Atoms In Laser Fields Research Articles

Understanding Tunneling Ionization of Atoms in Laser Fields using the Principle of Multiphoton Absorption**Supported by the National Natural Science Foundation of China under Grant Nos 11725417 and 11575027, the Joint Fund of the National Natural Science Foundation of China and the China Academy of Engineering Physics under Grant No U1730449, and the Science Challenge Project under Grant No TZ2018005.

The elaborate energy and momentum spectra of ionized electrons from atoms in laser fields suggest that the ionization dynamics described by tunneling theory should be modified. Although great efforts have been carried out within semiclassical models, there are few discussions describing the multiphoton absorption process within a quantum framework. Comparing the results obtained with the time-dependent Schrödinger equation (TDSE) and the Keldysh–Faisal–Reiss (KFR) theory, we study the nonperturbative effects of ionization dynamics beyond the KFR theory. The difference in momentum spectra between multiphoton and tunneling regimes is understood in a unified picture with virtual multiphoton absorption processes. For the multiphoton regime, the momentum spectra can be obtained by coherent interference of each periodic contribution. However, the interference of multiphoton absorption peaks will result in a complex structure of virtual multiphoton bands in the tunneling regime. It is shown that the virtual spectra will be almost continuous in the tunneling regime instead of the discrete levels found in the multiphoton regime. Finally, with a model combining the TDSE and the KFR theory, we try to understand the different effects of virtual multiphoton processes on ionization dynamics.

Coherent States in a Laser Cavity

A mathematical model was developed to obtain the population inversion of the atoms in laser field in a laser cavity by considering the electric field in the optical cavity and the atomic states of the medium to be quantized. The master equation of the density operator of the laser field was studied analytically and numerically. Using coherent states, the Fokker-Plank equation for the phase space density for the laser field was solved analytically for the time dependent and steady state situations. The laser field above the threshold can be represented by a randomly phased mixture of coherent states. As the pump parameter increases in the laser process, the phase density becomes narrower, tending toward a delta function, creating a coherence laser field.

Coherent States in a Laser Cavity

A mathematical model was developed to obtain the population inversion of the atoms in laser field in a laser cavity by considering the electric field in the optical cavity and the atomic states of the medium to be quantized. The master equation of the density operator of the laser field was studied analytically and numerically. Using coherent states, the Fokker-Plank equation for the phase space density for the laser field was solved analytically for the time dependent and steady state situations. The laser field above the threshold can be represented by a randomly phased mixture of coherent states. As the pump parameter increases in the laser process, the phase density becomes narrower, tending toward a delta function, creating a coherence laser field.

Mechanisms of Below-Threshold Harmonic Generation in Atoms

Most previous studies have focused on high-order harmonic generation beyond the ionization threshold; mechanisms of below-threshold harmonics are less understood. We schematically study the harmonic emission process in this region by numerically solving the time-dependent Schrödinger equation of an atom in laser fields. We show that, besides the quantum path interference mechanism recently identified, the effects induced by the Coulomb potential also have a critical impact on these harmonics. These mechanisms can be distinguished in the structure of harmonic spectra by changing the laser wavelength and peak intensity. We find that the long quantum orbits can influence lower-order harmonics at a higher laser intensity. In addition, we show that the intensity-dependent steps of harmonic yield can disappear for certain harmonic orders, due to the trapping in the Rydberg states before recombination, which can explain recent experimental observations.

Quantum carpets woven by cold atoms in a laser field

Propagation of wave packets of cold two-level atoms in a standing-wave laser field can be interpreted in the dressed-state basis as motion in two optical potentials. The three distinct regimes of the wavepacket motion are specified by the ratio of the squared atom–laser detuning to the normalized Doppler shift. We calculate the momentum and position probability densities, which form patterns with minima and maxima of probability both in the momentum and the position spaces known as quantum carpets. At small and large detunings, the atomic motion is substantially adiabatic, and the quantum carpets have a simple form. At intermediate detunings, the wave packet moves nonadiabatically, splitting at each node of the standing wave, which causes a proliferation or branching of atomic trajectories with a single atom. Nonadiabatic transitions produce beautiful quantum carpets with a rich structure.

Dynamic correlations with time-dependent quantum Monte Carlo

In this paper, we solve quantum many-body problem by propagating ensembles of trajectories and guiding waves in physical space. We introduce the "effective potential" correction within the recently proposed time-dependent quantum Monte Carlo methodology to incorporate the nonlocal quantum correlation effects between the electrons. The associated correlation length is calculated by adaptive kernel density estimation over the walker distribution. The general formalism is developed and tested on one-dimensional helium atom in laser field of different intensities and carrier frequencies. Good agreement with exact results for the atomic ionization is obtained.

