High-frequency Laser Field Research Articles

A polar diatomic molecule under a high-frequency laser field: classical analytical solution

AbstractDynamics of a polar diatomic molecule (represented as the oscillating rotator model) under external fields is the most fundamental problem and the testbed in molecular physics—analogously to the dynamics of hydrogenic atom (represented as the model of an electron in the Coulomb field) under external fields being the most fundamental problem and the testbed in atomic physics. We present the classical analytical study of the dynamical Stark effect in the oscillating rotator under a high-frequency laser field. We obtain the analytical results by using the method of effective potentials. We demonstrate that under the laser field, the rotation frequency increases, while the oscillation frequency decreases, and the amplitude of the oscillations increases. More significantly, the laser field causes the generation of the second harmonic in the oscillations of this system. This is an important, counterintuitive result in studying this fundamental physical system. We also drew attention to some flaws in the literature on this subject.

The impact of the laser field on the electronic properties of a hydrogen molecular ion in a Gaussian quantum dot

In this study, the influence of a circularly polarized non-resonant high-frequency laser field radiation on the electronic structure of a hydrogen molecular ion formed by two fixed hydrogen-like donor atoms bound to an electron confined in a two-dimensional Gaussian quantum dot is carried out. The low-lying energy states of the molecular complex were calculated by using the two-dimensional diagonalization method. The results show that the stability of the molecular complex is sensitive to the non-resonant laser field intensity and the internuclear distance. We conclude that the dissociation process of the molecular ion system can be tuned by changing the distance between donor atoms and the non-resonant laser field intensity. It was also concluded that if the molecular complex structure of the system is preserved, the binding energy is higher than in a fragmented state resulting from the dissociation process of the structure.

Single-photon ionization of aligned H with near-ionization-threshold photon energy

We study single-photon ionization of aligned H in a high-frequency low-intensity laser field. We focus on the cases where the laser frequency is near to or somewhat larger than the ionization potential of the target. The calculated photoelectron momentum distribution through numerical solution of time-dependent Schrödinger equation shows clear interference patterns. However, different from the cases of photon energy far larger than the ionization potential usually explored in experiments, the positions of interference maxima and minima for the present cases can not be explained by the interference of the electronic wave with the observed momentum between these two atomic centers of the molecule. By developing a theory model applicable for ionization of molecules in high-frequency laser field, we show that the Coulomb potential plays an important role in the momentum component of the emitting electronic wave near the nuclei, resulting in a remarkable shift of the interference pattern. A simple expression with Coulomb-modified momentum is obtained to predict the interference extrema, which gives suggestions for probing the structure and electron dynamics of the aligned molecule in single-photon ionization with lower photon energy.

Ionization induced by the ponderomotive force in intense and high-frequency laser fields.

Atomic stabilization is a universal phenomenon that occurs when atoms interact with intense and high-frequency laser fields. In this work, we systematically study the influence of the ponderomotive (PM) force, present around the laser focus, on atomic stabilization. We show that the PM force could induce tunneling and even over-barrier ionization to the otherwise stabilized atoms. Such effect may overweigh the typical multiphoton ionization under moderate laser intensities. Our work highlights the importance of an improved treatment of atomic stabilization that includes the influence of the PM force.

Capturing transient core-to-core resonances in Kr in intense extreme-ultraviolet laser fields by electron-ion coincidence spectroscopy

Resonances between core-hole states have been long hypothesized to understand dynamics of atoms and molecules exposed to intense XFEL pulses, but evaded clear identification due to their transient nature. The authors report clear evidence of core-to-core resonances by electron-ion coincidence spectroscopy on Kr atoms and elucidate the importance in nonlinear electronic responses of matter to high-frequency laser fields.

Многоуровневая модель многофотонных процессов в атоме гелия в сильном лазерном поле: учет ионизации

A multilevel model that makes it possible to describe multiphoton processes taking into account ionization in a multielectron atom irradiated by an intense laser field is proposed. Using the He atom as an example, it is shown that this model reproduces the main regularities of multiphoton ionization of an atom by an intense high-frequency laser field.

