Stimulated hyper-Raman scattering at high photon densities

Nonlinear effects. Three-photon process at high photon densities

We have calculated numerically the excitation spectra arising from the interaction of a two-level atom with two strong electromagnetic fields. In the limit of high photon densities, the excitation spectra are considered when one of two laser fields is at resonance while the frequency of the other laser field is varied as well as when both laser fields are off resonance. At resonance, the spectra consist of a central peak and several sidebands peaked at the frequencies ω = ω a ± m(ω a - ω b ), corresponding to the multi-frequency mixing of both laser fields where m is a positive integer. Sidebands also appear at fractional multiples of frequencies and are due to contributions arising from energy shifts induced by the laser fields. The computed spectra at resonance are discussed and compared with the observed ones. The off-resonance spectra are computed for a wide range of values of Rabi frequencies and detunings, and are presented graphically. It is found that in the off-resonance case, mixing of a larger number of light frequencies occurs from that in the resonance case. The intensity of the peaks in the off-resonance case are immensely enhanced in comparison with those at resonance. The enhancement of the intensities is in agreement with the observed ones and its occurrence is theoretically explained. It is shown that if the detunings are properly chosen then the desired peak describing the required mixing of frequencies of the laser fields can be immensely enhanced. The method may be useful to investigate multi-frequency resonances of the rotation or rotation-vibration spectra of excited states or excited states near their ionization continua.

Excitation spectrum of two-identical three-level atoms at high photon densities

We have studied the fluorescent spectra arising from the interaction of a four-level atom with a strong bichromatic field and a weak signal field simultaneously. The atomic system consists of two upper excited states \ensuremath{\Vert}3〉 and \ensuremath{\Vert}4〉 and two lower states \ensuremath{\Vert}1〉 and \ensuremath{\Vert}2〉 and the two laser fields, whose frequency modes ${\ensuremath{\omega}}_{a}$ and ${\ensuremath{\omega}}_{b}$ are initially populated, operate between the states \ensuremath{\Vert}2〉\ensuremath{\leftrightarrows}\ensuremath{\Vert}4〉 and \ensuremath{\Vert}2〉\ensuremath{\leftrightarrows}\ensuremath{\Vert}3〉, respectively. Using the Green-function formalism and a model Hamiltonian, where all the free and interacting fields are quantized, we have studied the transitions \ensuremath{\Vert}4〉\ensuremath{\leftrightarrows}\ensuremath{\Vert}1〉 and \ensuremath{\Vert}3〉\ensuremath{\leftrightarrows}\ensuremath{\Vert}1〉 of the signal field in the limit of high photon densities of both laser fields. The expression of the spectral function for the \ensuremath{\Vert}1〉\ensuremath{\rightarrow}\ensuremath{\Vert}4〉 transition describes stimulated one-photon and three-photon processes, respectively. The one-photon spectra near the frequency \ensuremath{\omega}\ensuremath{\approxeq}${\ensuremath{\omega}}_{41}$ of the signal field consist of a central peak and two pairs of sidebands whose intensities take always positive and negative values indicating that attenuation and amplification (stimulated emission) of the signal field takes place at the frequencies in question, respectively. The spectral function for the three-photon process near the frequency \ensuremath{\omega}\ensuremath{\approxeq}${\ensuremath{\omega}}_{41}$-2${\ensuremath{\omega}}_{a}$ describes two pairs of sidebands whose intensities are always negative implying that strong amplification of the signal field occurs. The computed one-photon and three-photon spectra are presented graphically for different values of Rabi frequencies and detunings of both laser fields, respectively. Then using a classical description of both laser fields, the spectral functions describing one-photon and three-photon processes are calculated and the derived results are compared with the corresponding ones when the fields are quantized. It is found that the results obtained when the fields are quantized and in the limit of high photon densities describe the classical as well as the quantum nature of the photons which is lost in the classical treatment.

