Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Brazilian Journal of Physics

Dependence of transition probabilities for non-linear photo-ionization of He atoms on the structure of the exciting radiation pulses

Alonso Castro, Thomas Möeller, H. Wabnitz, Tim Laarmann

Published Sep 1, 2005• 4 citations
Publisher

Abstract

We discuss the expected dependence of the probability transitions for 2-photon and 3-photon absorption in Helium gas on the spatial and temporal structure of the exciting radiation pulses. Regarding spatial structure, we assumed a Gaussian radial intensity distribution; we find, as expected, that the 2-photon and 3-photon processes become negligible at distances D away from the focus, where D is of the order of the beam waist FWHM. Regarding temporal structure, we compared transition probabilities for square, Gaussian and cosine squared temporal profiles; we find that for the same FWHM, Gaussian and cosine squared pulses give essentially the same transition probabilities, but the square pulses are about twice as efficient. We finally studied the effect of sharp versus smooth rise and fall edges in the light pulse; we find negligible correlation with the shape of the pulse edges, and strong correlation with the pulse FWHM, i.e., with pulse total energy, as might be expected.

DOI
10.1590/s0103-97332005000400008

Related papers

Spatio-temporal effects in resonant multiphoton ionisation of the caesium atom

Yves Gontier, M. Trahin

The time evolution of a resonance peak is studied for three- and four-photon ionisation of the caesium atom with square and Gaussian laser pulses. In the domain 10 -13 -10 -7 s two different regimes are defined according to whether the time is smaller or larger than a characteristic time t c . For t<t c the ionisation probability varies as t 3 whereas it is proportional to t when t>t c . The corresponding resonance width varies as t -1 in the first case becomes intensity independent in the second. The effects of the spatial distribution of the intensity in the focal volume are discussed and an excellent agreement is found between the theoretical and experimental values of the order of non-linearity, the resonance width and the absolute magnitude of the ion signal.

Journal of Physics B Atomic and Molecular Physics•Jan 28, 1980•26 citations

Manifestations of Rabi Dynamics in the Photoelectron Energy Spectra at Resonant Two-Photon Ionization of Atom by Intense Short Laser Pulses

N. S. Simonović, Duska B Popovic, Andrej Bunjac

We study the Rabi flopping of the population between the ground and excited 2p states of the hydrogen atom, induced by intense short laser pulses of different shapes and of carrier frequency ω=0.375 a.u. which resonantly couples the two states, and manifestations of this dynamics in the energy spectra of photoelectrons produced in the subsequent ionization of the atom from the excited state. It is found that, for Gaussian, half-Gaussian and rectangular pulses, characterized by the same pulse area, the final populations take the same values and the spectra consist of similar patterns having the same number of peaks and approximately the same separation between the prominent edge (Autler–Townes) peaks. The additional analysis in terms of dressed states showed that the mechanism of formation of multiple-peak structures during the photoionization process is the same regardless of the pulse shape. These facts disprove the hypothesis proposed in earlier studies with Gaussian pulse, that the multiple-peak pattern appears due to dynamic interference of the photoelectrons emitted with a time delay at the rising and falling sides of the pulse, since the hypothesis is not applicable to either a half-Gaussian pulse that has no rising part or a rectangular pulse whose intensity is constant.

Atoms•Jan 23, 2023•19 citations

Resonant multiphoton ionization of atomic hydrogen

Yves Gontier, N. K. Rahman, M. Trahin

The resonantly enhanced multiphoton ionization of atomic hydrogen is studied for the case of four-photon ionization (three-photon resonant). The time-dependent probabilities, the shape of the resonance profile at different intensities, and the nonlinear index are computed for coherent light at frequencies around the resonance (365 nm). The systematic dependence of the cross section as a function of the principal quantum number of the resonant state (as this tends towards the Rydberg states) is investigated at zero detuning. The probabilities of absorption of one photon more than necessary for the four-photon ionization process (resonantly enhanced above-threshold ionization) is computed and the relevant branching ratios are examined. Then it is shown that the effect of the spatio-temporal structures of the laser pulse is to red shift the maximum of the resonance profile, whereas that of an ideal chaotic light is to blue shift and broaden the resonance peak. The shape, shift, and width of the profile resulting from both these effects are in very fair agreement with the experimental ones.