Intense high-frequency laser-field control of spin-orbit coupling in GaInAs/AlInAs quantum wells: A laser dressing effect

The Rashba spin-orbit (SO) coupling can flexibly be controlled via an external gate, while the Dresselhaus term, which mainly depends on quantum confinement, is in general immune to electrical control. Here we theoretically report optical manipulation of the SO coupling by resorting to an intense high-frequency laser field, which ``dresses'' the confining potential for electrons as a result of optical stark effect and enables a flexible and simultaneous control of the Rashba and Dresselhaus couplings. Focusing on ordinary GaInAs/AlInAs quantum wells with two occupied subbands subject to both laser and gate fields, we perform a self-consistent Poisson-Schr\"odinger calculation in the Hartree approximation to determine electro-optical control of the intrasubband (intersubband) Rashba ${\ensuremath{\alpha}}_{\ensuremath{\nu}}$ ($\ensuremath{\eta}$) and Dresselhaus ${\ensuremath{\beta}}_{\ensuremath{\nu}}$ ($\mathrm{\ensuremath{\Gamma}}$) SO terms with $\ensuremath{\nu}=1,2$. Under the impact of laser field, we find that the Rashba terms of the two subbands ${\ensuremath{\alpha}}_{1}$ and ${\ensuremath{\alpha}}_{2}$ may remain locked to equal strength in a broad gate range, providing a means for unified manipulation of the two-subband Rashba couplings. Further, as the laser field varies, we observe that ${\ensuremath{\alpha}}_{1}$ and ${\ensuremath{\alpha}}_{2}$ may have either the same or opposite signs, or even ${\ensuremath{\alpha}}_{2}$ vanishes while ${\ensuremath{\alpha}}_{1}$ is finite, greatly fascinating for selective SO control of distinct subbands. For the Dresselhaus coupling, we disclose two distinct scenarios depending on the interplay of the well width and the laser field strength, and reveal that ${\ensuremath{\beta}}_{2}$ may decrease rapidly when the laser field strengthens, even though ${\ensuremath{\beta}}_{1}$ remains essentially constant. Regarding the intersubband Rashba ($\ensuremath{\eta}$) and Dresselhaus ($\mathrm{\ensuremath{\Gamma}}$) terms, which mainly depend on the overlap and parity of the wave functions of the two subbands, they have relatively weak dependence on the laser field. Moreover, the combined effect of intra- and intersubband SO terms may lead to crossings and avoided crossings of the energy dispersion of multiband spin branches and may even trigger the spin polarization of an originally spin degenerate (unpolarized) band, tunable by the laser field. Our results should stimulate experiments probing the laser field mediated multiband SO control and further enables its spintronic applications.

Dynamic stabilization of atomic ionization in a high-frequency laser field with different initial angular momenta

We investigated the ionization of an atom with different orbital angular momenta in a high-frequency laser field by solving the time-dependent Schrödinger equation. The results showed that the ionization stabilization features changed with the relative direction between the angular momentum of the initial state and the vector field of the laser pulse. The ionization mechanism of the atom irradiated by a high frequency was explained by calculating the transition matrix and evolution of the time-dependent wave packet. This study can provide comprehensive understanding to improve atomic nonadiabatic ionization.

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.

Relativistic Effects for a Hydrogen Rydberg Atom in a High-Frequency Laser Field: Analytical Results

Previously published analytical results for the effects of a high-frequency laser field on hydrogen Rydberg atoms demonstrated that the unperturbed elliptical orbit of the Rydberg electron, generally is engaged simultaneously in the precession of the orbital plane about the direction of the laser field and in the precession within the orbital plane. These results were obtained while disregarding relativistic effects. In the present paper, we analyze the relativistic effect for hydrogenic Rydberg atoms or ions in a high-frequency linearly- or circularly-polarized laser field, the effect being an additional precession of the electron orbit in its own plane. For the linearly-polarized laser field, the general case, where the electron orbit is not perpendicular to the direction of the laser field, we showed that the precession of the electron orbit within its plane can vanish at some critical polar angle θc of the orbital plane. We calculated analytically the dependence of the critical angle on the angular momentum of the electron and on the parameters of the laser field. Finally, for the particular situation, where the electron orbit is perpendicular to the direction of the laser field, we demonstrated that the relativistic precession and the precession due to the laser field occur in the opposite directions. As a result, the combined effect of these two kinds of the precession is smaller than the absolute value of each of them. We showed that by varying the ratio of the laser field strength F to the square of the laser field frequency ω, one can control the precession frequency of the electron orbit and even make the precession vanish, so that the elliptical orbit of the electron would become stationary. This is a counterintuitive result.

