Nonlinear optical response of an atom in the field of femtosecond laser pulses with near-atomic intensity

A theory of the nonresonant response of a single atom in a state with arbitrary magnitude and direction of the angular momentum of an atomic electron with respect to the polarization vector of the acting electromagnetic field has been developed. It has been shown that the atomic response current has a tensor structure and depends both on the direction of the angular momentum of the atom and on the polarization vector of the external field. The tensor character of the response is due to the effects of the anisotropy of probability density distribution of the atomic electron as compared to the case of the free atom. The selection rules for the axisymmetric problem of the atom in the field have been analyzed. The manifestation of the selection rules in the angular spectra of photoelectrons has been demonstrated. The probability of the ionization of the atom has been analyzed as a function of the amplitude and duration of the pulse. It has been shown that the width of the generation spectrum is a nonlinear function of the field strength and is saturated in the region of nearly atomic fields. Methods for controlling the parameters of the atomic response spectrum have been proposed on the basis of the use of a sequence of laser pulses with various time profiles, carrier frequencies, and polarization states. It has been shown that the generation of terahertz radiation is possible in the preionization regime, where the generation mechanism is attributed to atomic nonlinearity.     

Response of an atom interacting with an arbitrarily polarized electromagnetic field

We develop the theory of interaction of the electromagnetic field and a single atom being in an arbitrary state and having an arbitrary direction of the angular momentum of the atomic electron with respect to the direction of the field polarization vector. It is shown that the atom response current has a tensor structure and depends on both the direction of the angular momentum of the atom, and the polarization vector of the external field. The tensor character of the response is determined by the externally induced anisotropic distribution of the probability density of spatial localization of the atomic electron. It is shown that the induced-anisotropy effects clarify the harmonic generation mechanism at play during the non-resonance interaction of laser radiation with atomic media. The developed theory is applied to the analysis of the problem about the generation of terahertz waves in a two-color laser field. It is shown that the change in the mutual orientation of wave polarization vectors leads to a significant increase in the efficiency of conversion of high-frequency fields to low-frequency ones. It is shown for the first time that the generation of terahertz waves is possible in the preionization regime, when the generation mechanism is related to atomic nonlinearity.     

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.     

Multistability of the optical response in a system of quasi-two-dimensional exciton polaritons

The nonlinear dynamic properties of a system of polaritons in a planar semiconductor microcavity under conditions of external coherent photoexcitation have been investigated. It has been shown that the interaction between polaritons with identical projections of the total angular momentum (J _z ) can give rise to multistability of the response of the excited polariton state. As a result, nonequilibrium transitions between different stability branches become possible due to fluctuations or arbitrarily smooth variations of the excitation parameters and occur with abrupt changes in the intensity and optical polarization of the field in the microcavity. It has been demonstrated that a relatively weak attraction between polaritons with opposite total angular momenta J _z leads to a possibility of spontaneously breaking the symmetry of circularly polarized field components in the microcavity under strictly linear (symmetric) polarization conditions of external excitation.     

Single-photon emission via Raman scattering from the levels with partially resolved hyperfine structure

The probability of emission of a single-photon via Raman scattering of laser pulse on the three-level Λ - type atom in microcavity is studied. The duration of the pulse is considered to be short enough, so that the hyperfine structure of the upper level remains totally unresolved, while that of the lower level is totally resolved. The coherent laser pulse is assumed to be in resonance with the transition between one hyperfine-structure component of the lower atomic level and all hyperfine-structure components of the upper level, while the quantized cavity field is assumed to be in resonance with the transition between the other hyperfine-structure component of the lower level and all components of the upper one. The dependence of the photon emission probability on the mutual orientation of polarization vectors of the cavity mode and of the coherent laser pulse is analyzed. Particularly, the case is investigated, when the total electronic angular momentum of the lower atomic level equals 1/2, which is true for the ground states of alkali atoms employed in the experiments on deterministic single-photon emission. It is shown, that in this case the probability of photon emission equals zero for collinear polarizations of the photon and of the laser pulse, and the probability obtains its maximum value, when the angle between their polarizations equals 60°.     

The magnetic fields and rotation generators of free space electromagnetism

The relation is developed between rotation generators of the Lorentz group and the magnetic fields of free-space electromagnetism. Using these classical relations, it is shown that in the quantum field theory there exists a longitudinal photomagneton, a quantized magnetic flux density operator which is directly proportional to the photon spin angular momentum. Commutation relations are given in the quantum field between the longitudinal photomagneton and the usual transverse magnetic components of quantized electromagnetism. The longitudinal component is phase free, but the transverse components are phase dependent. All three components can magnetize material in general, but only the transverse components contribute to Planck's law. The photon therefore has three, not two, relativistically invariant degrees of polarization, an axial, longitudinal, polarization, and the usual right and left circular transverse polarizations. Since the longitudinal polarization is axial, it is a phase- free magnetic field.     

