Spatial diffusion in a periodic optical lattice: revisiting the Sisyphus effect

We numerically study the spatial diffusion of an atomic cloud experiencing Sisyphus cooling in a three-dimensional linlin optical lattice in a broad range of lattice parameters. In particular, we investigate the dependence on the size of the lattice sites which changes with the angle between the laser beams. We show that the steady-state temperature is largely independent of the lattice angle, but that the spatial diffusion changes significantly. It is shown that the numerical results fulfill the Einstein relations of Brownian motion in the jumping regime as well as in the oscillating regime. We finally derive an effective Brownian motion model from first principles which gives good agreement with the simulations. Received 8 August 2001 and Received in final form 6 November 2001     

Bright optical lattices in a longitudinal magnetic field. Experimental study of the oscillating and jumping regimes

All the bright optical lattices studied so far have been designed to obtain a circularly polarized light at the bottom of the optical potential wells. This condition minimizes the departure rate of the atoms from the fundamental adiabatic surface and permits an oscillating regime in a large range of parameters. We present here an experimental study of cesium atoms in a three-dimensional optical lattice, where the light is linearly polarized at the bottom of the potential wells. Temperature measurements and pump-probe spectroscopy give similar results for this lattice and for the conventional lin lin lattice (which have circular polarizations at the bottom of the wells) despite the fact that one lattice operates in the jumping regime and the other in the oscillating regime. We study the behaviour of the two types of lattices in a longitudinal magnetic field, with particular emphasis on the zero field and strong field regimes. The strong field situation is very simple because the eigenstates are then almost pure Zeeman substates and the adiabatic and diabatic potential surfaces are identical. The comparison between the zero-field and the high-field situations shows that the diabatic potentials are more appropriate to account for experimental observations in the novel lattice. Received: 9 October 1997 / Accepted: 6 November 1997     

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     

Feasibility of narrow-line cooling in optical dipole traps

We have investigated the influence of narrow-line laser cooling on the loading of Ca atoms into optical dipole traps. To describe the narrow-line cooling of alkaline-earth atoms in combination with optical dipole trapping, we have developed a model that takes into account the light shifts of the cooling transition in three dimensions. The model is compared with two experimental realizations of optical dipole traps for calcium at the wavelengths 514 nm and 10.6 μm.     

Sisyphus cooling of rubidium atoms on the line: The role of the neighbouring transitions

We study one-dimensional Sisyphus cooling on the transition of ⁸⁷ Rb atoms in the electric field created by two counter-propagating linearly polarized laser beams with an angle of between the polarization directions. The neighbouring F '=0 and F '=2 excited states are found to play an important role in the cooling mechanism, e.g., by inhibiting a significant population of the velocity-selective dark state. Our experimental data, such as temperatures and probe absorption coefficients, agree well with the results of quantum Monte-Carlo wavefunction simulations. Received 26 November 1998 and Received in final form 20 April 1999     

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     

Fragmentation of CO+ molecular ion through dissociative excited states produced by swift multicharged heavy ion impact on CO molecules

We report the observation of resonances in the intensity correlation spectra of a 3D rubidium optical lattice, which we attribute to light scattering from propagating atomic density fluctuations in the lattice. This process is the spontaneous analog of the stimulated scattering mechanism recently described by Courtois et al.. We investigate the dependence of the new resonances on the lattice angle and show that they disappear for large angles, thus resolving previous discrepancies on the subject. Received: 30 January 1997 / Accepted: 9 October 1997     

Pump-probe spectroscopy of atoms cooled in a 3D lin lin optical lattice

We describe the pump-probe spectroscopy of atoms cooled in a 3D lin⊥lin optical lattice. Our pump-probe configuration consists of two laser fields detuned with respect to the lattice fields. This scheme allows to clearly identify in the probe transmission spectrum the Brillouin and Raman resonances, by studying their positions as functions of the angle between the pump and probe beams. We describe these resonances in detail, and compare the experimental results to the theoretical predictions. Our conclusions are supported by transport-spectroscopy measurements, which allow to distinguish between contributions to the light scattering from propagating and non-propagating atoms. Received 8 April 2002 / Received in final form 9 September 2002 Published online 12 November 2002     

2D dark optical surface lattice with an efficient intensity-gradient cooling of atoms by evanescent wave interference

We propose a novel scheme to form a 2D dark optical surface lattice (DOSL) for cold atoms on the surface of the dense flint glass by using two sets of blue-detuned evanescent wave interference fields and a blue-detuned evanescent wave field. In the 2D DOSL, cold atoms will be trapped in the vicinity of minimum intensity and suffered the minimal light shift as well as the lowest coherence loss. The total potential and trap-depth of the individual optical micro-trap in the 2D DOSL are high enough to trap cold atoms (T = 120 μK) released from the standard magneto-optical trap (MOT), and atoms trapped in the 2D DOSL can be cooled to several μK with the efficient intensity-gradient Sisyphus cooling. The lattice constant of the DOSL can be controllable by changing the incident angles of lights.     

