(b) Write out the equations for the time dependence of ρ11, ρ22, ρ12 and ρ21 assuming that a light field interaction V = -μ12Ee iωt + c.c. couples only levels |1> and |2>, and that the excited levels exhibit spontaneous decay. (8 marks) (c) Under steady-state conditions, find the ratio of populations in states |2> and |3>. (3 marks) (d) Find the slowly varying amplitude ̃ ρ 12 of the polarization ρ12 = ̃ ρ 12e iωt . (6 marks) (e) In the limiting case that no decay is possible from intermediate level |3>, what is the ground state population ρ11(∞)? (2 marks) 2. (15 marks total) In a 2-level atom system subjected to a strong field, dressed states are created in the form |D1(n)> = sin θ |1,n> + cos θ |2,n-1> |D2(n)> = cos θ |1,n> sin θ |2,n-1>

The Quantum Theory of Light

Annual review of condensed matter physics

Journal of Physics Condensed Matter: Preface

This self-contained, comprehensive book describes the fundamental properties of soft x-rays and extreme ultraviolet (EUV) radiation and discusses their applications in a wide variety of fields, including EUV lithography for semiconductor chip manufacture and soft x-ray biomicroscopy. The author begins by presenting the relevant basic principles such as radiation and scattering, wave propagation, diffraction, and coherence. He then goes on to examine a broad range of phenomena and applications. The topics covered include EUV lithography, biomicroscopy, spectromicroscopy, EUV astronomy, synchrotron radiation, and soft x-ray lasers. He also provides a great deal of useful reference material such as electron binding energies, characteristic emission lines and photo-absorption cross-sections. The book will be of great interest to graduate students and researchers in engineering, physics, chemistry, and the life sciences. It will also appeal to practicing engineers involved in semiconductor fabrication and materials science.

X-Rays and Extreme Ultraviolet Radiation: Principles and Applications

When intense light interacts with an atomic gas, recollision between an ionizing electron and its parent ion creates high-order harmonics of the fundamental laser frequency. This sub-cycle effect generates coherent soft X-rays and attosecond pulses, and provides a means to image molecular orbitals. Recently, high harmonics have been generated from bulk crystals, but what mechanism dominates the emission remains uncertain. To resolve this issue, we adapt measurement methods from gas-phase research to solid zinc oxide driven by mid-infrared laser fields of 0.25 volts per angstrom. We find that when we alter the generation process with a second-harmonic beam, the modified harmonic spectrum bears the signature of a generalized recollision between an electron and its associated hole. In addition, we find that solid-state high harmonics are perturbed by fields so weak that they are present in conventional electronic circuits, thus opening a route to integrate electronics with attosecond and high-harmonic technology. Future experiments will permit the band structure of a solid to be tomographically reconstructed.

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Linking high harmonics from gases and solids

Processes involving ultrafast laser driven electron-phonon dynamics play a fundamental role in the response of quantum systems in a growing number of situations of interest, as evidenced by phenomena such as strongly driven phase transitions and light driven engineering of material properties. To show how these processes can be captured from a computational perspective, we simulate the transient absorption spectra and high harmonic generation signals associated with valley selective excitation and intra-band charge carrier relaxation in monolayer hexagonal boron nitride. We show that the multi-trajectory Ehrenfest dynamics approach, implemented in combination with real-time time-dependent density functional theory and tight-binding models, offers a simple, accurate and efficient method to study ultrafast electron-phonon coupled phenomena in solids under diverse pump-probe regimes which can be easily incorporated into the majority of real-time ab-initio software packages.

Revealing Ultrafast Phonon Mediated Inter-Valley Scattering through Transient Absorption and High Harmonic Spectroscopies

We study the electric transport and high-order harmonic generation in graphene with the quantum master equation. The microscopic mechanism of these THz-induced non-linear phenomena is understood from the viewpoint of the nonequilibrium steady state.

THz-induced nonlinear electric current and high-order harmonic generation in graphene

We investigate mechanisms of coherent phonon generation in time-dependent density-functional theory. It provides intuitive understanding of the generation mechanism as well as its change depending on electric field frequency.

Ab-initio theoretical approach to coherent phonon generation in solids

We perform a frequency-resolved analysis of electron dynamics in solids to obtain microscopic insight into linear and nonlinear optical phenomena. For the analysis, we first compute the electron dynamics under optical electric fields and evaluate the microscopic current density as a function of time and space. Subsequently, we perform the Fourier transformation on the microscopic current density and obtain the corresponding quantity in the frequency domain. The frequency-resolved microscopic current density provides insight into the microscopic electron dynamics in real-space at the frequency of linear and nonlinear optical responses. We apply frequency-resolved microscopic current density analysis to light-induced electron dynamics in aluminum, silicon, and diamond based on the first-principles electron dynamics simulation according to the time-dependent density functional theory. Consequently, the nature of delocalized electrons in metals and bound electrons in semiconductors and insulators is suitably captured by the developed scheme.

Frequency-resolved microscopic current density analysis of linear and nonlinear optical phenomena in solids

We develop a first-principles simulation method for attosecond time-resolved photoelectron spectroscopy. This method enables us to directly simulate the whole experimental processes, including excitation, emission and detection on equal footing. To examine the performance of the method, we use it to compute the reconstruction of attosecond beating by interference of two-photon transitions (RABBITT) experiments of gas-phase Argon. The computed RABBITT photoionization delay is in very good agreement with recent experimental results from [Kl\"under et al, Phys. Rev. Lett. 106 143002 (2011)] and [Gu\'enot et al, Phys. Rev. A 85 053424 (2012)]. This indicates the significance of a fully-consistent theoretical treatment of the whole measurement process to properly describe experimental observables in attosecond photoelectron spectroscopy. The present framework opens the path to unravel the microscopic processes underlying RABBITT spectra in more complex materials and nanostructures.

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Shunsuke A. Sato

Papers

Revealing Ultrafast Phonon Mediated Inter-Valley Scattering through Transient Absorption and High Harmonic Spectroscopies

THz-induced nonlinear electric current and high-order harmonic generation in graphene

Ab-initio theoretical approach to coherent phonon generation in solids

Frequency-resolved microscopic current density analysis of linear and nonlinear optical phenomena in solids

First-principles simulations for attosecond photoelectron spectroscopy based on time-dependent density functional theory