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F dependence of near-threshold behaviour of the photodetachment cross section, (151), with exact α(F; ω) for = √ 2. Dotted curve, F = 0.015; broken curve, F = 0.03; chain curve, F = 0.06; full curve with squares, F = 0.1; thin full curve, F = 0.15; bold full curve, F = 0.2678; full curve with circles, F = 0.5.
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This paper provides a general theoretical description of a weakly bound atomic system (a negative ion) interacting simultaneously with two (generally strong) fields, a static electric field and a monochromatic laser field having an arbitrary elliptical polarization. The zero-range δ-potential is used to model the interaction of a bound electron in...
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We examine the absorption of a weak probe beam in a laser-driven tripod-type atom with three closely lying ground levels, where both the driving and probe lasers interact simultaneously with the three transitions. The effects of spontaneously generated coherence (SGC) are taken into account. We introduce dipole moments in the dressed-state picture...
Citations
... In this work, we present an alternative to the existing theoretical approaches. Our approach is based on the analysis of integral equation for the quasistationary quasienergy state (QQES) in a periodic laser field for an arbitrary shortrange potential [28][29][30][31]. We show that the integral equation for QQES can be transformed to a form similar to that for the TDER model [22,24], however, in contrast to the TDER model, this equation involves explicitly the Fourier-transform of a short-range potential [see Eq. (10)]. ...
... where U (r) is a short-range potential. Equation (1) is supplemented by the spherical outgoing wave boundary condition at large distances, which ensures the complexity of quasienergy [28][29][30][31]. The eigenvalue problem (1) can be also formulated in terms of the homogeneous integral equation: ...
... where G(r, t; r , t ) is the retarded nonstationary Green's function of the free electron in a laser field (see, e.g., Appendix B in Ref. [30]). 1 As can be shown, at large distances from Eq. (2) follows an expansion of QQES wave function in terms of outgoing spherical waves (see Ref. [17] and Appendix A for details): ...
When He is ionized by a chirped xuv pulse, additional peaks are identified in the joint energy spectra besides ordinary ionization peaks. Our results are based on the solution of the full-dimensional time-dependent Schrödinger equation of helium. Further numerical studies show that these additional structures are sensitive to both the pulse duration and the chirp parameter. To reveal the underlying mechanism, we have developed an analytical model based on the symmetric ionization assumption and the second-order time-dependent perturbation theory, which can qualitatively reproduce these additional structures. By systematic comparison studies, one can attribute the origin of these structures to the interference of two indistinguishable electrons and the diffraction in the time domain. In addition, we find that the interference effect is absent when one uses a negatively chirped laser pulse, while the diffraction in the time domain always persists.
... We emphasize that this continuum intermediate state contributes to an atomic polarization response to the external XUV field, determining the amplitudes of elastic XUV-photon scattering [33] or second XUV-harmonic generation [34] by IR-dressed medium. It is well known that the continuum state of an atomic electron in the DC field contains rapidly oscillating terms resulting from an interference of two semiclassical paths of free electron [35,36] (see also review [37]): the first path represents the electron motion from the DC-induced barrier, while the second path consists in electron motion towards the barrier with subsequent reflection. This interference is more pronounced for weaker field strengths and lead to more rapid oscillations and non-analytical structure of IR-induced processes amplitudes with respect to IR field at its zeros. ...
... We will demonstrate this eliminating procedure within the three-dimensional δ-potential (or zero-range potential) model [44]. For the δ-potential model, the dynamic polarizability α(ω, F ) of an atomic system in the presence of a static electric field F was discussed in details in [37]. The explicit form for α(ω, F ) can be presented as ...
The adiabatic approximation is analyzed for non-perturbative interaction of an atomic system with an intense low-frequency laser field. We find that the well-known adiabatic ansatz, which consists in using the DC-based Green's and wave functions for an atom in the instantaneous AC field to calculate transition matrix elements, exceeds the level of accuracy of the adiabatic approximation and requires further theoretical revision. It is shown that the non-analyticity in the field strength of the DC-based Green's and wave functions leads to violation of the adiabaticity constrains and the appearance of rapidly oscillating components in the transition matrix elements. We suggest an improved adiabatic approach utilizing the analytical parts in the DC-based Green's and wave functions. We illustrate our revised adiabatic approach for analysis of atomic polarizability in two-component laser field with an intense infrared and perturbative extreme ultraviolet components within the zero-range potential model.
... It can be expressed in terms of the dynamic polarizability of an atom in the dc field: (11) where |˜ dc = [| dc ] * (see details in Refs. [51,54]) and the factor P (t ) = e − t −∞ (F )dt is introduced to describe depletion effects. Note that in the limit F → 0 the susceptibility χ 1 tends to the dynamic polarizability of a free atom. ...
The nonlinear response of an atomic system interacting with short extreme ultraviolet (XUV) and infrared (IR) pulses is considered within the adiabatic approach (for an IR field) and the perturbation theory (for an XUV pulse). The second-order perturbation theory in the XUV field is developed for the IR-dressed atom, and the laser-induced generation of a pulse with a doubled carrier XUV frequency is analyzed. We study the yield of harmonics in the frequency band of the generated doubled frequency XUV pulse as a function of the time delay between initial XUV and IR pulses. Our analytical and numerical results show that this dependence carries the time dependence of the intense IR pulse and can be utilized to retrieve the waveform of the IR pulse.
