A simple non-perturbative approach of atom ionisation by intense and ultra-short laser pulses

A simple theoretical approach based on Coulomb-Volkov states is introduced to predict ionisation of atoms by intense laser pulses in cases where the effective interaction time does not exceed one or two optical cycles [M. Nisoli et al., Opt. Lett. 22, 522 (1997)]. Under these conditions, the energy distributions of ejected electrons predicted by this non-perturbative approach are in very good agreement with “exact" results obtained by a full numerical treatment. The agreement is all the better that the principal quantum number of the initial state is high. For very strong fields, most electrons are ejected at an energy which is close to the classical kinetic energy that would be transferred to free electrons by the electromagnetic field during the pulse. The power of the present approach appears when keV. In this region, full numerical treatments become very lengthy and finally do not converge. However, the present Coulomb-Volkov theory still makes reliable predictions in very short computer times. Received 19 November 1999 and Received in final form 19 January 2000     

Cooling mechanisms in potassium magneto-optical traps

We report on a theoretical and experimental investigation of ³⁹K magneto-optical trapping. The small hyperfine splitting characterizing the upper level of the cooling transition affects the cooling mechanism. In order to model the atom-laser interaction, the whole level structure of the D₂ line has to be taken into account. Two different regimes have been recognized, one optimizing the loading of the trap, the second minimizing the temperature of the atoms. We investigated these two regimes experimentally and found results in agreement with the theoretical predictions. Received: 6 March 1998 / Received in final form: 13 May 1998 / Accepted: 13 May 1998     

White light transverse cooling of a helium beam

We report a study of transverse laser cooling on a metastable helium beam using spectrally broadened diode lasers (“white light") to increase its flux. For this purpose, beam profile and atomic flux versus laser power and other parameters have been characterized. We have performed experiments to compare this technique with other transverse cooling methods using monochromatic light. Best results are obtained with a “ziz-zag" configuration using “white light". Received 21 December 1998 and Received in final form 27 May 1999     

Photoionization cross-sections of the first excited states of sodium and lithium in a magneto-optical trap

A two element magneto-optical trap (MOT) for Na and ⁷Li or ⁶Li is used to cool and trap each of them separately. A fraction of the cold atoms is maintained in the first ²P_3/2 excited state by the cooling laser. These excited state atoms are ionized by laser light in the near-UV region, giving rise to a smaller number of trapped atoms and to different loading parameters. Photoionization cross-sections were derived out of these data. They are in reasonable agreement with data previously obtained using thermal samples and with theoretical predictions. Received 21 March 2001 and Received in final form 3 August 2001     

Nonlinear Hanle effect in Cs vapor under strong laser excitation

We report results of a theoretical and experimental study of the ground state nonlinear Hanle effect under strong laser excitation. It is shown that besides the well-known zero-magnetic field suppression of absorption on F _g = F→F _e = F - 1 transitions caused by population trapping, an optical pumping induced enhanced absorption occurs on F _g = F→F _e = F + 1 transitions for small B-fields. The latter effect becomes more pronounced for high F values. The experiment with atomic vapor of Cs (D₂ line, F _g = 4) confirms an increase of the spectrally unresolved fluorescence yield at zero magnetic field and 600 mW/cm² laser intensity by 9% or 42%, when excitation occurs with linearly or circularly polarized light, respectively. The results of the experiment agree with numerical simulation studies using equations of motion for a density matrix. Received 24 November 2001 / Received in final form 25 March 2002 Published online 24 September 2002     

An intense, slow and cold beam of metastable Ne(3s) 3 P 2 atoms

We employ laser cooling to intensify and cool an atomic beam of metastable Ne(3 s) atoms. Using several collimators, a slower and a compressor we achieve a ²⁰Ne^* flux of 6×10 ¹⁰ atoms/s in an 0.7 mm diameter beam traveling at 100 m/s, and having longitudinal and transverse temperatures of 25 mK and 300μK, respectively. This constitutes the highest flux in a concentrated beam achieved to date with metastable rare gas atoms. We characterize the action of the various cooling stages in terms of their influence on the flux, diameter and divergence of the atomic beam. The brightness and brilliance achieved are 2.1 ×10 ²¹ s^-1m^-2sr^-1 and 5.0 ×10 ²² s^-1m^-2sr^-1, respectively, comparable to the highest values reported for alkali-metal beams. Bright beams of the ²¹Ne and ²²Ne isotopes have also been created. Received 22 June 2001     

