Kramers-Henneberger Research Articles

The second, third harmonic generations and nonlinear optical rectification of the Mathieu quantum dot with the external electric, magnetic and laser field

In this study, the nonlinear optical properties of the InxGa1−xAs/GaAs Mathieu quantum dot (MQD) are investigated for the first time, focusing on the nonlinear optical rectification (NOR), second harmonic generation (SHG), and third harmonic generation (THG). The effects of external fields such as the electric field, magnetic field, and laser radiation field on the nonlinear optical properties of MQD are examined, along with structural parameters such as quantum dot depth and width determined by the indium concentration. The motivation of the study is to explain the NOR, SHG, and THG characteristics of MQD in response to changes in external fields and structural factors. To investigate the effects of the laser field, the time-dependent part of the laser field is transferred to the potential energy term of the wave equation using the Kramers–Henneberger (KH) and dipole approximations, creating a laser-dressed potential. Then, the effective potential wave equation is solved using the tridiagonal matrix method. The effects of external fields and structural parameters of MQD on the NOR, SHG, and THG coefficients are discussed in detail. The optimality of the structure for device design and applications considering MQD is revealed, and alternative parameter analysis is conducted for this optimality.

Dynamics of Kramers-Henneberger atoms in focused laser beams of circular polarization.

In intense laser fields, electrons of atoms will follow the laser field and undergo quiver motion just like free electrons but still weakly bound to the atomic core, thus forming a set of specific dressed states named Kramers-Henneberger (KH) states, which comprise the KH atoms. In a focused laser beam, in addition to Ponderomotive (PM) force, KH atoms will experience KH force, which is unique to KH atoms. We examine both PM and KH forces as well as corresponding velocity gain of hydrogen and helium atoms in a focused laser field with circular polarization. We work out laser parameters which can be used in experimental confirmation of circularly polarized KH atoms.

Interference patterns in ionization of Kramers–Henneberger atom

We combine IR pump and XUV probe laser pulses to visualize the Kramers–Henneberger (KH) state of the potassium atom. We demonstrate that ionization of such an atom exhibits some molecular-like features such as low order interference maxima in photoelectron momentum spectra. The locations of these maxima allow to estimate spatial dimensions of the KH atom and can be used for accurate calibration of high intensity laser fields. At the same time, we show that an analogy between the KH atom and a homo-nuclear diatomic molecule cannot be extended too far. In particular, higher order interference maxima are very difficult to observe in the case of the KH state. We attribute this to a particular structure of the KH potential which does not confine electron motion to a well-defined potential well unlike in real diatomic molecules.

Laser-Dressed Molecular Point Groups in the Kramers-Henneberger Oscillating Frame-of-Reference: Selection Rules for Higher Harmonic Generation.

Point groups of molecules in a laser, within the Kramers-Henneberger (KH) oscillating frame for laser-dressed states, is given in this work. In a Fourier series of the time-dependent potential, the zeroth-order time-average yields the point group of the laser-dressed molecule. Various laser polarizations and relative molecular orientation induce a new point group or retain the original point group. The dynamical Fourier components (KH potentials) classify as irreducibles of this new laser-dressed point group. Recurrence of unique irreducibles in the Fourier expansion dictates the dynamical symmetry of the Floquet Hamiltonian. Hence, selection rules for harmonic generation spectra are Nk ± 1 in harmonic order, where N is the number of unique irreducibles and .

Resonant tunneling of deuteron-triton fusion in strong high-frequency electromagnetic fields

We investigate deuteron-triton (DT) fusion in the presence of linearly polarized strong electromagnetic fields in high-frequency limit, in which a complex spherical square-well potential is exploited to describe the nuclear potential. Within the framework of the Kramers-Henneberger (KH) transformation, we have calculated the total and angular differential fusion cross sections by investigating the asymptotical phase shifts of the Coulomb wavefunctions. With introducing a dimensionless quantity of $n_d$ representing the ratio of the particle quiver oscillation amplitude to the radius of nuclear potential, we find that, even though the tunneling probability of passing through the Coulomb repulsive potential keeps almost identical to that in the absence of electromagnetic fields, the peak of total fusion sections shows an apparent shift from the well known value of 110 keV to 78 keV for $n_d=0.01$. The angular differential cross sections also show some resonance peaks that shift from zero inclination angle to $\pi/2$ with increasing the parameter $n_d$. The corresponding astrophysical $S$-factors are found to be enhanced by several times in amplitudes. With the help of Wentzel-Kramers-Brillouin (WKB) approximate wavefunctions, the shape-resonance tunneling mechanism of the above findings are uncovered and some implications are discussed.