Dipole and quadrupole forces exerted on atoms in laser fields: The nonperturbative approach

Manipulation of cold atoms by lasers has so far been studied solely within the framework of the conventional dipole approximation, and the atom-light interaction has been treated using low order perturbation theory. Laser control of atomic motions has been ascribed exclusively to the corresponding light-induced dipole forces. In this work, we present a general theory to derive the potential experienced by an atom in a monochromatic laser field in a context analogous to the Born-Oppenheimer approximation for molecules in the field-free case. The formulation goes beyond the dipole approximation and gives rise to the field-atom coupling potential terms which so far have not been taken into consideration in theoretical or experimental studies. Contrary to conventional approaches, our method is based upon the many electron Floquet theory and remains valid also for high intensity laser fields (i.e., for a strongly nonperturbative atom-light interaction). As an illustration of the developed theory, we investigate the trapping of cold atoms in optical lattices. We find that for some atoms for specific laser parameters, despite the absence of the dipole force, the laser trapping is still possible due to the electric quadrupole forces. Namely, we show that by using realistic laser parameters one can formmore » a quadrupole optical lattice which is sufficiently strong to trap Ca and Na atoms.« less

Spectral fitting method for the solution of time-dependent Schrödinger equations: Applications to atoms in intense laser fields

A spectral fitting method for solving the time-dependent Schr\"odinger equation has been developed and applied to the atom in intense laser fields. This method allows us to obtain a highly accurate time-dependent wave function with a contribution from the high-order term of $▵t.$ Moreover, the time-dependent wave function is determined on a small number of discrete mesh points, thus making calculations simple and accurate. This method is illustrated by computing wave functions and harmonic generation spectra of a model atom in laser fields.

Mixed gauge approach to multiphoton wavefunctions

We present a novel method for obtaining Floquet or time-dependent wavefunctions for atoms in laser fields. This method has the potential to be more stable and/or faster than previous methods. The main idea is to include the effects of the laser field in a gauge that smoothly changes character as a function of distance. This transformation allows us to formally account for the analytic behaviour of the wavefunction as r to infinity and as r to 0. We demonstrate the feasibility of this mixed gauge approach through Floquet calculations on a one-dimensional model problem and three-dimensional calculations for the hydrogen atom. Time-dependent calculations for a one-dimensional model problem are performed with the mixed gauge. This approach may also be useful for exploring analytic and perturbative properties of the wavefunction in the high-field limit.

A Criterion of Validity of Traditional Radiation-Perturbation Theory11The project supported by National Natural Science Foundation of China

A perturbation variational approach to atomic behavior in strong laser fields is expressed briefly. For a wide range of , the ground state energy of H atom in laser fields is obtained by the application of the perturbation variational approach. The obtained energy values agree with the previous values given by T. C. Landgraf and M. Gavrila. According to the obtained energy values, a new value of limit of validity of traditional radiation-perturbation theory (TRPT) is given.

Introduction to the Theory of Laser–Atom Interactions

Basic Ideas. States in a Weak-Near-Resonant Field. More General States of an Atom in a Laser Field. Spontaneous Radiation by Atoms in Lasers. Deflection of Atoms in Laser Fields and External Fields. Potential Scattering of Charged Particles in a Laser Field. Multiphoton Ionization. Electron-Atom Scattering in a Laser Field. Atom-Atom Scattering in the Field of a Laser. Index.

Excitation of two-level atoms in mode-locked laser fields

The excitation of two-level atoms in a laser field comprising many equally spaced coupled laser modes corresponding to a coherent pulse train is examined. The atom-field interaction is analysed via the optical Bloch equations for a rotating wave. In the limit of weak excitation they can be solved analytically and the time-averaged atomic excitation turns out to be a linear superposition of the contributions from the individual laser modes. Thus excitation spectra simply reflect the mode structure of the laser spectrum. Excitation spectra for strong fields are obtained by numerical integration of the optical Bloch equations. They exhibit a saturation behaviour differing significantly from the well known single-mode case. The temporal evolution towards the steady state is calculated for several numerical examples to clarify the origin of this behavior. For achieving maximum excitation, the laser pulse area, as in the single-pulse case, should be an odd multiple of π, and the mode spacing (pulse repetition rate) should exceed the natural linewidth of the atomic transition considerably. Under these conditions the time-averaged excited-state population approaches 1/2 while saturation broadening ensures nearly frequency-independent excitation within an extended fraction of the laser bandwidth.