One and two-photon detachment cross-sections of Ps-

We present detailed calculations for one- and two-photon above-threshold detachment (ATD) cross-sections of the negative positronium ion Ps ^- ( e ⁺ e ^- e ^- ), below the threshold of Ps(n = 2), using a configuration interaction (CI) method on a B splines basis. Both the one- and two-photon detachment cross-sections have a form similar to the corresponding spectra of the H^- ion, scaled accordingly. The peak value of the one-photon cross-section agrees very well with the calculations by Bathia and Drachman [1], while it differs from those by Igarashi et al. [2], which give a value of 15% lower. Two-photon detachment cross-sections are also reported. Received 24 January 2002 / Received in final form 9 April 2002 Published online 19 July 2002     

Spin-polarized Dirac-Slater calculations on the energies of hollow argon atom

In this work, the multiplet splitting in terms of a spin-dependent model is analyzed. The spin-polarized and unpolarized single configuration Dirac-Fock-Slater wavefunctions have been used in the evaluation of the total energies of highly ionized argon with different L shell population The transition energies of hollow argon atom with initial configurations 1s ⁰ _1/22s ^m _1/22p ⁿ _1/22p ^l _3/2 with m = 0 to 2 and n + l varying from 6 to 1 are reported in this work. The calculations have been carried out by taking into account a relativistic exchange potential in the Dirac-Slater potential. To account for the correlation effects, a correction term has also been considered perturbatively. The present calculations show that the spin-polarized technique which is mainly applied to the ground states of atoms may also be applied to atoms ionized in the inner shells with a good degree of accuracy. Received 5 December 2000 and Received in final form 9 April 2001     

The multiphoton ionization rate and the energy shift of atoms interacting with weak dichromatic fields with commensurate frequencies are simple functions of the phase difference

By implementing a time-independent, nonperturbative many-electron, many-photon theory (MEMPT), cycle-averaged complex eigenvalues were obtained for the He atom, whose real part gives the field-induced energy shift, Δ(ω ₁, F ₁;ω ₂, F ₂,ϕ), and the imaginary part is the multiphoton ionization rate, Γ(ω ₁, F ₁;ω ₂, F ₂,ϕ), where ω is the frequency, F is the field strength and ϕ is the phase difference. Through analysis and computation we show that, provided the intensities are weak, the dependence of Γ(ω ₁, F ₁;ω ₂, F ₂,ϕ) on ϕ is simple. Specifically, for odd harmonics, Γ varies linearly with cos(ϕ) whilst for even harmonics it varies linearly with cos(2ϕ). In addition, this dependence on ϕ holds for Δ(ω ₁, F ₁;ω ₂, F ₂,ϕ) as well. These relations may turn out to be applicable to other atomic systems as well, and to provide a definition of the weak field regime in the dichromatic case. When the combination of (ω ₁, F ₁) and (ω ₂, F ₂) is such that higher powers of cos(ϕ) and cos(2ϕ) become important, these rules break down and we reach the strong field regime. The herein reported results refer to Γ(ω ₁, F ₁;ω ₂, F ₂,ϕ) and Δ(ω ₁, F ₁;ω ₂, F ₂,ϕ) for He irradiated by a dichromatic ac-field consisting of the fundamental wavelength λ = 248 nm and its 2nd, 3rd and 4th higher harmonics. The intensities are in the range 1.0×10¹²-3.5×10¹⁴ W/cm², with the intensity of the harmonics being 1-2 orders of magnitude smaller. The calculations incorporated systematically electronic structure and electron correlation effects in the discrete and in the continuous spectrum, for ¹S, ¹P, ¹D, ¹F, ¹G, and ¹H two-electron states of even and odd parity. Received 9 July 2000 and Received in final form 2 November 2000     