Enhanced proton-boron nuclear fusion cross sections in intense high-frequency laser fields

We investigate the proton-boron nuclear fusion cross sections under the influence of the intense linearly polarized monochromatic laser fields with high frequency. First, we rewrite the time-dependent Schrödinger equation using Kramers-Henneberger (KH) transformation which allows for shifting all time dependence of the problem into the potential function. Then, for the intense laser fields that satisfy the high frequency limit, the time-averaged scheme in the KH framework should be valid. We can use WKB approximation to evaluate Coulomb barrier penetrability and then calculate proton-boron nuclear fusion cross sections by a phenomenological Gamow form. We show that the corresponding Coulomb barrier penetrability increases significantly due to the depression of the time-averaged potential barrier. As a result, we find that proton-boron nuclear fusion cross sections can be enhanced effectively depending on a dimensionless quantity nd, which equals the ratio of the quiver oscillation amplitude to the geometrical touching radius of the proton and boron nucleus. For nd=9, we predict that the resonance peak of the fusion cross-section is enhanced by about 26 times at the incident energy of ε=148 keV. And for another incident energy of ε=586 keV, the resonance peak of fusion cross-section is not only enhanced but also shifted to lower energy of ε=392 keV due to the mechanism of over-barrier fusion.

Phase-dependent cross sections of deuteron-triton fusion in dichromatic intense fields with high-frequency limit

We investigate the influence of strong dichromatic laser fields (i.e. 1{\omega}-2{\omega} and 1{\omega}-3{\omega}) with high-frequency limit on the cross sections of deuteron-triton(DT) fusion in Kramers-Henneberger(KH) frame. We focus on the transitions of phase-dependent effects depending on a dimensionless quantity n_{d} , which equals the ratio of the quiver oscillation amplitude to the geometrical touching radius of the deuteron and triton as defined in our previous research. Theoretical calculations show that the angle-dependent as well as phase-dependent Coulomb barrier penetrabilities can be enhanced in dichromatic intense fields, and the corresponding angle-averaged penetrabilities and the fusion cross sections increase significantly compared with field-free case. Moreover, we find that there are twice shifts of the peak in the cross sections whenever the frequency becomes sufficiently low or the intensity sufficiently high. The reason for the first shift is the angle-dependence effects for sub-barrier fusion, while the second shift is due to the accumulation of over-barrier fusion, these mechanisms are analyzed in detail in this paper.

Effect of terahertz laser field on anisotropic optical absorption and refractive index changes of coaxial square quantum well wires

The influence of terahertz laser field on nonlinear anisotropic optical properties, such as optical absorption and refractive index changes is studied. By solving the Schrödinger equation of the system in the framework of effective mass with the Kramers–Henneberger (KH) transformation, the eigenfunctions and energy eigenvalues of the system are obtained. The optical absorption and refractive index changes are deduced by the compact density matrix form and the scheme of iterative method. The results show that the polarization angle and intensity of terahertz laser field have a strongly influence on the peak of optical absorption and refractive index change in different directions respectively.

Symmetry breaking of Kramers-Henneberger atoms by ponderomotive force.

It was believed that Kramers-Henneberger (KH) atoms in a linearly polarized superintense laser field exhibit the structure of "dichotomy." At large quiver amplitude, the two lowest-lying eigenstates are degenerated and both have a dichotomous symmetric structure. However, this is not a common structure for KH atoms because KH atoms practically can only exist in the focused laser field. However, in a focused laser, KH state electrons usually experience the ponderomotive force, which will lift the degeneracy and break the symmetry.

The laser field controlling on the nonlinear optical specifications of the electric field-triggered Rosen-Morse quantum well

We consider, for the first time, optical specifications such as the nonlinear optical rectification (NOR), the second harmonic generation (SHG) and the third harmonic generation (THG) of quantum well (QW) that has the Rosen-Morse potential confinement and is generated by GaAs/GaAlAs heterostructure. To do this, QW structure is firstly asymmetrized by applying an external electric field, as 10 kV/cm. Therefore, the electric field-triggered (F=10 kV/cm) Rosen-Morse QW (eftRMQW) is taken into consideration throughout the study. In this study, it is elucidated that how to control NOR, SHG and THG optical responses through monochromatic linearly polarized intense laser field (ILF). In order to be able to investigate the ILF effects, the time-dependent of ILF is removed to potential energy term of the wave equation by using Kramers-Henneberger (KH) and the dipole approximations, building the laser-dressed potential. Then, the bound state energies and the wave functions of eftRMQW are obtained using the diagonalization method within the effective mass approach and the parabolic approximation. The influences of the ILF and structural parameters of eftRMQW on NOR, SHG and THG coefficients are discussed in detail. The optimum of structure is ferreted out for devices design and applications that will consider eftRMQW, and for this optimum the alternative parameter analysis is carried out.