Circular Rydberg States of Lithium Atoms or Lithium-like Ions in a High-Frequency Laser Field: The Break of the Algebraic Symmetry

There have been publications presenting studies of relatively simpleatomic systems in a high-frequency laser field. The systems studied under sucha field were highly excited (Rydberg) hydrogen atoms and hydrogen-like ions, aswell as highly-excited helium atoms and helium-like ions. These studies wereperformed classically, as appropriate for Rydberg states and revealed celestialanalogies, various kinds of the precession of the electron orbit and a shift ofthe energy. In the current paper we analyze a lithium atom or a lithium-likeion, one of the three electrons being in a Rydberg state, subjected to a laserfield of high frequency. We used the generalized method of effectivepotentials. We showed that for a relatively small distance of the outerelectron from the nucleus, the system has higher than geometrical symmetry. Foran arbitrary separation of the outer electron from the nucleus, we dealt withthe broken algebraic symmetry reduced to the geometrical (axial) symmetry. Wedescribe analytically the following two outcomes for circular Rydberg states.One of the outcomes is the precession of the plane of the orbit of the highlyexcited electron – the precession whose frequency we calculate analytically. Itleads to the following modification of the radiation spectrum: The appearanceof satellites at the distances from the unperturbed frequency of the spectralline equal to multiples of the precession frequency. The other outcome is anenergy shift of the Rydberg electron. Its dependence on the nuclear charge wasfound to be a non-monotonic function. This is a counterintuitive result.

Intensity-dependent angular distribution of low-energy electrons generated by intense high-frequency laser pulse.

By solving the three-dimensional time-dependent Schrödinger equation, we investigate the angular distributions of the low-energy electrons when an intense high-frequency laser pulse is applied to the hydrogen atom. Our numerical results show that the angular distributions of the low-energy electrons which generated by the nonadiabatic transitions sensitively depend on the laser intensity. The angular distributions evolve from a two-lobe to a four-lobe structure as the laser intensity increases. By analyzing nonadiabatic process in the Kramers-Henneberger frame, we illustrate that this phenomenon is attributed to the intensity-dependent adiabatic evolution of the ground state wavefunction. When the laser intensity further increases, the pathway of nonadiabatic transition from the ground state to the excited state and then to the continuum states is non-negligible, which results in the ring-like structure in the photoelectron momentum distribution. The angular distributions of the low-energy electrons provide a way to monitor the evolution of the electron wavefunction in the intense high frequency laser fields.

Circular Rydberg states of helium atoms or helium-like ions in a high-frequency laser field

Abstract In the literature, there were studies of Rydberg states of hydrogenic atoms/ions in a high-frequency laser field. It was shown that the motion of the Rydberg electron is analogous to the motion of a satellite around an oblate planet (for a linearly polarized laser field) or around a (fictitious) prolate planet (for a circularly polarized laser field): it exhibits two kinds of precession – one of them is the precession within the orbital plane and another one is the precession of the orbital plane. In this study, we study a helium atom or a helium-like ion with one of the two electrons in a Rydberg state, the system being under a high-frequency laser field. For obtaining analytical results, we use the generalized method of the effective potentials. We find two primary effects of the high-frequency laser field on circular Rydberg states. The first effect is the precession of the orbital plane of the Rydberg electron. We calculate analytically the precession frequency and show that it differs from the case of a hydrogenic atom/ion. In the radiation spectrum, this precession would manifest as satellites separated from the spectral line at the Kepler frequency by multiples of the precession frequency. The second effect is a shift of the energy of the Rydberg electron, also calculated analytically. We find that the absolute value of the shift increases monotonically as the unperturbed binding energy of the Rydberg electron increases. We also find that the shift has a nonmonotonic dependence on the nuclear charge Z: as Z increases, the absolute value of the shift first increases, then reaches a maximum, and then decreases. The nonmonotonic dependence of the laser field-caused energy shift on the nuclear charge is a counterintuitive result.