... Thus,φ ω (r) = φ ω (r, θ, −ϕ), which leads to the normalization condition (41). We mention that, taking into account Eq. (51b), this complies with the normalization condition for Floquet states in a circularly polarized laser field [18,108]. ...
We show that the time-dependent Schrödinger equation describing in the dipole approximation the interaction of a one-electron atom with a monochromatic circularly polarized electromagnetic field can be reduced to a stationary Schrödinger equation in the form which allows to separate variables in the asymptotic region and explicitly formulate outgoing-wave boundary conditions. The solutions to this equation are called atomic Siegert states (SSs) in a rotating electric field. We develop the theory of such states and propose an efficient method to construct them using powerful techniques of stationary scattering theory. The method yields not only the SS eigenvalue defining the Stark-shifted energy and total ionization rate of the state, but also the SS eigenfunction defining partial ionization amplitudes and the photoelectron momentum distribution. The theory is illustrated by calculations for a model potential.
... Here we have considered that (i) the effects of the external fields on the initial bound electron state are negligible, i.e., the external fields do not contribute to the detachment of electrons, H ext (t) |ϕ b → 0; therefore, (ii) the initial bound state is an eigenstate of the atomic Hamiltonian, H a |ϕ b = E b |ϕ b ; and (iii) since H L (t) is weak, it does not contribute on the dynamics of the excited electron state, i.e., H L (t) |Ψ(t) → 0. Furthermore, for single-active-electron atomic photodetachment problems, within the dipole approximation, the interaction Hamiltonian H L (t) in the length gauge has the form [22,38,39] ...
The closed-orbit theory is used for the study of the photodetachment rate of electrons from single-charged anions in presence of a homogeneous magnetic field that is perpendicular to a time-dependent electric field. The photodetachment process in the near-threshold region is achieved by a weak laser field. We describe in detail the semiclassical method to derive the general formula for the instant photodetachment rate in time-dependent systems. We find that the photodetachment rate is affected by the presence of the static magnetic field since, within the semiclassical picture, it contributes to fold back the electron trajectories back to their emission position: generating closed orbits. For weak magnetic fields, however, the number of closed orbits does not change, then the modulation of the photodetachment rate is virtually unaffected when it is compared to the case with no magnetic field. On the contrary, the modulation is clearly distinctive and complicated for strong magnetic field intensities due to the contribution of a larger number of closed orbits. Despite we provide general formulas, numerical experiments and discussions are focused on the emission of electrons as s-waves and p z -waves.
... In this work, we present an alternative to the existing theoretical approaches. Our approach is based on the analysis of integral equation for the quasistationary quasienergy state (QQES) in a periodic laser field for an arbitrary shortrange potential [28][29][30][31]. We show that the integral equation for QQES can be transformed to a form similar to that for the TDER model [22,24], however, in contrast to the TDER model, this equation involves explicitly the Fourier-transform of a short-range potential [see Eq. (10)]. ...
... where U (r) is a short-range potential. Equation (1) is supplemented by the spherical outgoing wave boundary condition at large distances, which ensures the complexity of quasienergy [28][29][30][31]. The eigenvalue problem (1) can be also formulated in terms of the homogeneous integral equation: ...
... where G(r, t; r , t ) is the retarded nonstationary Green's function of the free electron in a laser field (see, e.g., Appendix B in Ref. [30]). 1 As can be shown, at large distances from Eq. (2) follows an expansion of QQES wave function in terms of outgoing spherical waves (see Ref. [17] and Appendix A for details): ...
Generation of electron vortices in photodetachment driven by linearly polarized laser pulses is demonstrated, both within the strong-field approximation and by numerically solving the time-dependent Schrödinger equation. The sensitivity of the resulting vortex patterns in the momentum distributions of photoelectrons to the laser pulse parameters (including the pulse duration, its intensity, and the carrier-envelope phase) is analyzed. It is shown that, for a nonzero carrier-envelope phase of the driving pulse, vortex structures in the probability amplitude of detachment occur, similar to von Kármán vortex streets in fluid mechanics. In addition, hexagonal regions of high probability (honeycomb patterns) are observed, with vortex-antivortex pairs located at their vertices.
... We shall analyze the complex quasienergy in a periodic laser field with a period T and corresponding frequency ω τ = 2π/T within the framework of TDER theory [73,74]. The TDER theory is based on the boundary condition for a quasistationary quasienergy wave function (r, t ) [77,116] formulated at small distances from the core [73,74] (see Appendix A for details): ...
... where G(r, t; r , t ) is the retarded Green's function for a free electron in a laser field with vector potential A(t ) [116], and Y l m (n) is a solid harmonic. In our analytical model, we take into account only two phases δ l (k) with l = 0 and l = 1. ...
... The boundary condition (A1) should be modified for the case of the long-range, periodic-in-time electron-laser interaction [73,74]. Indeed, in accord with the theory of quasistationary quasienergy states [77,116], the wave function for a complex quasienergy has the form ...
