onto the emission of higher-order harmonics. Our work provides an opportunity for the study of geometric phases, leading to a variety of observations in light-driven topological phenomena and attosecond solid-state physics.

Symmetry-aware deep neural networks for high harmonic spectroscopy in solids.

Neural networks are a prominent tool for identifying and modeling complex patterns, which are otherwise hard to detect and analyze. While machine learning and neural networks have been finding applications across many areas of science and technology, their use in decoding ultrafast dynamics of quantum systems driven by strong laser fields has been limited so far. Here we use standard deep neural networks to analyze simulated noisy spectra of highly nonlinear optical response of a 2-dimensional gapped graphene crystal to intense few-cycle laser pulses. We show that a computationally simple 1-dimensional system provides a useful "nursery school" for our neural network, allowing it to be retrained to treat more complex 2D systems, recovering the parametrized band structure and spectral phases of the incident few-cycle pulse with high accuracy, in spite of significant amplitude noise and phase jitter. Our results offer a route for attosecond high harmonic spectroscopy of quantum dynamics in solids with a simultaneous, all-optical, solid-state based complete characterization of few-cycle pulses, including their nonlinear spectral phase and the carrier envelope phase.

Imprinting Chirality on Atoms Using Synthetic Chiral Light Fields.

Atoms are usually thought of as achiral objects. However, one can construct superpositions of atomic states that are chiral [1]. Here, we show how to excite such superpositions with tailored light fields both in the weak-field and strong-field regimes, using realistic laser parameters. First, we use time-dependent Schrödinger equation simulations to demonstrate the creation of a time-dependent bound chiral wave packet in sodium atoms. Second, we show how the time-dependent handedness of this wave packet can be probed by photoelectron circular dichroism, in spite of the central symmetry of the core potential. Third, we use time-dependent Schrödinger equation simulations to show how chirality can be directly imprinted on a photoelectron wave packet created by strong-field ionization and introduce an unambiguous chiral measure that allows us to characterize its handedness.

Non-instantaneous third-order optical response of gases in low-frequency fields.

It is commonly assumed that for low-intensity short optical pulses far from resonance, the third-order optical nonlinear response is instantaneous. We solve the three-dimensional time-dependent Schrödinger equation for the hydrogen atom and show that this is not the case: the polarization is not simply proportional to the cube of the electric field even at low intensities. We analyze the fundamental-frequency and third-harmonic nonlinear susceptibilities of hydrogen, investigate their dependence on intensity, and find that the delays in the Kerr response rapidly approach the femtosecond time-scale at higher intensities, while the delays in the third harmonic generation remain much lower. We also propose an experimental scheme to detect and characterize the above effects.

All-optical valley switch and clock of electronic dephasing.

2D materials with broken inversion symmetry posses an extra degree of freedom, the valley pseudospin, that labels in which of the two energy-degenerate crystal momenta, K or K', the conducting carriers are located. It has been shown that shining circularly-polarized light allows to achieve close to 100% of valley polarization, opening the way to valley-based transistors. Yet, switching of the valley polarization is still a key challenge for the practical implementation of such devices due to the short valley lifetimes. Recent progress in ultrashort laser technology now allows to produce trains of attosecond pulses with controlled phase and polarization between the pulses. Taking advantage of such technology, we introduce a coherent control protocol to turn on, off and switch the valley polarization at faster timescales than electron-hole decoherence and valley depolarization, that is, an ultrafast optical valley switch. We theoretically demonstrate the protocol for hBN and MoS2 monolayers calculated from first principles. Additionally, using two time-delayed linearly-polarized pulses with perpendicular polarization, we show that we can extract the electronic dephasing time T2 from the valley Hall conductivity.

Enantiosensitive steering of free-induction decay.

Chiral discrimination, a problem of vital importance, has recently become an emerging frontier in ultrafast physics, with remarkable progress achieved in multiphoton and strong-field regimes. Rydberg excitations, unavoidable in the strong-field regime and intentional for few-photon processes, arise in all these approaches. Here, we show how to harness this ubiquitous feature by introducing a new phenomenon, enantiosensitive free-induction decay, steered by a tricolor chiral field at a gentle intensity, structured in space and time. We demonstrate theoretically that an excited chiral molecule accumulates an enantiosensitive phase due to perturbative interactions with the tricolor chiral field, resulting in a spatial phase gradient steering the free-induction decay in opposite directions for opposite enantiomers. Our work introduces a general, extremely sensitive, all-optical enantiosensitive detection technique that avoids strong fields and takes full advantage of recent advances in structuring light.