An atom faucet

We present a simple and efficient source of slow atoms. From a background vapour loaded magneto-optical trap (MOT), a thin laser beam extracts a continuous jet of cold rubidium atoms. The jet that is typical to leaking MOT systems is created without any optical parts placed inside the vacuum chamber. We also present a simple three dimensional numerical simulation of the atomic motion in the presence of these multiple saturating laser fields combined with the inhomogeneous magnetic field of the MOT. At a pressure of P _Rb87 = 10^-8 mbar and with a moderate laser power of 10 mW per beam, we generate a flux Φ = 1.3×10⁸ atoms/s with a mean velocity of 14 m/s and a divergence of 10 mrad. Received 13 January 2001     

Near threshold photoionization of excited alkali atoms Ak(np) (Ak = Na, K, Rb, Cs; n = 3-6)

The effect of the polarization of the atomic core by the outer electron on near threshold photoionization of excited alkali atoms Ak(np) (Ak = Na-Cs; n=3-6) is investigated. Partial and total cross-sections for photo-ionization of the np-electron were computed utilizing the configuration interaction technique with Pauli-Fock atomic orbitals (CIPF) and including the long range core polarization potential (CP). To calculate the core polarization potential the variational principle is applied. Comparison with previous theoretical results and with available experimental data is made for the total cross-section , for the electron angular distribution parameter , for the ratio of the reduced electric dipole matrix elements and for the phase shift difference , associated with the d-wave and s-wave continua, respectively. In the comparison, new experimental results for , , and , measured for laser-excited, polarized ³⁹K(4p _3/2) atoms, have been included. Received 21 July 1999 and Received in final form 14 October 1999     

Electron angular distributions in double photoionization: Use of effective Sommerfeld parameters

We present calculations of the fivefold differential cross-section (FDCS) for double photoionization of helium at excess energies of 6 and 20 eV above threshold. Our results are obtained using for the final double-continuum state a product of three Coulomb wave functions, with the Sommerfeld parameters modified to describe the strength of interaction of any two particles affected by the third particle. Our calculations are compared with recent absolute measurements by D?rner et al. (Phys. Rev. A 57, 1074 (1998)), both in coplanar and non-coplanar geometries. Very good agreement is obtained for the shape of the angular distributions, and differences in the absolute magnitude exist in comparison with the standard choice of Sommerfeld parameters. Received: 17 July 1998 / Received in final form and Accepted: 23 October 1998     

Ionization of barium through a coherent excitation of two bound intermediate states

We have investigated theoretically the asymmetrical photoionization yields into the 6s _1/2, 5d _3/2 and 5d _5/2 continuum channels of atomic barium observed by Wang, Chen and Elliott [Phys. Rev. Lett. 77, 2416 (1996)] in the study of coherent control through two-color resonant interfering paths. The atomic parameters obtained from a theoretical approach based on a combination of jj-coupled eigenchannel R-matrix and Multichannel Quantum Defect Theory are used to analyze the photoionization spectra from the and 6s7p states with polarized light beams. The studied energy range includes the 6p7p autoionizing resonances. The dynamics of the two-color photoionization is governed by the coherent excitation of the 6s6p and intermediate states. This excitation is described as an adiabatic process in the rotating wave approximation. The influence of the radiative decay, spatial distribution of the intensities of the laser beams and hyperfine interaction is discussed. Received 28 September 1999     

3D dissipative motion of atoms in a strongly coupled driven cavity

We develop quantum models for the combined external and internal motion of atoms in a strongly coupled driven cavity mode including the transverse degrees of freedom. Using a simplified Gaussian mode function we determine the parameter regimes and prospects of 3D cooling and confinement of one or two atoms in the cavity field. Analysing the field dynamics for slow atoms traversing the cavity, we show that the spectrum of the transmitted and spontaneously scattered light contains ample information on the motional dynamics of the atom and can be nicely used to investigate the cooling properties of the system. Including several atoms in the dynamics we show how motional correlations build up by the common interaction with the cavity field. This can be looked upon as collisions at far distance and can be monitored via the transmitted field dynamics. Received 5 March 1999 and Received in final form 4 May 1999     