Physical Review A•Jun 1, 1988•15 citations

Field-Correlation Effects in Multiphoton Absorption Processes

G. S. Agarwal

The dependence of the multiphoton absorption probability for an atomic system on the statistical properties of the incident light is investigated. It is shown, by means of $n\mathrm{th}$-order time-dependent perturbation theory, that the multiphoton absorption probability depends on the $(n, n)\mathrm{th}$ normally ordered correlation functions of the electromagnetic field. For stationary fields, the transition probability per unit time is constant and is directly related to the reduced cross-spectral correlation function of the electromagnetic field. This expression for the transition probability is then analyzed under various conditions of coherence. Explicit calculations are carried out for thermal light and for laser light, and the transition rates are compared when each has a Lorentzian spectrum. In particular, when the width of the final atomic level is much larger than the bandwidth of the field, the transition rate for thermal light is $n$! times higher than with laser light of the same mean intensity. The other extreme case, i.e., when the width of the final atomic level is much smaller than the bandwidth of the field, is also considered in detail. An equation for the density operator of the field is derived; this equation governs the change in the statistical properties of the photon system in $n$-photon absorption processes. On the basis of this equation, the time-dependent properties of the photon system are then studied and some physical consequences of these equations are discussed. Some numerical solutions relating to the time dependence of the factorial moments in two-photon absorption processes are presented.

Physical Review A•May 1, 1970•216 citations

Laser temporal and spatial effects on ionization suppression

Justin B. Peatross, David D. Meyerhofer, Mikhail Vladimirovich Fedorov

Ionization suppression can be defined as the decrease of photoinduced atomic ionization rates with an increased applied field intensity. The temporal and spatial intensity distribution of a focused laser pulse introduces difficulty in observing ionization suppression. An analysis of the effect of a temporally Gaussian laser pulse on ionization suppression from Rydberg levels is given. It is found that ionization suppression by the Gaussian pulse is still apparent, even though the low-intensity tails of the pulse produce moderate ionization. Further, the spatial effects are examined for a scheme whereby a narrow atomic beam is passed through the focus of a laser at which ionization is detected. Ionization suppression in the more intense region of the laser focus is predicted to be apparent above the background ionization from the relatively large region of low intensity surrounding the laser focus.

Journal of the Optical Society of America B•Aug 1, 1992•6 citations

Ionization dynamics in double resonance involving autoionizing states in helium: the effect of pulse shapes

Spyros I. Themelis, P. Lambropoulos, M. Meyer

We discuss the dynamics of doubly resonant ionization in helium involving the strong coupling of two doubly excited autoionizing resonances, under the influence of XUV radiation of short duration (DESY FEL) and a synchronized optical laser. We explore the possibility of using the photoelectron spectra to extract information about the pulse shape of the FEL. We present in addition new calculations of the expected AC Stark splitting due to the strong coupling of the two resonances and show that, within the range of intensities and pulse durations expected in the experiments, additional structure, beyond the usual doublet, is to be expected.