Near-field characteristics of highly non-paraxial subwavelength optical fields with hybrid states of polarization

The vectorial structure of an optical field with hybrid states of polarization(So P) in the near-field is studied by using the angular spectrum method of an electromagnetic beam. Physical images of the longitudinal components of evanescent waves are illustrated and compared with those of the transverse components from the vectorial structure. Our results indicate that the relative weight integrated over the transverse plane of the evanescent wave depends strongly on the number of the polarization topological charges. The shapes of the intensity profiles of the longitudinal components are different from those of the transverse components, and it can be manipulated by changing the initial So P of the field cross-section. The longitudinal component of evanescent wave dominates the near-field region. In addition, it also leads to three-dimensional shape variations of the optical field and the optical spin angular momentum flux density distributions.     

运动三能级原子与驻波激光场斜交相互作用的理论分析

分析了一个运动的三能级原子与一个驻波激光场地斜交相互作用时的动量传递行为。结果表明，当原子和光场由于多普勒效应满足一定条件时，将产生受激拉曼跃迁。如果作用光相对于原子而言为一个“π／２脉冲”光时，那么经过作用后，原子将处于一个相干迭加态，其中一个态与加始相同。     

Angular momentum conversion of elliptically polarized beams focused by high numerical-aperture phase Fresnel zone plates

Based on the vectorial Debye theory, we investigate the tight focusing of elliptically polarized light beams by high numerical-aperture (NA) phase Fresnel zone plates (FZP). The conversion of the spin angular momentum (SAM) and the orbital angular momentum (OAM) in the tight focusing of the elliptically polarized beams is investigated in great detail. It is shown that the direction and magnitude of the OAM can be directly modulated by the input polarization, providing effective evidence that the SAM carried by an elliptically polarized light beam is converted into OAM in the tight focusing process. The properties of phase retardation between x and y components of the focused field are also investigated. It is found that focused field of x and y components still keeps its original elliptical polarization state, indicating that the focused field composed of x and y components still carries SAM, whereas the focused field of z component is changed into carrying OAM. The influences of the total zone number and the phase difference of binary phase FZPs with high NA on the intensity distribution in the focal plane are also investigated.     

Steady state of a low-density ensemble of atoms in a monochromatic field taking into account recoil effects

A method has been developed for obtaining the steady-state solution of a quantum kinetic equation for the atomic density matrix in an arbitrarily polarized monochromatic field with the complete inclusion of recoil effects and degeneracy of atomic levels in the projection of the angular momentum. This method makes it possible to obtain the most general solution beyond the previously accepted approximations (semiclassical approximation, secular approximation, etc.). In particular, it has been shown that the laser cooling temperature is a function of not only the depth of the optical potential (as was previously thought), but also the mass of an atom.     

Properties of circularly polarized vortex beams

The properties of circularly polarized vortex beams in cylindrical polarization bases are studied. A circularly polarized vortex beam is decomposed into radial and azimuthal polarization. With the proper combination of vortex charge and the handedness of the circular polarization, a focal field with an extremely strong longitudinal component as well as a flat-topped profile can be obtained. The cylindrical decomposition also sheds light on the connections between orbital angular momentum and the spin of the light beams.     

Tunneling and above-barrier ionization of atoms in a laser radiation field

Calculations are made of the energy and angular distributions of photoelectrons during tunneling ionization of an atom or an ion under the action of high-power laser radiation (for all values of the Keldysh parameter γ). Cases of linear, circular, and elliptic polarizations of the electromagnetic wave are considered. The probability of above-barrier ionization of hydrogen atoms in a low-frequency laser field is calculated. Formulas are given for the momentum spectrum of the electrons when an atomic level is ionized by a general type of alternating electric field (for the case of linear polarization). An analysis is made of tunneling interference in the energy spectrum of the photoelectrons. Analytic approximations are discussed for the asymptotic coefficient C _κ of the atomic wave function at infinity (for s-wave electrons).     

The fine structure splitting of the level of lithium in Rydberg states

The Hamiltonian of the four-body problem for a lithium atom is expanded in series. The level shift and level formula of a lithium atom in Rydberg states are achieved by means of the calculation of polarization of the atomic core (including the contribution of dipole, quadrupole and octupole components). We also consider the effect of relativity theory, the orbital angular momentum L and the spin angular momentum S coupling scheme (LS coupling) and high-order correction of the effective potential to the level shift. The fine structure splitting (N=5-12, L=4-9, J=L±1/2) and level intervals in Rydberg states have been calculated by the above-mentioned formula and compared with recent experimental data.     

