A focussing funnel for metastable helium

We have constructed a magneto-optical funnel for He atoms and studied its properties using a laser cooled, highly mono-energetic atomic beam. A simple model of its action allows us to quantitatively understand the observed spot size and “focal length”. We show that for a fast beam, the velocity damping coefficient plays an important role in determining the focal length of the device. The observed spot size is limited mainly by transverse heating processes which impose a transverse velocity spread. The device also permits easy scanning of the focussed spot. Received 30 October 1998 and Received in final form 27 January 1999     

A continuous cold atomic beam from a magneto-optical trap

We have developed and characterized a new method to produce a continuous beam of cold atoms from a standard vapour-cell magneto-optical trap (MOT). The experimental apparatus is very simple. Using a single laser beam it is possible to hollow out in the source MOT a direction of unbalanced radiation pressure along which cold atoms can be accelerated out of the trap. The transverse cooling process that takes place during the extraction reduces the beam divergence. The atomic beam is used to load a magneto-optical trap operating in an ultra-high vacuum environment. At a vapour pressure of 10^-8mbar in the loading cell, we have produced a continuous flux of 7×10⁷atoms/s at the recapture cell with a mean velocity of 14 m/s. A comparison of this method with a pulsed transfer scheme is presented. Received 19 February 2001     

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     

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     

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     

Canonical dressing in the multimode two-quantum Jaynes-Cummings model

Based upon the hidden Lie SU(1,1) symmetry, we have constructed the unitary decoupling transformation which diagonalizes the multimode two-quantum Jaynes-Cummings model and provides us with an extremely convenient basis to gain a deeper understanding of the dressing processes present in the matter-field interaction. This canonical transformation approach is very simple and can be easily extended to other generalized Jaynes-Cummings models. Received: 5 July 1997 / Revised: 3 November 1997 / Accepted: 14 November 1997     

Laser cooling of molecules via single spontaneous emission

A general scheme for reducing the center-of-mass entropy is proposed. It is based on the repetition of a cycle, composed of three concepts: velocity selection, deceleration and irreversible accumulation. Well-known laser techniques are used to represent these concepts: Raman π-pulse for velocity selection, STIRAP for deceleration, and a single spontaneous emission for irreversible accumulation. No closed pumping cycle nor repeated spontaneous emissions are required, so the scheme is applicable to cool a molecular gas. The quantum dynamics are analytically modelled using the density matrix. It is shown that during the coherent processes the gas is translationally cooled. The internal states serve as an entropy sink, in addition to spontaneous emission. This scheme provides new possibilities to translationally laser-cool molecules for high precision molecular spectroscopy and interferometry. Received 25 June 2002 / Received in final form 28 September 2002 Published online 12 November 2002 RID="a" ID="a"e-mail: ooi@spock.physik.uni-konstanz.de RID="b" ID="b"e-mail: Peter.Marzlin@uni-konstanz.de RID="c" ID="c"e-mail: Juergen.Audretsch@uni-konstanz.de     

Atom optics with rotating Bose-Einstein condensates

The atom optics of Bose-Einstein condensates containing a vortex of circulation one is discussed. We first analyze in detail the reflection of such a condensate falling on an atomic mirror. In a second part, we consider a rotating condensate in the case of attractive interactions. We show that for sufficiently large nonlinearity the rotational symmetry of the rotating condensate is broken. Received 16 September 2002 / Received in final form 17 November 2002 Published online 11 February 2003     

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     

Interaction of frequency modulated light pulses with rubidium atoms in a magneto-optical trap

The spatial displacement of the ⁸⁵Rb atoms in a Magneto-Optical Trap (MOT) under the influence of series of frequency modulated light pulse pairs propagating opposite to each other is measured as a function of the time elapsed after the start of the pulse train, and compared with the results of simulations. Adiabatic excitation and consecutive de-excitation take place between the ground 5²S_1/2 (F=3) and the 5²P_3/2 (F'=2, 3, 4) excited levels as the result of the interaction. The displacement of the ⁸⁵Rb atoms is calculated as the solution of simple equation of motion where the expelling force is that arising from the action of the frequency modulated light pulses. The restoring and friction forces of the MOT are taken into account also. The system of Bloch equations for the density matrix elements is solved numerically for transitions between six working hyperfine levels of the atom interacting with the sequence of the frequency modulated laser pulses. According to these simulations, the momentum transferred by one pulse pair is always smaller than the expected 2ħk, (1) where ħ is the Plank constant and k=2π/λ where λ is the wavelength, (2) having a maximum value in a restricted region of variation of the laser pulse peak intensity and the chirp.     

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.     

Loading of a cold atomic beam into a magnetic guide

We demonstrate experimentally the continuous and pulsed loading of a slow and cold atomic beam into a magnetic guide. The slow beam is produced using a vapor loaded laser trap, which ensures two-dimensional magneto-optical trapping, as well as cooling by a moving molasses along the third direction. It provides a continuous flux larger than 10⁹ atoms/s with an adjustable mean velocity ranging from 0.3 to 3 m/s, and with longitudinal and transverse temperatures smaller than 100 μK. Up to 3×10⁸ atoms/s are injected into the magnetic guide and subsequently guided over a distance of 40 cm. Received 19 February 2002 Published online 28 June 2002     

Quantum motion of three trapped ions in one dimension

The hyperspherical-coordinate approach is employed to a one-dimensional model of three ions in a Paul trap. It is shown that the eigen wave functions have well-defined nodal structure indicating a near separability in the hyperspherical coordinates, then two approximate good quantum numbers are introduced to classify the eigenstates. Three important classical periodic motions, including the breathing motion and the (distorted-)symmetric or anti-symmetric stretching motion, are found to dominate the wave function distribution. Received: 10 February 1999 / Received in final form: 25 March 1999     

A moving magnetic mirror to slow down a bunch of atoms

A fast packet of cold atoms is coupled into a magnetic guide and subsequently slowed down by reflection on a magnetic potential barrier (`mirror') moving along the guide. A detailed characterization of the resulting decelerated packet is performed. We show also how this technique can be used to generate a continuous and intense flux of slow, magnetically guided atoms.     

Condensation of laser cooled gases

We study a dynamical scheme for condensation of bosonic trapped gases beyond the Lamb-Dicke limit, when the photon-recoil energy is larger than the energy spacing of the trap. Using quantum master equation formalism we demonstrate that dark-state cooling methods similar to those designed for a single trapped atom allow for the condensation of a collection of bosons into a single state of the trap, either the ground, or an excited state. By means of Monte-Carlo simulations we analyse the condensation dynamics for different dimensions, and for different cooling schemes. Received 30 November 1998 and Received in final form 20 March 1999     

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     

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.     

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.