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

Influence of Phase Matching on the Cooper Minimum in Ar High Harmonic Spectra

We study the influence of phase matching on interference minima in high harmonic spectra. We concentrate on structures in atoms due to interference of different angular momentum channels during recombination. We use the Cooper minimum (CM) in argon at 47 eV as a marker in the harmonic spectrum. We measure 2d harmonic spectra in argon as a function of wavelength and angular divergence. While we identify a clear CM in the spectrum when the target gas jet is placed after the laser focus, we find that the appearance of the CM varies with angular divergence and can even be completely washed out when the gas jet is placed closer to the focus. We also show that the argon CM appears at different wavelengths in harmonic and photo-absorption spectra measured under conditions independent of any wavelength calibration. We model the experiment with a simulation based on coupled solutions of the time-dependent Schr\"odinger equation and the Maxwell wave equation, including both the single atom response and macroscopic effects of propagation. The single atom calculations confirm that the ground state of argon can be represented by its field free $p$ symmetry, despite the strong laser field used in high harmonic generation. Because of this, the CM structure in the harmonic spectrum can be described as the interference of continuum $s$ and $d$ channels, whose relative phase jumps by $\pi$ at the CM energy, resulting in a minimum shifted from the photoionization result. We also show that the full calculations reproduce the dependence of the CM on the macroscopic conditions. We calculate simple phase matching factors as a function of harmonic order and explain our experimental and theoretical observation in terms of the effect of phase matching on the shape of the harmonic spectrum. Phase matching must be taken into account to fully understand spectral features related to HHG spectroscopy

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

High harmonic generation from Bloch electrons in solids

We study the generation of high harmonic radiation by Bloch electrons in a model transparent solid driven by a strong mid-infrared laser field. We solve the single-electron time-dependent Schr\"odinger equation (TDSE) using a velocity-gauge method [New J. Phys. 15, 013006 (2013)] that is numerically stable as the laser intensity and number of energy bands are increased. The resulting harmonic spectrum exhibits a primary plateau due to the coupling of the valence band to the first conduction band, with a cutoff energy that scales linearly with field strength and laser wavelength. We also find a weaker second plateau due to coupling to higher-lying conduction bands, with a cutoff that is also approximately linear in the field strength. To facilitate the analysis of the time-frequency characteristics of the emitted harmonics, we also solve the TDSE in a time-dependent basis set, the Houston states [Phys. Rev. B 33, 5494 (1986)], which allows us to separate inter-band and intra-band contributions to the time-dependent current. We find that the inter-band and intra-band contributions display very different time-frequency characteristics. We show that solutions in these two bases are equivalent under an unitary transformation but that, unlike the velocity gauge method, the Houston state treatment is numerically unstable when more than a few low lying energy bands are used

Beyond the single-atom response in absorption lineshapes: Probing a dense, laser-dressed helium gas with attosecond pulse trains

We investigate the absorption line shapes of laser-dressed atoms beyond the single-atom response, by using extreme ultraviolet (XUV) attosecond pulse trains to probe an optically thick helium target under the influence of a strong infrared (IR) field. We study the interplay between the IR-induced phase shift of the microscopic time-dependent dipole moment and the resonant-propagation-induced reshaping of the macroscopic XUV pulse. Our experimental and theoretical results show that as the optical depth increases, this interplay leads initially to a broadening of the IR-modified line shape, and subsequently to the appearance of new, narrow features in the absorption line.Comment: 5 pages, 5 figure

Attosecond pulse shaping around a Cooper minimum

High harmonic generation (HHG) is used to measure the spectral phase of the recombination dipole matrix element (RDM) in argon over a broad frequency range that includes the 3p Cooper minimum (CM). The measured RDM phase agrees well with predictions based on the scattering phases and amplitudes of the interfering s- and d-channel contributions to the complementary photoionization process. The reconstructed attosecond bursts that underlie the HHG process show that the derivative of the RDM spectral phase, the group delay, does not have a straight-forward interpretation as an emission time, in contrast to the usual attochirp group delay. Instead, the rapid RDM phase variation caused by the CM reshapes the attosecond bursts.Comment: 5 pages, 5 figure

Transient absorption and reshaping of ultrafast XUV light by laser-dressed helium

We present a theoretical study of transient absorption and reshaping of extreme ultraviolet (XUV) pulses by helium atoms dressed with a moderately strong infrared (IR) laser field. We formulate the atomic response using both the frequency-dependent absorption cross section and a time-frequency approach based on the time-dependent dipole induced by the light fields. The latter approach can be used in cases when an ultrafast dressing pulse induces transient effects, and/or when the atom exchanges energy with multiple frequency components of the XUV field. We first characterize the dressed atom response by calculating the frequency-dependent absorption cross section for XUV energies between 20 and 24 eV for several dressing wavelengths between 400 and 2000 nm and intensities up to 10^12 W/cm^2. We find that for dressing wavelengths near 1600 nm, there is an Autler-Townes splitting of the 1s ---> 2p transition that can potentially lead to transparency for absorption of XUV light tuned to this transition. We study the effect of this XUV transparency in a macroscopic helium gas by incorporating the time-frequency approach into a solution of the coupled Maxwell-Schr\"odinger equations. We find rich temporal reshaping dynamics when a 61 fs XUV pulse resonant with the 1s ---> 2p transition propagates through a helium gas dressed by an 11 fs, 1600 nm laser pulse.Comment: 13 pages, 8 figures, 1 table, RevTeX4, revise

Effective Gap Equation for the Inhomogeneous LOFF Superconductive Phase

We present an approximate gap equation for different crystalline structures of the LOFF phase of high density QCD at T=0. This equation is derived by using an effective condensate term obtained by averaging the inhomogeneous condensate over distances of the order of the crystal lattice size. The approximation is expected to work better far off any second order phase transition. As a function of the difference of the chemical potentials of the up and down quarks, $\delta\mu$, we get that the octahedron is energetically favored from $\delta\mu=\Delta_0/\sqrt 2$ to $0.95\Delta_0$, where $\Delta_0$ is the gap for the homogeneous phase, while in the range $0.95\Delta_0-1.32\Delta_0$ the face centered cube prevails. At $\delta\mu=1.32\Delta_0$ a first order phase transition to the normal phase occurs.Comment: 11 pages, 5 figure