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

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

Testing over-representation of observations in subsets of a DEA technology

This paper proposes a test for whether data are over-represented in a given production zone, i.e. a subset of a production possibility set which has been estimated using the non-parametric Data Envelopment Analysis (DEA) approach. A binomial test is used that relates the number of observations inside such a zone to a discrete probability weighted relative volume of that zone. A Monte Carlo simulation illustrates the performance of the proposed test statistic and suggests good estimation of both facet probabilities and the assumed common inefficiency distribution in a three dimensional input space.Data Envelopment Analysis (DEA); Over-representation; Data density; Binomial test; Convex hull

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

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

The adenomatous polyposis coli protein unambiguously localizes to microtubule plus ends and is involved in establishing parallel arrays of microtubule bundles in highly polarized epithelial cells

Loss of full-length adenomatous polyposis coli (APC) protein correlates with the development of colon cancers in familial and sporadic cases. In addition to its role in regulating β-catenin levels in the Wnt signaling pathway, the APC protein is implicated in regulating cytoskeletal organization. APC stabilizes microtubules in vivo and in vitro, and this may play a role in cell migration (Näthke, I.S., C.L. Adams, P. Polakis, J.H. Sellin, and W.J. Nelson. 1996. J. Cell Biol. 134:165–179; Mimori-Kiyosue, Y., N. Shiina, and S. Tsukita. 2000. J. Cell Biol. 148:505–517; Zumbrunn, J., K. Inoshita, A.A. Hyman, and I.S. Näthke. 2001. Curr. Biol. 11:44–49) and in the attachment of microtubules to kinetochores during mitosis (Fodde, R., J. Kuipers, C. Rosenberg, R. Smits, M. Kielman, C. Gaspar, J.H. van Es, C. Breukel, J. Wiegant, R.H. Giles, and H. Clevers. 2001. Nat. Cell Biol. 3:433–438; Kaplan, K.B., A. Burds, J.R. Swedlow, S.S. Bekir, P.K. Sorger, and I.S. Näthke. 2001. Nat. Cell Biol. 3:429–432). The localization of endogenous APC protein is complex: actin- and microtubule-dependent pools of APC have been identified in cultured cells (Näthke et al., 1996; Mimori-Kiyosue et al., 2000; Reinacher-Schick, A., and B.M. Gumbiner. 2001. J. Cell Biol. 152:491–502; Rosin-Arbesfeld, R., G. Ihrke, and M. Bienz. 2001. EMBO J. 20:5929–5939). However, the localization of APC in tissues has not been identified at high resolution. Here, we show that in fully polarized epithelial cells from the inner ear, endogenous APC protein associates with the plus ends of microtubules located at the basal plasma membrane. Consistent with a role for APC in supporting the cytoskeletal organization of epithelial cells in vivo, the number of microtubules is significantly reduced in apico-basal arrays of microtubule bundles isolated from mice heterozygous for APC

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

Spatial separation of large dynamical blue shift and harmonic generation

We study the temporal and spatial dynamics of the large amplitude and frequency modulation that can be induced in an intense, few cycle laser pulse as it propagates through a rapidly ionizing gas. Our calculations include both single atom and macroscopic interactions between the non-linear medium and the laser field. We analyze the harmonic generation by such pulses and show that it is spatially separated from the ionization dynamics which produce a large dynamical blue shift of the laser pulse. This means that small changes in the initial laser focusing conditions can lead to large differences in the laser frequency modulation, even though the generated harmonic spectrum remains essentially unchanged.Comment: 4 pages, 5 figures. Under revisio