INTERACTION BETWEEN A MOVING ATOM AND AN ELECTROMAGNETIC WAVE

Dynamics of a two-level atom moving in an electromagnetic field is studied. The atomic motion gives rise to a momentum-dependent detuning which holds back the atomic transition, and leads to a momentum-dependent Rabi oscillation which causes an overlapping among different Rabi oscillations. When the field is in a Fock state, the atomic population and the mean momentum of the atom exhibit damping oscillation, the damping rate is related to the momentum distribution; the collapse-revival phenomena of the atomic population and the mean momentum will occur if the atomic momentum has some special distribution. When the field is in a superposition state, the collapse-revival phenomena are modified by the atomic momentum distribution and disappear for the wider atomic momentum wavepackets. We also find that each atomic level will split into two sublevels with the same energy difference when the field is in a Fock state and the atom has a definite momentum.     

Linear momentum conservation in coherent population trapping: A case study for a quantum filtering process

We discuss the question of linear momentum conservation when an atom coupled to a laser field enters into a state which is not an eigenstate of the linear momentum. Such a situation happens in the recently demonstrated laser cooling of atoms by velocity selective coherent population trapping. We show that this process can be understood as a filtering of the atomic state by the laser field taken as a classical measuring apparatus. In a different approach, the laser field can be taken as a quantized system; then the filtering process leads to an entangled state of the atom and the field.     

Faraday effect on the Rb <Emphasis Type="Italic">D</Emphasis> <Subscript>1</Subscript> line in a cell with a thickness of half the wavelength of light

The rotation of the radiation polarization plane in a longitudinal magnetic field (Faraday effect) on the D₁ line in atomic Rb vapor has been studied with the use of a nanocell with the thickness L varying in the range of 100–900 nm. It has been shown that an important parameter is the ratio L/λ, where λ = 795 nm is the wavelength of laser radiation resonant with the D₁ line. The best parameters of the signal of rotation of the radiation polarization plane have been obtained at the thickness L = λ/2 = 397.5 nm. The fabricated nanocell had a large region with such a thickness. The spectral width of the signal reached at the thickness L = 397.5 nm is approximately 30 MHz, which is much smaller than the spectral width (≈ 500 MHz) reached with ordinary cells with a thickness in the range of 1–100 mm. The parameters of the Faraday rotation signal have been studied as functions of the temperature of the nanocell, the laser power, and the magnetic field strength. The signal has been reliably detected at the laser power P_L ≥ 1 μW, magnetic field strength B ≥ 0.5 G, and the temperature of the nanocell T ≥ 100°C. It has been shown that the maximum rotation angle of the polarization plane in the longitudinal magnetic field is reached on the F_g = 3 → F_e = 2 transition of the ⁸⁵Rb atom. The spectral profile of the Faraday rotation signal has a specific shape with a sharp peak, which promotes its applications. In particular, Rb atomic transitions in high magnetic fields about 1000 G are split into a large number of components, which are completely spectrally resolved and allow the study of the behavior of an individual transition.     

Linear polarization of luminescence in Bose-Einstein condensation of indirect excitons and spontaneous symmetry breaking

The linear polarization of luminescence from the Bose-Einstein condensate of dipolar (indirect) excitons accumulated in the ring lateral traps in GaAs/AlGaAs Schottky-diode heterostructures with a wide single quantum well has been observed. Luminescence from direct excitons remains unpolarized under the same experimental conditions. It has been shown that the linear polarization of the exciton condensate may arise from the anisotropic electron-hole (e–h) exchange interaction associated with the lateral anisotropy of the confining potential. The interaction mixes and splits the ground state of optically active excitons on heavy holes (with angular momentum projections of m=±1). The split spectral components from the corresponding angular momentum projections are linearly polarized in mutually orthogonal directions. Under this e–h exchange, the condensate component of excitons should appear in the lowest of the split states and luminescence from the Bose-Einstein condensate of excitons in such a split state becomes linearly polarized along the 〈110〉 crystallographic direction in the quantum well plane. The observed effect is a manifestation of spontaneous symmetry breaking in Bose-Einstein condensation of excitons.     

Local dynamical characteristics of Bessel beams upon reflection near the Brewster angle

We analytically and numerically study the local dynamical characteristics of the Bessel beams reflected from an airglass interface near the Brewster angle.A Taylor series expansion based on the angular spectrum component is applied to correct the reflection coefficients near the Brewster angle.Using a hybrid angular spectrum representation and vector potential method,the explicit expressions for the electric and magnetic field components of the reflected Bessel beams are derived analytically under paraxial approximation.The local energy,momentum,spin,and orbital angular momentum of the Bessel beams upon reflection near the Brewster angle are examined numerically by utilizing a canonical approach.Numerical simulation results show that the properties of these dynamical quantities for the Bessel beams near Brewster angle incidence change abruptly,and are significantly affected by their topological charge,half-cone angle,and polarization state.The present study has its importance in understanding the dynamical aspects of optical beams with vortex structure and diffraction-free nature during the reflection process.