An analytic description of high-order harmonic generation (HHG) is proposed in the adiabatic (low-frequency) limit for an initial s state and a laser field having an arbitrary wave form. The approach is based on the two-state time-dependent effective range theory and is extended to the case of neutral atoms and positively charged ions by introducing ad hoc the Coulomb corrections for HHG. The resulting closed analytical form for the HHG amplitude is discussed in terms of real classical trajectories. The accuracy of the results of our analytic model is demonstrated by comparison with numerical solutions of the time-dependent Schrödinger equation for a strong bicircular field composed of two equally intense components with carrier frequencies ω and 2ω and opposite helicities. In particular, we demonstrate the effect of ionization gating on HHG in a bicircular field, both for the case that the two field components are quasimonochromatic and for the case that the field components are time-delayed short pulses. We show how ionization in a strong laser field not only smooths the usual peak structures in HHG spectra but also changes the positions and polarization properties of the generated harmonics, seemingly violating the standard dipole selection rules. These effects appear for both short and long incident laser pulses. In the case of time-delayed short laser pulses, ionization gating provides an effective tool for control of both the HHG yield and the harmonic polarizations [Frolov et al., Phys. Rev. Lett. 120, 263203 (2018)]. For the case of short laser pulses, we introduce a simple two-dipole model that captures the physics underlying the harmonic emission process, describing both the oscillation patterns in HHG spectra and also the dependence of the harmonic polarizations on the harmonic energy.
... Using more advanced analytical derivation based on Siegert states, Tolstikhin et al have recently achieved an asymptotic derivation of the ionization rate at higher orders for atoms [27][28][29], and molecules [30][31][32] including nuclear motion in the Born Oppenheimer approximation [12,33]. At the same time, Manakov et al performed a derivation for negative atomic [34] and molecular ions [35]. Corrections to take multielectron effects into account were also recently investigated, see [43] and references therein. ...
Weak-field asymptotic formulas for the tunnel ionization rate of atoms and molecules in strong laser fields are often used for the analysis of strong field recollision experiments. We investigate their accuracy and domain of validity for different model systems by confronting them to exact numerical results, obtained by solving the time dependent Schrödinger equation. We find that corrections that take the dc-Stark shift into account are a simple and efficient way to improve the formula. Furthermore, analyzing the different approximations used, we show that error compensation plays a crucial role in the fair agreement between exact and analytical results.
... He clarified the connection between a semi-classical external field drive and its quantized strong, resonant single-mode field counterpart applied to an N -level atom based on general considerations using Floquet's theorem. Various extensions of this work, which focused on the semi-classical picture suggested by the strong-intensity nature of laser fields, have been reviewed in [5][6][7]. ...
... where N is the number of states in the system. In the vectorized form, i.e. by re-stacking the columns of the matrix representation of ρ(t) into an N 2 -dimensional vector (ρ 00 , ρ) T , the master equation (6) turns into d dt ...
We present a general method to calculate the quasi-stationary state of a driven-dissipative system coupled to a transmission line (and more generally, to a reservoir) under periodic modulation of its parameters. Using Floquet's theorem, we formulate the differential equation for the system's density operator which has to be solved for a single period of modulation. On this basis we also provide systematic expansions in both the adiabatic and high-frequency regime. Applying our method to three different systems -- two- and three-level models as well as the driven nonlinear cavity -- we propose periodic modulation protocols of parameters leading to a temporary suppression of effective dissipation rates, and study the arising non-adiabatic features in the response of these systems.
... The TDER theory is based on the quasistationary quasienergy state (QQES) approach [56][57][58][59] and effective range theory [60]. The QQES approach is used for the quantum description of the laser-atom interaction, assuming the laser field is approximated by a periodic (in time) electric field. ...
... The QQES approach is used for the quantum description of the laser-atom interaction, assuming the laser field is approximated by a periodic (in time) electric field. In the framework of the QQES approach the quantum state (QQES state) of an atomic electron in a periodic laser field is characterized by a complex quasienergy, whose real part gives the position of the atomic level (including the nonlinear Stark effect), while the imaginary part describes the total laserinduced width of the atomic level in the laser field [56][57][58][59]. The corresponding QQES wave function satisfies the complex boundary condition appropriate for an outgoing spherical wave at large distances, which ensures the complexity of the quasienergy. ...
Threshold phenomena (or channel-closing effects) are analyzed in high-order harmonic generation (HHG) by atoms in a two-color laser field with orthogonal linearly polarized components of a fundamental field and its second harmonic. We show that the threshold behavior of HHG rates for the case of a weak second harmonic component is sensitive to the parity of a closing multiphoton ionization channel and the spatial symmetry of the initial bound state of the target atom, while for the case of comparable intensities of both components, suppression of threshold phenomena is observed as the relative phase between the components of a two-color field varies. A quantum orbit analysis as well as phenomenological considerations in terms of Baz’ theory of threshold phenomena [Zh. Eksp. Teor. Fiz. 33, 923 (1957)] are presented in order to describe and explain the major features of threshold phenomena in HHG by a two-color field.