Dynamical interference of H and H2+ in one-photon ionization

The non-Hermitian Floquet theory is applied to systematically calculate both the ac-Stark shift $\ensuremath{\delta}$ and the decay rate $\ensuremath{\gamma}$ for hydrogen atoms and hydrogen molecular ions, when placed in a high-frequency laser field with an intensity ranging from the perturbation to the stabilization region. This allows us to trace the appearance of dynamical interference in ionization. We find that both the stabilization and the dynamical interference are easier to achieve at a frequency close to the ionization threshold. For the molecular case, the effects of nuclear motion are discussed based on the Born-Oppenheimer approximation. Although the dynamical interference condition $\ensuremath{\delta}g\sqrt{\ensuremath{\pi}}\ensuremath{\gamma}$ seems to be satisfied at a low frequency for a fixed-nuclei ${{\mathrm{H}}_{2}}^{+}$ in the perturbation region, the effects of the nuclear motion are shown to destroy the interference patterns in this region. Meanwhile, for the sake of confirmation, the photoelectron energy distributions are calculated by solving the time-dependent Schr\odinger equation for the parameters where the dynamical interference is predicted by the non-Hermitian Floquet theory.

Analytical results for one-electron Rydberg quasimolecules in a high-frequency laser field

The detailed description of electron terms in the field of two stationary Coulomb centers of charges Z and Z ′ separated by a distance R is one of the most fundamental problems in quantum mechanics. When the charges Z and Z ′ approach each other and share the only one electron that they have, they form a quasimolecule. Such quasimolecules are encountered in various kinds of plasmas and play an important role in theoretical and experimental studies of charge exchange. When the electron is in a highly-excited state, it is a one-electron Rydberg quasimolecule (OERQ). There are extensive analytical studies of the OERQ by the methods of classical mechanics (which are appropriate for Rydberg states). In one of our previous papers we studied the OERQ subjected to a laser field in the situation where the laser frequency was much smaller than the highest frequency of the unperturbed system. In the present paper we consider the situation where the OERQ is subjected to a laser field whose frequency is much greater than the highest frequency of the unperturbed system. For obtaining analytical results we use a generalization of the method of effective potentials. We show that as the amplitude of the laser field increases, in the case of the linearly-polarized laser field, the structure of the energy terms becomes more complex. Moreover the number of the energy terms increases in this case. We also calculated analytically the shift of the radiation frequency of OERQ caused by the laser field. As the amplitude of the laser field increases, so does the shift. The radiation frequency is shifted to the blue in the case of the linearly-polarized laser field, and to the red in the case of the circularly-polarized laser field. For a known amplitude of the laser field, by measuring the relative shift of the radiation frequency it should be possible to determine experimentally the distance of the orbital plane of the electron from the nucleus of the smaller nuclear charge.

Effective production of gammas, positrons, and photonuclear particles from optimized electron acceleration by short laser pulses in low-density targets

Electron acceleration has been optimized based on 3D particle-in-cell simulations of a short laser pulse interacting with low-density plasma targets to find the pulse propagation regime that maximizes the charge of high-energy electron bunches. This regime corresponds to laser pulse propagation in a self-trapping mode where the diffraction divergence is balanced by the relativistic nonlinearity such that relativistic self-focusing on the axis does not happen and the laser beam radius stays unchanged during pulse propagation in a plasma over many Rayleigh lengths. Such a regime occurs for a near-critical density if the pulse length considerably exceeds both the plasma wavelength and the pulse width. Electron acceleration occurs in a traveling cavity filled with a high-frequency laser field and a longitudinal electrostatic single-cycle field (“self-trapping regime”). Monte Carlo simulations demonstrated that a high electron yield allows an efficient production of gamma radiation, electron–positron pairs, neutrons, and even pions from a catcher-target.

