Symmetry is one of the most generic and useful concepts in science, often leading to conservation laws and selection rules. Here we formulate a general group theory for dynamical symmetries (DSs) in time-periodic Floquet systems, and derive their correspondence to observable selection rules. We apply the theory to harmonic generation, deriving closed-form tables linking DSs of the driving laser and medium (gas, liquid, or solid) in (2+1)D and (3+1)D geometries to the allowed and forbidden harmonic orders and their polarizations. We identify symmetries, including time-reversal-based, reflection-based, and elliptical-based DSs, which lead to selection rules that are not explained by currently known conservation laws. We expect the theory to be useful for ultrafast high harmonic symmetry-breaking spectroscopy, as well as in various other systems such as Floquet topological insulators.

High harmonic generation (HHG) is an extremely nonlinear effect generating coherent broadband radiation and pulse durations reaching attosecond timescales. Conventional models of HHG that treat the driving and emitted fields classically are usually very successful but inherently cannot capture the quantum-optical nature of the process. Although prior work considered quantum HHG, it remains unknown in what conditions the spectral and statistical properties of the radiation depart considerably from the known phenomenology of HHG. The discovery of such conditions could lead to novel sources of attosecond light having squeezing and entanglement. Here, we present a fully-quantum theory of extreme nonlinear optics, predicting quantum effects that alter both the spectrum and photon statistics of HHG, thus departing from all previous approaches. We predict the emission of shifted frequency combs and identify spectral features arising from the breakdown of the dipole approximation for the emission. Our results show that each frequency component of HHG can be bunched and squeezed and that each emitted photon is a superposition of all frequencies in the spectrum, i.e., each photon is a comb. Our general approach is applicable to a wide range of nonlinear optical processes, paving the way towards novel quantum phenomena in extreme nonlinear optics.

We propose and numerically demonstrate a new chiral spectroscopy method that is based on a universal system-independent mechanism of dynamical symmetry breaking in high harmonic generation (HHG). The proposed technique relies only on intense electric-dipole transitions and not on their interplay with magnetic dipole transitions. The symmetry breaking results in the emission of otherwise “forbidden” harmonics from chiral media (i.e., that are not emitted from achiral or racemic media), yielding a huge, nearly background-free, chiral-achiral signal that is correlated to the magnitude of the medium’s enantiomeric excess. The handedness of the medium can be directly detected by measuring the polarization helicity of the emitted harmonics. Moreover, the strength of the “allowed” harmonics (that are not related to symmetry breaking) is chirality independent; hence, they can be used as a reference to probe chiral degrees of freedom within a single measurement. We numerically demonstrate up to 99% chiral-achiral signal level (normalized difference between the chiral and achiral HHG spectra) from microscopic gas-phase emission using state-of-the-art models for HHG in bromochlorofluoromethane and propylene oxide. We expect the new method to give rise to precise tabletop characterization of chiral media in the gas phase and for highly sensitive time-resolved probing of dynamical chiral processes with femtosecond-to-attosecond temporal resolution.

We predict the generation of bulk photocurrents in materials driven by bichromatic fields that are circularly polarized and corotating. The nonlinear photocurrents have a fully controllable directionality and amplitude without requiring carrier-envelope-phase stabilization or few-cycle pulses, and can be generated with photon energies much smaller than the band gap (reducing heating in the photoconversion process). We demonstrate with ab initio calculations that the photocurrent generation mechanism is universal and arises in gaped materials (Si, diamond, MgO, hBN), in semimetals (graphene), and in two- and three-dimensional systems. Photocurrents are shown to rely on sub-laser-cycle asymmetries in the nonlinear response that build-up coherently from cycle to cycle as the conduction band is populated. Importantly, the photocurrents are always transverse to the major axis of the co-circular lasers regardless of the material’s structure and orientation (analogously to a Hall current), which we find originates from a generalized time-reversal symmetry in the driven system. At high laser powers ($\sim {10}^{13}\mathrm{W}/{\mathrm{cm}}^2$) this symmetry can be spontaneously broken by vast electronic excitations, which is accompanied by an onset of carrier-envelope-phase sensitivity and ultrafast many-body effects. Our results are directly applicable for efficient light-driven control of electronics, and for enhancing sub-band-gap bulk photogalvanic effects.