Bose–Einstein condensates in 1D- and 2D optical lattices

Bose–Einstein condensates of rubidium atoms are transferred into one- and two-dimensional optical lattice potentials. The phase coherence of the condensate wavefunction in the lattice potential is studied by suddenly releasing the atoms from the trapping potential and observing the multiple matter-wave interference pattern of several thousand expanding quantum gases. We show how arbitrary phase gradients can be mapped onto the periodic wavefunction through the application of a potential gradient. Furthermore, the experimentally measured strength of the momentum components is compared to a theoretical model of the condensate wavefunction in the lattice. Received: 3 July 2001 / Revised version: 26 September 2001 / Published online: 23 November 2001     

A nonadiabatic semi-classical method for dynamics of atoms in optical lattices

We develop a semi-classical method to simulate the motion of atoms in a dissipative optical lattice. Our method treats the internal states of the atom quantum mechanically, including all nonadiabatic couplings, while position and momentum are treated as classical variables. We test our method in the one-dimensional case. Excellent agreement with fully quantum mechanical simulations is found. Our results are much more accurate than those of earlier semi-classical methods based on the adiabatic approximation.     

Accumulation of chromium metastable atoms into an optical trap

We report the fast accumulation of a large number of metastable ⁵²Cr atoms in a mixed trap, formed by the superposition of a strongly confining optical trap and a quadrupolar magnetic trap. The steady state is reached after about 400 ms, providing a cloud of more than one million metastable atoms at a temperature of about 100 μK, with a peak density of 10¹⁸ atoms m^-3. We have optimized the loading procedure, and measured the light shift of the ⁵D₄ state by analyzing how the trapped atoms respond to a parametric excitation. We compare this result to a theoretical evaluation based on the available spectroscopic data for chromium atoms.     

Controllable Photonic Band Gap and Defect Mode in a 1D CO2-Laser Optical Lattice

We propose a new method to form a novel controfiable photonic crystal with cold atoms and study the photonic band gap （PBG） of an infinite 1D CO2-laser optical lattice of SSRb atoms under the condition of quantum coherence. A significant gap generated near the resonant frequency of the atom is founded and its dependence on physical parameters is also discussed. Using the eigenquation of defect mode, we calculate the defect mode when a defect is introduced into such a lattice. Our study shows that the proposed new method can be used to optically probe optical lattice in situ and to design some novel and controllable photonic crystals.     

The S-FFT calculation of Collins formula and its application in digital holography

We study analytically and numerically the properties of one-dimensional chain of cold ions placed in a periodic potential of optical lattice and global harmonic potential of a trap. In close similarity with the Frenkel-Kontorova model, a transition from sliding to pinned phase takes place with the increase of the optical lattice potential for the density of ions incommensurate with the lattice period. We show that at zero temperature the quantum fluctuations lead to a quantum phase transition and melting of pinned instanton glass phase at large values of dimensional Planck constant. After melting the ion chain can slide in an optical lattice. The obtained results are also relevant for a Wigner crystal placed in a periodic potential.     

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     

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     

Acceleration of cold Rb atoms by frequency modulated light pulses

The displacement of Rb atoms in a magneto-optical trap (MOT) caused by the force of a finite time series of counter-propagating frequency modulated light pulse pairs is measured as a function of the chirp of the pulses. The frequency modulated light pulses induced ⁸⁵Rb 5²S_1/2 F=3 ↔ ⁸⁵Rb 5²P_3/2 F'=2, 3, 4 excitation and de-excitation of the atoms. The result of this excitation de-excitation process is a force causing the acceleration and, consequently, the displacement of the maximum of the spatial distribution of the trap atoms. The time dependence of the populations of the levels of the atom are calculated — including also the ⁸⁵Rb 5²S_1/2 F=2 and F'=1 states — as the result of the interaction with the finite train of counter propagating frequency modulated light pulses by the solution of the Bloch equations. As the result of the measurement the interval of the chirp of the frequency modulated light of given intensity where the transitions take place, are determined. The results of the experiment and the expectation on the basis of model calculations are in qualitative agreement.     

Long-range Rydberg-Rydberg interactions and molecular resonances

We present a detailed theoretical treatment to describe the lineshape of molecular resonances in a cold dense gas of rubidium Rydberg atoms. Molecular potentials in Hund's case (c) are calculated by diagonalization of an interaction matrix. We show how the strong ℓ-mixing due to long-range Rydberg-Rydberg interactions can lead to resonances in excitation spectra. Such resonances were first reported in [S.M. Farooqi et al., Phys. Rev. Lett. 91, 183002 (2003)], where single UV photon excitations from the 5s ground state occurred at energies corresponding to normally forbidden transitions or very far detuned from the atomic energies. Here, we focus our attention on resonances at energies corresponding to excited atom pairs (n - 1)p_3/2+(n + 1)p_3/2. Very good agreement between the theoretical and experimental lineshapes is found.     

Single-beam optical bottle for cold atoms using a conical lens

We report a new method to generate an optical dipole potential with a null intensity region surrounded in all directions by light walls. This is achieved with a simple scheme based on a conical lens. Applications to optical trapping of neutral atoms are discussed. Received 4 September 2000 and Received in final form 21 January 2001