Structure- and laser-gauges for the semiconductor Bloch equations in high-harmonic generation in solids

The semiconductor Bloch equations (SBEs) are routinely used for simulations of strong-field laser-matter interactions in condensed matter. In systems without inversion or time-reversal symmetries, the Berry connections and transition dipole phases (TDPs) must be included in the SBEs, which in turn requires the construction of a smooth and periodic structure gauge for the Bloch states. Here, we illustrate a general approach for such a structure-gauge construction for topologically trivial systems. Furthermore, we investigate the SBEs in the length and velocity gauges, and discuss their respective advantages and shortcomings for the high-harmonic generation (HHG) process. We find that in cases where we require dephasing or separation of the currents into interband and intraband contributions, the length gauge SBEs are computationally more efficient. In calculations without dephasing and where only the total current is needed, the velocity gauge SBEs are structure-gauge independent and are computationally more efficient. We employ two systems as numerical examples to highlight our findings: an 1D model of ZnO and the 2D monolayer hexagonal boron nitride (h-BN). The omittance of Berry connections or TDPs in the SBEs for h-BN results in nonphysical HHG spectra. The structure- and laser-gauge considerations in the current work are not restricted to the HHG process, and are applicable to all strong-field matter simulations with SBEs

Time-frequency representations of high order harmonics

We calculate time-frequency representations (TFRs) of high-order short pulse harmonics generated in the interaction between neon atoms and an intense laser field, including macroscopic effects of propagation and phase matching in the non-linear medium. The phase structure of the harmonics is often complicated and the TFR can help to resolve the different components of this structure. The harmonic pulses exhibit an overall negative chirp, which can be attributed in part to the intensity dependence of the harmonic dipole phase. In some cases, the harmonic field separates in the time-frequency domain and clearly exhibits two different chirps. We also compute an experimental realization of a TFR (using Frequency Resolved Optical Gating, FROG) for a high harmonic. Due to the complicated time structure of the harmonics, the FROG trace is visually complex. © 2001 Optical Society of America

Laser-induced bound-state phases in high-order harmonic generation

We present single-molecule and macroscopic calculations showing that laser-induced Stark shifts contribute significantly to the phase of high-order harmonics from polar molecules. This is important for orbital tomography, where phases of field-free dipole matrix elements are needed in order to reconstruct molecular orbitals. We derive an analytical expression that allows the first-order Stark phase to be subtracted from experimental measurements

Characterizing Anomalous High-Harmonic Generation in Solids

Anomalous high-harmonic generation (HHG) arises in certain solids when irradiated by an intense laser field, as the result of a nonlinear perpendicular current akin to a Hall current. Here, we theoretically characterize the anomalous HHG mechanism, via development of an ab-initio methodology for strong-field laser-solid interaction that allows a rigorous decomposition of the total current. We identify two key characteristics of the anomalous harmonic yields: an overall increase with laser wavelength; and pronounced minima at certain intensities or wavelengths around which the emission time profiles drastically change. Such signatures can be exploited to disentangle the anomalous harmonics from the competing interband harmonics, and thus pave way for the experimental identification and time-domain control of pure anomalous harmonics.Comment: 7 pages, 4 figure

Expanded view of electron-hole recollisions in solid-state high-order harmonic generation: Full-Brillouin-zone tunneling and imperfect recollisions

We theoretically investigate electron-hole recollisions in high-harmonic generation (HHG) in band-gap solids irradiated by linearly and elliptically polarized drivers. We find that in many cases the emitted harmonics do not originate in electron-hole pairs created at the minimum band gap, where the tunneling probability is maximized, but rather in pairs created across an extended region of the Brillouin zone (BZ). In these situations, the analogy to gas-phase HHG in terms of the short- and long-trajectory categorizations is inadequate. Our analysis methodology comprises three complementary levels of theory: the numerical solutions to the semiconductor Bloch equations, an extended semiclassical recollision model, and a quantum wave packet approach. We apply this methodology to two general material types with representative band structures: a bulk system and a hexagonal monolayer system. In the bulk, the interband harmonics generated using elliptically-polarized drivers are found to originate not from tunneling at the minimum band gap $\Gamma$, but from regions away from it. In the monolayer system driven by linearly-polarized pulses, tunneling regions near different symmetry points in the BZ lead to distinct harmonic energies and emission profiles. We show that the imperfect recollisions, where an electron-hole pair recollide while being spatially separated, are important in both bulk and monolayer materials. The excellent agreement between our three levels of theory highlights and characterizes the complexity behind the HHG emission dynamics in solids, and expands on the notion of interband HHG as always originating in trajectories tunnelled at the minimum band gap. Our work furthers the fundamental understanding of HHG in periodic systems and will benefit the future design of experiments.Comment: 18 pages, 13 figure

Quantum interference in attosecond transient absorption of laser-dressed helium atoms

We calculate the transient absorption of an isolated attosecond pulse by helium atoms subject to a delayed infrared (\ir) laser pulse. With the central frequency of the broad attosecond spectrum near the ionization threshold, the absorption spectrum is strongly modulated at the sub-\ir-cycle level. Given that the absorption spectrum results from a time-integrated measurement, we investigate the extent to which the delay-dependence of the absorption yields information about the attosecond dynamics of the atom-field energy exchange. We find two configurations in which this is possible. The first involves multi photon transitions between bound states that result in interference between different excitation pathways. The other involves the modification of the bound state absorption lines by the IR field, which we find can result in a sub-cycle time dependence only when ionization limits the duration of the strong field interaction

Semi-Classical Wavefunction Perspective to High-Harmonic Generation

We introduce a semi-classical wavefunction (SCWF) model for strong-field physics and attosecond science. When applied to high harmonic generation (HHG), this formalism allows one to show that the natural time-domain separation of the contribution of ionization, propagation and recollisions to the HHG process leads to a frequency-domain factorization of the harmonic yield into these same contributions, for any choice of atomic or molecular potential. We first derive the factorization from the natural expression of the dipole signal in the temporal domain by using a reference system, as in the quantitative rescattering (QRS) formalism [J. Phys. B. 43, 122001 (2010)]. Alternatively, we show how the trajectory component of the SCWF can be used to express the factorization, which also allows one to attribute individual contributions to the spectrum to the underlying trajectories