Strong chiral response in non-collinear high harmonic generation driven by purely electric-dipole interactions.

High harmonic generation (HHG) records the ultrafast electronic response of matter to light, encoding key properties of the interrogated quantum system, such as chirality. The first implementation of chiral HHG [Cireasa et al, Nat. Phys.11, 654 (2015)10.1038/nphys3369] relied on the weak electronic response of a medium of randomly oriented chiral molecules to the magnetic component of an elliptically polarized wave, yielding relatively weak chiro-optical signals. Here we apply state-of-the-art semi-analytical modelling to show that elliptically polarized light can drive a strong chiral response in chiral molecules via purely electric-dipole interactions - the magnetic component of the wave does not participate at all. This strong chiro-optical response, which remains hidden in standard HHG experiments, can be mapped into the macroscopic far-field signal using a non-collinear configuration, creating new opportunities for imaging chiral matter and chiral dynamics on ultrafast time scales.

Enantio-sensitive unidirectional light bending.

Structured light, which exhibits nontrivial intensity, phase, and polarization patterns in space, has key applications ranging from imaging and 3D micromanipulation to classical and quantum communication. However, to date, its application to molecular chirality has been limited by the weakness of magnetic interactions. Here we structure light's local handedness in space to introduce and realize an enantio-sensitive interferometer for efficient chiral recognition without magnetic interactions, which can be seen as an enantio-sensitive version of Young's double slit experiment. Upon interaction with isotropic chiral media, such chirality-structured light effectively creates chiral emitters of opposite handedness, located at different positions in space. We show that if the distribution of light's handedness breaks left-right symmetry, the interference of these chiral emitters leads to unidirectional bending of the emitted light, in opposite directions in media of opposite handedness, even if the number of the left-handed and right-handed emitters excited in the medium is exactly the same. Our work introduces the concepts of polarization of chirality and chirality-polarized light, exposes the immense potential of sculpting light's local chirality, and offers novel opportunities for efficient chiral discrimination, enantio-sensitive optical molecular fingerprinting and imaging on ultrafast time scales.

Concluding remarks: The age of molecular movies.

This Faraday Discussion has demonstrated enormous progress towards using advanced light sources, together with a variety of experimental and theoretical tools and techniques, to film the motion of both electrons and nuclei in molecules undergoing photo-induced reactions. The new tools are beginning to offer reliable opportunities for achieving the required spatio-temporal resolution, all the way to sub-femtosecond and sub-angstrom scales. The age of quantum molecular movies has arrived.

Topological protection versus degree of entanglement of two-photon light in photonic topological insulators.

Topological insulators combine insulating properties in the bulk with scattering-free transport along edges, supporting dissipationless unidirectional energy and information flow even in the presence of defects and disorder. The feasibility of engineering quantum Hamiltonians with photonic tools, combined with the availability of entangled photons, raises the intriguing possibility of employing topologically protected entangled states in optical quantum computing and information processing. However, while two-photon states built as a product of two topologically protected single-photon states inherit full protection from their single-photon "parents", a high degree of non-separability may lead to rapid deterioration of the two-photon states after propagation through disorder. In this work, we identify physical mechanisms which contribute to the vulnerability of entangled states in topological photonic lattices. Further, we show that in order to maximize entanglement without sacrificing topological protection, the joint spectral correlation map of two-photon states must fit inside a well-defined topological window of protection.

Extracting sub-cycle electronic and nuclear dynamics from high harmonic spectra.

We present a new methodology for measuring few-femtosecond electronic and nuclear dynamics in both atoms and polyatomic molecules using multidimensional high harmonic generation (HHG) spectroscopy measurements, in which the spectra are recorded as a function of the laser intensity to form a two-dimensional data set. The method is applied to xenon atoms and to benzene molecules, the latter exhibiting significant fast nuclear dynamics following ionization. We uncover the signature of the sub-cycle evolution of the returning electron flux in strong-field ionized xenon atoms, implicit in the strong field approximation but not previously observed directly. We furthermore extract the nuclear autocorrelation function in strong field ionized benzene cations, which is determined to have a decay of [Formula: see text] fs, in good agreement with the [Formula: see text] fs obtained from direct dynamics variational multi-configuration Gaussian calculations. Our method requires minimal assumptions about the system, and is applicable even to un-aligned polyatomic molecules.