Journal of Physics B Atomic Molecular and Optical Physics•Oct 27, 2004•40 citations
We discuss the expected dependence of the probability transitions for 2-photon and 3-photon absorption in Helium gas on the spatial and temporal structure of the exciting radiation pulses. Regarding spatial structure, we assumed a Gaussian radial intensity distribution; we find, as expected, that the 2-photon and 3-photon processes become negligible at distances D away from the focus, where D is of the order of the beam waist FWHM. Regarding temporal structure, we compared transition probabilities for square, Gaussian and cosine squared temporal profiles; we find that for the same FWHM, Gaussian and cosine squared pulses give essentially the same transition probabilities, but the square pulses are about twice as efficient. We finally studied the effect of sharp versus smooth rise and fall edges in the light pulse; we find negligible correlation with the shape of the pulse edges, and strong correlation with the pulse FWHM, i.e., with pulse total energy, as might be expected.
The time evolution of a resonance peak is studied for three- and four-photon ionisation of the caesium atom with square and Gaussian laser pulses. In the domain 10 -13 -10 -7 s two different regimes are defined according to whether the time is smaller or larger than a characteristic time t c . For t<t c the ionisation probability varies as t 3 whereas it is proportional to t when t>t c . The corresponding resonance width varies as t -1 in the first case becomes intensity independent in the second. The effects of the spatial distribution of the intensity in the focal volume are discussed and an excellent agreement is found between the theoretical and experimental values of the order of non-linearity, the resonance width and the absolute magnitude of the ion signal.
We study the Rabi flopping of the population between the ground and excited 2p states of the hydrogen atom, induced by intense short laser pulses of different shapes and of carrier frequency ω=0.375 a.u. which resonantly couples the two states, and manifestations of this dynamics in the energy spectra of photoelectrons produced in the subsequent ionization of the atom from the excited state. It is found that, for Gaussian, half-Gaussian and rectangular pulses, characterized by the same pulse area, the final populations take the same values and the spectra consist of similar patterns having the same number of peaks and approximately the same separation between the prominent edge (Autler–Townes) peaks. The additional analysis in terms of dressed states showed that the mechanism of formation of multiple-peak structures during the photoionization process is the same regardless of the pulse shape. These facts disprove the hypothesis proposed in earlier studies with Gaussian pulse, that the multiple-peak pattern appears due to dynamic interference of the photoelectrons emitted with a time delay at the rising and falling sides of the pulse, since the hypothesis is not applicable to either a half-Gaussian pulse that has no rising part or a rectangular pulse whose intensity is constant.
The resonantly enhanced multiphoton ionization of atomic hydrogen is studied for the case of four-photon ionization (three-photon resonant). The time-dependent probabilities, the shape of the resonance profile at different intensities, and the nonlinear index are computed for coherent light at frequencies around the resonance (365 nm). The systematic dependence of the cross section as a function of the principal quantum number of the resonant state (as this tends towards the Rydberg states) is investigated at zero detuning. The probabilities of absorption of one photon more than necessary for the four-photon ionization process (resonantly enhanced above-threshold ionization) is computed and the relevant branching ratios are examined. Then it is shown that the effect of the spatio-temporal structures of the laser pulse is to red shift the maximum of the resonance profile, whereas that of an ideal chaotic light is to blue shift and broaden the resonance peak. The shape, shift, and width of the profile resulting from both these effects are in very fair agreement with the experimental ones.
The dependence of the multiphoton absorption probability for an atomic system on the statistical properties of the incident light is investigated. It is shown, by means of nthn\mathrm{th}nth-order time-dependent perturbation theory, that the multiphoton absorption probability depends on the (n,n)th(n, n)\mathrm{th}(n,n)th normally ordered correlation functions of the electromagnetic field. For stationary fields, the transition probability per unit time is constant and is directly related to the reduced cross-spectral correlation function of the electromagnetic field. This expression for the transition probability is then analyzed under various conditions of coherence. Explicit calculations are carried out for thermal light and for laser light, and the transition rates are compared when each has a Lorentzian spectrum. In particular, when the width of the final atomic level is much larger than the bandwidth of the field, the transition rate for thermal light is nnn! times higher than with laser light of the same mean intensity. The other extreme case, i.e., when the width of the final atomic level is much smaller than the bandwidth of the field, is also considered in detail. An equation for the density operator of the field is derived; this equation governs the change in the statistical properties of the photon system in nnn-photon absorption processes. On the basis of this equation, the time-dependent properties of the photon system are then studied and some physical consequences of these equations are discussed. Some numerical solutions relating to the time dependence of the factorial moments in two-photon absorption processes are presented.
Ionization suppression can be defined as the decrease of photoinduced atomic ionization rates with an increased applied field intensity. The temporal and spatial intensity distribution of a focused laser pulse introduces difficulty in observing ionization suppression. An analysis of the effect of a temporally Gaussian laser pulse on ionization suppression from Rydberg levels is given. It is found that ionization suppression by the Gaussian pulse is still apparent, even though the low-intensity tails of the pulse produce moderate ionization. Further, the spatial effects are examined for a scheme whereby a narrow atomic beam is passed through the focus of a laser at which ionization is detected. Ionization suppression in the more intense region of the laser focus is predicted to be apparent above the background ionization from the relatively large region of low intensity surrounding the laser focus.
We discuss the dynamics of doubly resonant ionization in helium involving the strong coupling of two doubly excited autoionizing resonances, under the influence of XUV radiation of short duration (DESY FEL) and a synchronized optical laser. We explore the possibility of using the photoelectron spectra to extract information about the pulse shape of the FEL. We present in addition new calculations of the expected AC Stark splitting due to the strong coupling of the two resonances and show that, within the range of intensities and pulse durations expected in the experiments, additional structure, beyond the usual doublet, is to be expected.