We have considered the excitation spectra for a three-level atom interacting simultaneously with a strong pump field and a weak signal field. The atom consists of an upper excited state ‖2〉 and two lower states ‖1〉 and ‖3〉 where the transition ‖1〉↔‖3〉 is electric-dipole forbidden from parity considerations. The pump field, whose frequency mode ωb is initially populated, operates near resonance between the states ‖2〉 and ‖3〉, ‖2〉↔‖3〉, while the signal field describes the radiative decays ‖2〉→‖3〉 and ‖2〉→‖1〉, respectively. Using the Green function method, the spectral functions for the signal field have been calculated in the limit of high photon densities of the pump field describing the following processes: (i) one-photon process; the spectra consist of a main peak at the signal frequency ω=ω21 and a pair of sidebands at ω=ω21±Ω−(ω23−ωb)/2, where Ω2=Ω2b/2+(ω23−ωb)2/4 with Ωb and (ω23−ωb) being the Rabi frequency and the detuning of the pump field, respectively. The intensity of the main peak at ω=ω21 is positive indicating signal-field absorption while those of the sidebands are always negative implying amplification (stimulated emission) of the signal field. The sum of the intensities (in absolute value) of the sidebands is twice that of the main peak at resonance while in the off-resonance case it depends on the value of the ratio (ω23−ωb)/2Ω. (ii) Stimulated three-photon process; the spectra consists of a pair of sidebands peaked at ω=ω21−2ωb±Ω−(ω23−ωb)/2 whose intensity is negative indicating amplification. At resonance the sidebands have equal intensities but at finite detuning asymmetry arises enhancing one peak while diminishing the intensity of the other. (iii) Stimulated two-photon process; the stimulated Raman spectra consist of a peak at ω=ω31, which has a delta function distribution, and a pair of strongly amplified sidebands at ω=ω31±Ω+(ω23−ωb)/2. The computed spectra for the three processes are presented graphically for different values of Rabi frequencies and detunings.

Topological phase transitions in free fermion systems can be characterized by closing of single-particle gap and change in topological invariants. However, in the presence of electronic interactions, topological phase transitions are more complicated. In paper I of this series (arXiv:1510.07816), we have developed an efficient scheme to evaluate the topological invariants based on Green's function formalism. Here, in paper II, we demonstrate four interaction-drive topological phase transitions (TPTs) in two-dimensional (2D) interacting topological insulators (TIs) via large-scale quantum Monte Carlo (QMC) simulations, based on the scheme of evaluating topological invariants presented in paper I. Across these transitions, the defining symmetries of the TIs have been neither explicitly nor spontaneously broken. In the first two models, the topological invariants calculated from Green's function formalism succeed in characterizing interaction-driven TPTs. However, in the second two models, we find single-particle gap does not close and the topological invariants constructed from single-particle Green's function acquire no change across the TPTs. Unexpected breakdown of the Green's function formalism in constructing topological invariants is thus discovered. We thence classify the TPTs in interacting TIs into two categories: those have noninteracting correspondence can be characterized successfully by the topological invariants constructed from Green's functions, while for the others that do not have noninteracting correspondence, the Green's function formalism experiences a breakdown but more interesting and exciting phenomena, such as emergent collective critical modes at the transition, arise. Discussion on the success and breakdown of topological invariants constructed from the Green's function formalism in the context of symmetry protected topological (SPT) states is presented.

Photon density-density correlation spectrum of a three-level atom at high photon densities

Herein, a highly practical first‐principles approach for studying phonon transport across various materials, ranging from low‐dimensional systems to three‐dimensional bulk structures, as well as nanostructures, is presented. This method integrates the nonequilibrium Green's function (NEGF) formalism with ab initio calculations of dynamical matrices generated by Quantum Espresso. A detailed technical approach for extracting atomistic force constants and forming dynamical matrices that adhere to the tri‐diagonal technique within the NEGF framework is provided. Additionally, an efficient method for constructing dynamical matrices of conventional cells from those of primary cells is introduced, remarkably reducing the computational costs associated with density‐functional theory calculations. The robustness and applicability of this methodology are validated through several case studies.

The problem of currents induced in the scanning tunnelling microscope due to incident laser radiation is analysed. The authors uses a light-binding description of the microscope tunnelling junction, and the interaction with the laser field is taken into account by an effective time-dependent coupling between tip and sample. The currents generated at frequencies that are linear combinations of the incident frequencies are then obtained with the help of a nonequilibrium Green's function formalism. Particular attention is paid to the rectification and difference frequency generation effects. In this work they extend previous results for the rectified current to the case where a direct bias is applied in addition to the laser field. It is shown that in the limit of very low frequencies the dynamical response may be deduced from the static characteristic curve. In order to compare with recent experimental data, they perform model calculations for a graphite sample and study the induced photocurrent as a function of bias voltage, tip-sample distance and photon energy. The limitations of the adiabatic approximation are discussed. Finally, they present results for the rectified current in the presence of an adsorbed molecule with a characteristic vibrational mode. The contribution from inelastic processes is obtained to the lowest order in the electron-phonon coupling. It is shown that the onset of inelastic tunnelling should be reflected as a singularity in the rectified current as a function of both bias voltage and photon energy.

This paper describes the point defect treatment in nanowire MOSFETs. The 3D Poisson equation is self-consistently coupled to the Schrodinger equation. We adopt the mode-space representation in which the 3D Schrodinger equation is divided into a 2D equation, including the confinement of the cross-section, and an ID equation describing the ballistic transport based on the nonequilibrium Green's function formalism (NEGF). We use the simplest form of the tight-binding theory, with one orbital per atom, and considering only the first-neighbor-interactions. In this framework, equivalent to the ellipsoidal energy band approximation, influence of point defects on electronic transport is discussed.