Friction and diffusion coefficients for cooling of atoms in laser fields with multidimensional periodicity.

Methods are presented that allow numerical calculations of the friction and momentum diffusion coefficients for atomic motion in laser fields with periodicity in one, two, and three dimensions. Polarization gradients in the fields lead to increased friction on atoms with a Zeeman sublevel structure, and new features arising in the cases of motion in two and three dimensions are discussed. There is a marked position dependence of the calculated quantities, and the consequence for the forces on atoms following specified trajectories is studied. Temperatures determined from the position-averaged friction and diffusion coefficients scale with the laser power divided by the frequency detuning, except in some special configurations. Of relevance for experiments on cooling, the relative merits of four different laser configurations in three dimensions are studied.

Forces on atoms in laser fields with multidimensional periodicity

A description is given of a method for calculating forces on atoms from periodic laser fields in an arbitrary number of dimensions. A crucial approximation is the introduction of an average force which depends on the magnitude and direction of the particle velocity but not on position. A simple two-dimensional example is studied and a strong force component perpendicular to the two-dimensional atomic velocity is found. It may become of interest for the construction of well collimated atomic beams of high intensity. Fluctuations are not included but results from simulations at high laser intensity indicate that average forces alone serve as useful guides in the prediction of modifications of velocity distributions.

Trajectory method for time-dependent Thomas-Fermi equations and application to Ar atoms in laser fields

The classical trajectory method is applied to the time-dependent Thomas-Fermi model. With this model we describe the electron density of an Ar atom in an intense laser field. Cross sections for photoabsorption are calculated and the dynamics of the electron density is discussed.

Nonperturbative calculation of partial differential rates for multiphoton ionization of a hydrogen atom in a strong laser field

We show how the multiphoton-ionization matrix element for an atom in a laser field at intensities beyond the regime of perturbation theory can be calculated from the standard Floquet expansion of the electron wave function. We expand the harmonic components in a discrete complex Sturmian basis set, and we evaluate the resulting (divergent) sum for the matrix element by using the Pad\'e method. We present results for partial rates and angular distributions for hydrogen.

Intensity dependence of the ionisation potential of an atom in a resonant laser field

The ionisation potential of an atom in a laser field is known to be intensity dependent. Previous theories apply only to a non-resonant field. The result is extended to the case of the Nr photon resonance where Nr is any positive integer. The new result contains several new features. Rapid frequency dependence is one and a dependence upon the conditions in which the atom enters the field is another.

Laser radiation pressure on free atoms

Theoretical and experimental investigations into the action of laser radiation pressure on atoms are reviewed. The paper describes briefly the history of the problem, presents the foundations of the theory of light pressure, describes and analyzes experimental work and discusses possible applications of light pressure to various fields of physics. In presenting the theory of light pressure primary attention is centered on the analysis of atomic motion in travelling and standing light waves. When discussing the possible applications of light pressure particular emphasis is placed upon the ways of realizing such principal ideas as radiative cooling, trapping and storing of atoms in laser fields.

Trapping and storage of atoms in a laser field

Analysis of the possibility of spatial trapping of cold atoms in a standing-wave laser field is presented. It is shown that cold atoms can be trapped for a long time in region ≈ λ in a nonresonant standing-wave field. In a resonant standing-wave field cold atoms can be stored for a long time in the region determined by the cross-section of the laser beam. Trapping and storage together with cooling of atoms that has been suggested earlier allow us in specific cases to increase the sensitivity and the resolution of spectroscopic studies.

Particle scattering by two level atoms in a strong radiation field

A set of coupled equations for the particle scattering by a two level atom in a strong near resonant radiation field is derived from the time dependent Schrodinger equation. This set of equations is discussed in a first and second order approximation. The result can be visualized in terms of a scheme in which the two well separated (nondegenerate) atomic states split, each into two energy levels. The splitting depends on the strength of the field and on the difference between the resonance frequency and the frequency of the incident light and is typically a few meV. In this scheme all possible elastic, quasielastic, inelastic and superelastic transitions between the four levels can be induced by collision processes. In addition, multiphoton processes may occur if the scattered particle remains long enough in the interaction region. Estimates of the two photon gain process for electron and heavy particle scattering by sodium atoms in a dye laser field are given. It is suggested that the superelastic processes may play an important role in laser induced gas breakdown, even if the laser frequency does not coincide with any atomic transition. Spontaneous emission of atoms in laser fields is also treated. The results are similar to the particle scattering processes.