Amplification of intense light fields by nearly free electrons.

Light can be used to modify and control properties of media, as in the case of electromagnetically induced transparency or, more recently, for the generation of slow light or bright coherent XUV and X-ray radiation. Particularly unusual states of matter can be created by light fields with strengths comparable to the Coulomb field that binds valence electrons in atoms, leading to nearly-free electrons oscillating in the laser field and yet still loosely bound to the core [1,2]. These are known as Kramers-Henneberger states [3], a specific example of laser-dressed states [2]. Here, we demonstrate that these states arise not only in isolated atoms [4,5], but also in rare gases, at and above atmospheric pressure, where they can act as a gain medium during laser filamentation. Using shaped laser pulses, gain in these states is achieved within just a few cycles of the guided field. The corresponding lasing emission is a signature of population inversion in these states and of their stability against ionization. Our work demonstrates that these unusual states of neutral atoms can be exploited to create a general ultrafast gain mechanism during laser filamentation.

Attosecond recorder of the polarization state of light.

High harmonic generation in multi-color laser fields opens the opportunity of generating isolated attosecond pulses with high ellipticity. Such pulses hold the potential for time-resolving chiral electronic, magnetization, and spin dynamics at their natural timescale. However, this potential cannot be realized without characterizing the exact polarization state of light on the attosecond timescale. Here we propose and numerically demonstrate a complete solution of this problem. Our solution exploits the extrinsic two-dimensional chirality induced in an atom interacting with the chiral attosecond pulse and a linearly polarized infrared probe. The resulting asymmetry in the photoelectron spectra allows to reconstruct the complete polarization state of the attosecond pulse, including its possible time dependence. The challenging problem of distinguishing circularly polarized, partially polarized, or unpolarized pulses in the extreme ultraviolet range is also resolved. We expect this approach to become the core ingredient for attosecond measurements of chiral-sensitive processes in gas and condensed phase.

Time-resolved high harmonic spectroscopy of dynamical symmetry breaking in bi-circular laser fields: the role of Rydberg states.

The bi-circular scheme for high harmonic generation, which combines two counter-rotating circular fields with frequency ratio 2:1, has recently permitted to generate high harmonics with essentially circular polarization, opening the way for ultrafast chiral studies. This scheme produces harmonic lines at 3N + 1 and 3N + 2 multiples of the fundamental driving frequency, while the 3N lines are forbidden owing to the three-fold symmetry of the field. It is generally established that the routinely observed signals at these forbidden harmonic lines come from a slight ellipticity in the driving fields, which breaks the three-fold symmetry. We find that this is neither the only nor it is the dominant mechanism responsible. The forbidden lines can be observed even for perfectly circular, long driving pulses. We show that they encode rich information on the sub-cycle electronic dynamics that occur during the generation process. By varying the time delay and relative intensity between the two drivers, we demonstrate that when the second harmonic either precedes or is more intense than the fundamental field, the weak effects of dynamical symmetry breaking caused by finite pulse duration are amplified by electrons trapped in Rydberg orbits (i.e., Freeman resonances), and that the forbidden harmonic lines are a witness of this.

Strong-field ionization of clusters using two-cycle pulses at 1.8 µm.

The interaction of intense laser pulses with nanoscale particles leads to the production of high-energy electrons, ions, neutral atoms, neutrons and photons. Up to now, investigations have focused on near-infrared to X-ray laser pulses consisting of many optical cycles. Here we study strong-field ionization of rare-gas clusters (103 to 105 atoms) using two-cycle 1.8 µm laser pulses to access a new interaction regime in the limit where the electron dynamics are dominated by the laser field and the cluster atoms do not have time to move significantly. The emission of fast electrons with kinetic energies exceeding 3 keV is observed using laser pulses with a wavelength of 1.8 µm and an intensity of 1 × 1015 W/cm2, whereas only electrons below 500 eV are observed at 800 nm using a similar intensity and pulse duration. Fast electrons are preferentially emitted along the laser polarization direction, showing that they are driven out from the cluster by the laser field. In addition to direct electron emission, an electron rescattering plateau is observed. Scaling to even longer wavelengths is expected to result in a highly directional current of energetic electrons on a few-femtosecond timescale.