Enhanced deuterium-tritium fusion cross sections in the presence of strong electromagnetic fields

We investigate deuterium-tritium (DT) fusion cross sections in the presence of electromagnetic fields with high intensity and high frequency. With the help of the Kramers-Henneberger (KH) transformation, we show that the corresponding Coulomb barrier penetrability increases significantly due to the depression of the time-averaged potential barrier. As a result, we find that DT fusion cross sections can be enhanced depending effectively on a dimensionless quantity ${n}_{\mathrm{d}}$, which equals the ratio of the quiver oscillation amplitude to the geometrical touching radius of the deuterium and tritium nuclei. For ${n}_{\mathrm{d}}=9$, we predict that the fusion cross section is almost five times the value in the absence of electromagnetic fields, which implies that the famous Lawson criterion might be relaxed to some extent.

Nonlinear optical properties of morse quantum well modulated by THz laser fields

In this study, the influence of structure parameter (η) and intense laser field (ILF) on the optical properties such as the nonlinear optical rectification (NOR) coefficient, second and third harmonic generation (SHG and THG) coefficients related to intersubband transitions in a quantum well with Morse confinement potential are theoretically studied. The energy levels and corresponding wave functions of the system are obtained by solving the one-electron Hamiltonian within the framework of the effective-mass, parabolic-band approximations and Kramers-Henneberger (KH) transformation. The optical properties of the structure are calculated through the compact density matrix approach. Numerical calculations are brought out for a typical GaAs quantum well. The results unveil significant influences of ILF and structure parameters of Morse confinement potential on resonant peak position and peak intensity of the NOR, SHG and THG coefficients.

Optical specifications of laser-induced Rosen-Morse quantum well

In this study, for the first time, the influences of a monochromatic linearly polarized laser field on the total refractive index changes (TRICs) and the total absorption coefficients (TACs) of quantum well (QW) with the Rosen-Morse potential confinement by constituting GaAs/GaAlAs heterostructure are considered. Time-dependent in the Schrödinger equation is modified through the Kramers-Henneberger (KH) transformation and the dipole approximation, and then the laser-dressed counterpart of well potential is generated by using the Ehlotzky approximation. The bound state energy values and the wave functions of the Rosen-Morse quantum well (RMQW) under the influence of the intense laser field (ILF) are obtained by using the diagonalization method in the framework of the effective mass approach and the parabolic band approximation. The effects of structure parameters on TRICs and TACs of RMQW are also explained in detail, as well as the ILF's ones. In addition to these, the alternativeness to each other of the structure parameters and the ILF on the optical specifications is also discussed. The results of the present work are necessary and crucial in optimization of the optical specifications of RMQW to be fabricated for devices applications.

Stark effect of Kramers-Henneberger atoms.

The Electric Stark effect of a Kramers-Henneberger (KH) state of hydrogen atoms in both linearly and circularly polarized laser fields is studied. For the ground KH state of H atoms with a small quiver amplitude, the quadratic Stark effect is observed. For a large quiver amplitude, the Stark effect is quadratic only in a weak electric field and quickly changes to linear as the electric field increases. The atomic structure of the KH state is very sensitive to the electric field and can be easily polarized. The huge polarizability and induced dipole moment are comparable to those of Rydberg atoms.

Limit on Excitation and Stabilization of Atoms in Intense Optical Laser Fields.

Atomic excitation in strong optical laser fields has been found to take place even at intensities exceeding saturation. The concomitant acceleration of the atom in the focused laser field has been considered a strong link to, if not proof of, the existence of the so-called Kramers-Henneberger (KH) atom, a bound atomic system in an intense laser field. Recent findings have moved the importance of the KH atom from being purely of theoretical interest toward real world applications; for instance, in the context of laser filamentation. Considering this increasing importance, we explore the limits of strong-field excitation in optical fields, which are basically imposed by ionization through the spatial field envelope and the field propagation.