Buffer-gas loaded magnetic traps for atoms and molecules: A primer

Over the past three years we have developed the technique of buffer-gas cooling and loading of atoms and molecules into magnetic traps. Buffer-gas cooling relies solely on elastic collisions (thermalization) of the species-to-be-trapped with a cryogenically cooled helium gas and so is independent of any particular energy level pattern. This makes the cooling technique general and potentially applicable to any species trappable at the temperature of the buffer gas (as low as 240 mK). Using buffer-gas loading, paramagnetic atoms (europium and chromium) as well as a molecule (calcium monohydride) were trapped at temperatures around 300 mK. The numbers of the trapped atoms and molecules were respectively about 10¹² and 10⁸. The atoms and molecules were produced by laser ablation of suitable solid precursors. In conjunction with evaporative cooling, buffer-gas loaded magnetic traps offer the means to further lower the temperature and increase the density of the trapped ensemble to study a large variety of both static (spectra) and dynamic (collisional cross-sections) properties of many atoms and molecules at ultra-low temperatures. In this article we survey our main results obtained on Cr, Eu, and CaH and outline prospects for future work. Received 2 November 1998 and Received in final form 19 February 1999     

Flux enhancement model for cold cesium fine-structure changing collisions

The measurements of fine-structure changing collisions in a cesium magneto-optical trap, reported in a previous work [A. Fioretti et al., Phys. Rev. A 55, R3999 (1997)], are reanalyzed within a model based on the flux enhancement effect, which takes place in cold atomic collisions. In the present analysis, we consider the cooperative effect of the long-range and the shorter-range excitation by the strong trap laser. We evidence also the important role of the hyperfine structure of the Cs₂ molecular levels asymptotically connected to the ground-state and excited-state dissociation limits. Received 22 July 1999 and Received in final form 4 May 2000     

Reflection of cold atoms from an array of current-carrying wires

We report the realization of a new type of magnetostatic mirror for slowly moving atoms which comprises a planar array of parallel wires alternately carrying electric current in opposite directions. One of the features of this atomic mirror is that the magnetic field may be readily varied, switched or modulated by altering the current in the wires. Reflection signals close to 100% at a pulsed current of 3 A are demonstrated for a beam of free-falling laser-cooled cesium atoms at normal incidence. The current dependence of the reflection signals exhibits structure which is associated with the sequential onset of reflection of cesium 6² S _1/2 , F=4 atoms in the m=+4, +3, +2 and +1 magnetic states. Measurements of the spatial distribution of the reflected atoms indicate the reflection is predominantly specular at currents of 3 A. Received: 31 August 1998 / Accepted: 6 October 1998     

Temperatures in 3D optical lattices influenced by neighbouring transitions

A detailed experimental study of the steady-state temperature in a 3D optical lattice for cesium has been performed for a wide range of detunings. Specifically, we have investigated the situation with the cooling and trapping light detuned far red of a ( J _g↦J _e = J _g + 1)-transition, where the blue detuned interaction with a ( J _g↦J _e = J _g)-transition can not be neglected. We find that the temperature scales with the optical potential due to the interaction with just the ( J _g↦J _e = J _g + 1)-transition. This indicates that blue Sisyphus cooling has essentially no effect on the dynamics of the system, when there exists a neighbouring red detuned transition. Received 6 June 2000 and Received in final form 26 September 2000     

Inversion analysis of K 2 coupled electronic states with the Fourier grid method

We present a new determination of the potential curves and interactions of the coupled electronic states A ¹ Σ ⁺ _u and b ³ Π _u of the potassium dimer, based on new laser spectroscopy measurements within a molecular beam, combined with data available in the literature. We used a new global deperturbation approach, involving the Fourier Grid Hamiltonian method for energy level calculation. A standard deviation of 1.2 is obtained corresponding to a variance of 7.5×10 ^-3 cm^-1, representing a significant improvement compared to the standard deviation of 4 yielded by the traditional local deperturbation approach. Received 12 June 2001 and Received in final form 3 September 2001     

Pulsed polarization gradient cooling in an optical dipole trap with a Laguerre-Gaussian laser beam

We utilized a blue-detuned Laguerre-Gaussian (doughnut) laser beam to trap cold rubidium atoms by optical dipole force. ”Pulsed” polarization gradient cooling was applied to the trapped atoms to suppress the trap loss due to heating caused by random photon scattering of the trapping light. In this trap about 10⁸ atoms were initially captured and the trap lifetime was 1.5 s, which was consistent with losses due to background gas collisions. This trap can readily be applied to atom guiding, compression, and evaporative cooling. Received: 10 July 1997 / Received in final form: 5 January 1998 / Accepted: 16 January 1998