Understanding two-photon double ionization of helium from the perspective of the characteristic time of dynamic transitions

By using the B-spline numerical method, we investigate a two-photon double-ionization (TPDI) process of helium in a high-frequency laser field with its carrier frequency ranging from 1.6 to 3.0 a.u. and the pulse duration ranging from 75 to 160 attoseconds. We found that there exists a characteristic time tc for a TPDI process, such that the pattern of energy distribution of two ionized electrons presents a peak or two, depending respectively on whether the pulse duration is shorter or longer than tc. Especially, when the pulse duration is larger than tc, the TPDI spectrum shows a double-peak structure which is attributed to the fact that most of the electron–electron Coulomb interaction energy is acquired by a single electron during their oscillation around the nucleus before the two electrons leave, and hence the double-peak structure cannot be identified as a signal of sequential ionization. Additionally, if the carrier frequency is less than the ionization energy of He+, i.e. that carrier frequency is in the so called correlated region, tc is not a fixed value, and it increases as the carrier frequency decreases; while if the carrier frequency is greater than the ionization energy of He+, i.e. the carrier frequency is in the so called non-correlated region, tc is fixed at about 105 attoseconds. We further found that, for a helium-like ion in its ground state, the characteristic time for when the carrier frequency is larger than the ionization energy of the second electron has a key relation with the Coulomb interaction energy between the two electrons, which can be expressed as , a type of quantum mechanical uncertainty relation between time and energy. In addition, this relation can be attributed to the existence of a minimal evolution time from the ground state to a double ionization state with two electrons carrying different energies. These results may shed light on a deeper understanding of many-electron quantum dynamical processes.

Mini-Review: Hydrogen Atoms in a High-Frequency Laser Field

Because of the continuing advances in developing lasers in the far-ultraviolet and x-ray ranges, studies of the behavior of atoms under a high-frequency laser field are of theoretical and practical interest. In the present paper, we review various analytical results obtained by the method of separating rapid and slow subsystems for various polarizations of the laser field. Specifically, we review the corresponding analytical results both in terms of the quantum description of the phenomena involved and in terms of the classical description of the phenomena involved. We point out that, for the classical description of hydrogen atoms in a high-frequency laser field, there are interesting celestial analogies. We discuss hidden symmetries of these physical systems, the advantages of this analytical method, and the connection between these results and the transition to chaos.

Manipulating the anisotropy of the Dirac-Cone in graphene by laser fields

One of the most striking properties of graphene is the relativistic-like Dirac-Cone spectrum of charge carriers. By applying high-frequency laser fields, the system can be described with the use of similar spectrum which is based on a concept of electron quasi-energy. There in this spectrum a creation and annihilation of new Dirac points and cones as well as opening a gap may arise. This allows controlling electron motion without applying DC periodic fields which are effectively described by graphene superlattices. Here we demonstrate that coherent electromagnetic fields applied to graphene can generate new Dirac and Weyl points, induce Lifshitz quantum phase transition for slightly doped graphene and produce an anisotropy of the Dirac cones, which can be even infinite.Graphical abstract

Laser light and external magnetic field control of polaron in asymmetric quantum dot

The possibility of controlling a polaron in an asymmetric quantum dot with external magnetic field and laser light is examined in this paper. Analytical studies are done using a modified Lee-Low-Pines method. We calculate the fundamental and first state energies which form a single qubit and further determine the probability density and the Shannon's entropy. These quantities as well as the mobility are influenced by the laser parameters, the size of the system and the magnetic field. The results performed show that the energy increases with the cyclotron frequency and the confinement strength of the potential. The analytical results highlight the fact that the application of the magnetic fields and laser enhances the possibility of finding discrete electronic states in quantum dots. The decoherence process is found to be greatly affected by the high-frequency laser field considered. Furthermore, it is reduced when particles are more confined in the nanostructure. It is established that a strong magnetic field and a low laser frequency enable the trapping and cooling of the polaron.