The electronic structure of transition metal tricarbonyl derivatives in the ground state and the cationic hole-states. A semiempirical indo mo investigation based on the Green's function formalism

A laser field is a potential control tool for operating ultrafast electronic devices due to a wide variety of options such as field strength, frequency, and polarization. To investigate these variables upon electron transport through a single-molecule device, we simulate a phenyl-acetylene macrocycle (PAM) within a linear-polarized laser field using single-particle Green's functions combined with the non-Hermitian Floquet theory. In the absence of the laser field, the PAM behaves as a perfect insulator due to destructive quantum interference. In the weak-field regime, field-amplitude power laws for one-, two-, and three-photon assisted tunneling are evident in the computational results. The study reveals a range of experimentally feasible field strengths for the observation of picoampere current caused by photon assisted tunneling. In addition, we find that the light-driven current is proportional to the cosine square of the polarization angle, and molecular electronic structure is revealed by the current-frequency characteristics. The origin of these behaviors is established using non-Hermitian Floquet perturbation analysis. The computations show that PAM-based optoelectronic switches have robust large on-off switching ratios under weak-field operating conditions, which are not sensitive to asymmetric molecule-lead couplings.

We extend the self-consistent Green's functions formalism to take into account three-body interactions. We analyze the perturbative expansion in terms of Feynman diagrams and define effective one- and two-body interactions, which allows for a substantial reduction of the number of diagrams. The procedure can be taken as a generalization of the normal ordering of the Hamiltonian to fully correlated density matrices. We give examples up to third order in perturbation theory. To define nonperturbative approximations, we extend the equation of motion method in the presence of three-body interactions. We propose schemes that can provide nonperturbative resummation of three-body interactions. We also discuss two different extensions of the Koltun sum rule to compute the ground state of a many-body system.

Several ultrasound-based techniques for the estimation of soft tissue elasticity are currently being investigated. Most of them study the medium response to dynamic excitations. Such responses are usually modeled in a purely elastic medium using a Green's function solution of the motion equation. However, elasticity by itself is not necessarily a discriminant parameter for malignancy diagnosis. Modeling viscous properties of tissues could also be of great interest for tumor characterization. We report in this paper an explicit derivation of the Green's function in a viscous and elastic medium taking into account shear, bulk, and coupling waves. From this theoretical calculation, 3D simulations of mechanical waves in viscoelastic soft tissues are presented. The relevance of the viscoelastic Green's function is validated by comparing simulations with experimental data. The experiments were conducted using the supersonic shear imaging (SSI) technique which dynamically and remotely excites tissues using acoustic radiation force. We show that transient shear waves generated with SSI are modeled very precisely by the Green's function formalism. The combined influences of out-of-plane diffraction, beam shape, and shear viscosity on the shape of transient waves are carefully studied as they represent a major issue in ultrasound-based viscoelasticity imaging techniques.

The electron-gas problem is investigated by means of a self-consistent Green's-function formalism with the aim of developing practical approximation schemes for metallic densities. The work is based on the Dyson equation for the single-particle propagator $G[U]$ as a functional of an external potential $U$. The self-energy functional $\ensuremath{\Sigma}[U]$, appearing in the Dyson equation, is evaluated by perturbation theory in terms of the exact $G[U]$, thereby leading to a self-consistent problem. A hierarchy of approximations is generated by summing successively larger sets of graphs for $\ensuremath{\Sigma}[U]$. The Dyson equation is expanded in a functional Taylor series in $U$ and yields a nonlinear integral equation for the $U=0$ propagator as well as linear integral equations for the $U=0$ higher-order Green's functions, with kernels dependent on $\frac{\ensuremath{\delta}\ensuremath{\Sigma}}{\ensuremath{\delta}U}$. In applications of the theory, the emphasis is on calculating the longitudinal dielectric function $\ensuremath{\epsilon}$ in terms of the contracted four-point Green's function. The linear integral equation for the latter is solved after making a low-momentum dominance approximation to the kernel. The result is a general, but approximate, closed-form expression for $\ensuremath{\epsilon}$ which can be used for different choices of $\ensuremath{\Sigma}$. The following five approximations for $\ensuremath{\epsilon}$, based on different approximations for $\ensuremath{\Sigma}$, are presented: the Hartree-Fock, random-phase, generalized random-phase, second-stage random-phase, and low-high-density approximations. The last approximation is designed to work well at the two extremes of the density spectrum and, hopefully, also at metallic densities. The long-wavelength plasmon dispersion relations obtained from two different versions of the generalized random-phase approximation for $\ensuremath{\epsilon}$ agree closely with the results of Kanazawa et al. and of Singwi et al.