An electron of helium atom under a high-intensity laser field

We scrutinize the behavior of eigenvalues of an electron in a helium (He) atom as it interacts with electric field directed along the z-axis and is exposed to linearly polarized intense laser field radiation. To achieve this, we freeze one electron of the He atom at its ionic ground state and the motion of the second electron in the ion core is treated via a more general case of screened Coulomb potential model. Using the Kramers–Henneberger (KH) unitary transformation, which is the semiclassical counterpart of the Block–Nordsieck transformation in the quantized field formalism, the squared vector potential that appears in the equation of motion is eliminated and the resultant equation is expressed in the KH frame. Within this frame, the resulting potential and the corresponding wave function are expanded in Fourier series and using Ehlotzky’s approximation, we obtain a laser-dressed potential to simulate intense laser field. By fitting the more general case of screened Coulomb potential model into the laser-dressed potential, and then expanding it in Taylor series up to , we obtain the solution (eigenvalues and wave function) of an electron in a He atom under the influence of external electric field and high-intensity laser field, within the framework of perturbation theory formalism. We found that the variation in frequency of laser radiation has no effect on the eigenvalues of a He electron for a particular electric field intensity directed along z-axis. Also, for a very strong external electric field and an infinitesimal screening parameter, the system is strongly bound. This work has potential application in the areas of atomic and molecular processes in external fields including interactions with strong fields and short pulses.

Hydrogen atom in a laser-plasma

We scrutinize the behaviour of the eigenvalues of a hydrogen atom in a quantum plasma as it interacts with an electric field directed along θ = π and is exposed to linearly polarized intense laser field radiation. We refer to the interaction of the plasma with the laser light as laser-plasma. Using the Kramers–Henneberger (KH) unitary transformation, which is the semiclassical counterpart of the Block–Nordsieck transformation in the quantized field formalism, the squared vector potential that appears in the equation of motion is eliminated and the resultant equation is expressed in the KH frame. Within this frame, the resulting potential and the corresponding wavefunction have been expanded in Fourier series, and using Ehlotzky’s approximation we obtain a laser-dressed potential to simulate an intense laser field. By fitting the exponential-cosine-screened Coulomb potential into the laser-dressed potential, and then expanding it in Taylor series up to , we obtain the eigensolution (eigenvalues and wavefunction) of the hydrogen atom in laser-plasma encircled by an electric field, within the framework of perturbation theory formalism. Our numerical results show that for a weak external electric field and a very large Debye screening parameter length, the system is strongly repulsive, in contrast with the case for a strong external electric field and a small Debye screening parameter length, when the system is very attractive. This work has potential applications in the areas of atomic and molecular processes in external fields, including interactions with strong fields and short pulses.

The role of the Kramers–Henneberger atom in the higher-order Kerr effect

We discuss the connection between strong-field ionization, saturation of the Kerr response and the formation of the Kramers–Henneberger (KH) atom and long-living excitations in intense infrared (IR) external fields. We present a generalized model for the intensity-dependent response of atoms in strong IR laser fields, describing deviations in the nonlinear response at the frequency of the driving field from the standard model. We show that shaping the driving laser pulse allows one to reveal signatures of the excited KH states in the Kerr response of an individual atom.

He–He chemical bonding in high-frequency intense laser fields

On the basis of the Kramers–Henneberger (KH) high-frequency approximation, we carried out an ab initio molecular orbital calculation for He2 in intense laser fields. The potential energy curve is found to be attractive, indicating that a He–He chemical bond is formed. The formation of the He–He chemical bond is ascribable to changes in the nature of KH molecular orbitals. Intense laser fields cause a kind of sp hybridization of KH atomic orbitals. The degree of the hybridization depends on the internuclear distance, and reaches a maximum at around the equilibrium internuclear distance. This hybridization remarkably strengthens/weakens the bonding/anti-bonding character of the 1σg/1σu KH molecular orbitals, respectively.

Applicability of the Kramers-Henneberger approximation in the theory of strong-field ionization

The ionization of the one-dimensional model system with a short-range potential by a linearly polarized laser field is studied by direct numerical integration of the non-stationary Schrödinger equation. The results are interpreted in terms of both field-free atomic states and Kramers-Henneberger (KH) eigenstates. The dynamics of the system is analysed to determine which potential (atomic or KH) is physically more appropriate to describe the ionization process. The justification of the KH approach is also examined. A new limitation of the validity of the KH approximation is found to exist in the case of low laser frequencies.