One-dimensional Optical Molasses Research Articles

A laser-cooled chromium atomic beam under 1 mrad for direct-write atom-lithography

We have developed an apparatus for laser-cooling chromium atomic beams using one-dimensional optical molasses. The divergence of the atomic beam was reduced from 4.5 mrad to 0.87 mrad and the intensity of fluorescence was increased by 1.79 times with a 45 mW laser power.

Doppler cooling of an optically dense cloud of magnetically trapped atoms

We have studied a general technique for laser cooling a cloud of polarized trapped atoms down to the Doppler temperature. A one-dimensional optical molasses using polarized light cools the axial motional degree of freedom of the atoms in the trap. Cooling of the radial degrees of freedom can be modelled by reabsorption of scattered photons in the optically dense cloud. We present experimental results for a cloud of chromium atoms in a magnetic trap. A simple model based on rate equations shows quantitative agreement with the experimental results. This scheme allows us to readily prepare a dense cloud of atoms in a magnetic trap with ideal starting conditions for evaporative cooling.

Cooling and resonance fluorescence of two atoms in a one-dimensional optical molasses.

We derive a generalized master equation, which describes the quantized cooling of identical atoms in the laser fields. The effects of the dipole-dipole interaction between the atoms are included explicitly in the master equation. We then calculate the steady-state density matrix of two atoms cooled by a one-dimensional optical molasses. It is shown that when the mean separation between these atoms reduces below the optical wavelength \ensuremath{\lambda}/2\ensuremath{\pi}, cooling will be significantly limited due to the enhanced atom-atom interaction. Based on the quantum regression theorem, we also calculate the resonance fluorescence spectrum emitted by these two atoms, which exhibits features different from those of isolated atoms.

Four-wave mixing in one-dimensional optical molasses.

We present a detailed calculation of the four-wave-mixing signal from one-dimensional optical molasses, in which atoms are cooled by a pair of counterpropagating, cross-polarized fields. The contributions from both Raman and Rayleigh resonances between the discrete motional bound states and the recoil-induced resonances between the motional continuum states are analyzed. It is shown that the recoil-induced resonances can lead to a narrow central resonance peak in the four-wave-mixing signal with a width given by the transverse residual Doppler width. The calculated Raman sidebands also exhibit an asymmetry in the signal strength, a feature observed in recent experiments.

Contribution of energy continuum states to probe the absorption signal of atoms in one-dimensional optical molasses.

We present a calculation of the probe absorption spectrum of atoms in a one-dimensional optical molasses formed by a pair of counterpropagating, cross-polarized fields. When the finite angle \ensuremath{\theta} between the propagation direction of a probe field and that of one of the cooling fields is taken into account, we find that, apart from the contributions to the probe absorption signal that are related to the Raman and Rayleigh resonances between the discretized atomic motional states in the molasses direction, there is also a signal arising from the recoil-induced resonances between atomic states with different center-of-mass momenta in the directions transverse to the molasses beams. The magnitudes of these different contributions are compared.

Semiclassical laser-cooling theory for a trapped multistate ion.

We present a semiclassical laser-cooling theory for an ion bound in a quadratic potential well, allowing for an arbitrary internal level scheme of the ion and an arbitrary polarization of the light field. The special case that the ion moves in a region much smaller than the wavelength of the exciting light (Lamb-Dicke limit), as well as an additional low-intensity limit, are worked out in detail. Explicit general expressions are given for the damping and diffusion tensors of the center-of-mass motion of the ion, and the light-induced renormalization of the mechanical oscillation frequencies is discussed. The formalism is implemented analytically using a computer program mathematica for an ion with a j=1/2\ensuremath{\rightarrow}j=3/2 transition moving in a one-dimensional optical molasses consisting of two counterpropagating laser beams with perpendicular linear polarizations (lin \ensuremath{\perp} lin). For a weakly bound ion at negligible saturation, the greatest lower limit of excitation energy turns out to be (33/20${)}^{1/2}$-1/2\ensuremath{\approxeq}0.78 vibrational quanta above the zero-point energy.

Quantum wave function simulation of the resonance fluorescence spectrum from one-dimensional optical molasses.

Using recently developed quantum wave function techniques, we have performed a simulation of $^{85}\mathrm{Rb}$ atoms in a one-dimensional optical molasses, formed from counterpropagating laser beams with orthogonal linear polarizations. Both internal and external degrees of freedom are treated quantum mechanically in one dimension and the spectrum of resonance fluorescence is calculated and compared to recent experiments. Excellent agreement is obtained for the spectrum and additional insight is gained into the experimental evidence for quantized motion in the optical potentials.

Probe transmission in a one-dimensional optical molasses: Theory for circularly-cross-polarized cooling beams.

We present a detailed theoretical investigation of the transmission spectrum of a probe beam interacting with atoms in a one-dimensional optical molasses obtained with linearly cross-polarized counterpropagating pump beams. The study is performed for a ${\mathit{J}}_{\mathit{g}}$=1/2\ensuremath{\rightarrow}${\mathit{J}}_{\mathit{e}}$=3/2 atomic transition in the limit where the Hamiltonian part of the atom-field coupling is predominant over the relaxation part. We analyze the stimulated Raman transitions occurring between different vibrational levels of the atoms in the periodic potential created by the light shifts, and we show a dramatic lengthening of the damping time of coherences between such levels due to the Lamb-Dicke effect. Very narrow Rayleigh resonances with a shape sensitive to the probe polarization appear for a probe frequency close to the pump frequency. We interpret these resonances in terms of scattering of the pump waves on density and magnetization gratings, and show that they provide important information about the dynamics and localization of atoms at the bottom of the potential wells. Such information should also be accessed by phase-conjugation experiments. Finally, indications on the treatment of other atomic transitions are given.

Theory of radiation forces and momenta for mobile atoms in light fields.

A theory for a bound system of charges interacting with electromagnetic fields is developed, with special emphasis on the radiation-pressure effects imposed by the fields on the gross motion of the charges. The theory is particularly simple and transparent for the case of two opposite charges of finite mass M in the electric-dipole approximation. This enables a rigorous description to be given for the quantum electrodynamics of the problem with the various interaction terms affecting the gross motion being easily identified. Here, too, it becomes clear that, even in the dipole approximation, the conventional interaction term should be supplemented by the so-called R\ontgen term. Besides ensuring the consistency of the theory for the overall (charges plus fields) system regarding conservation laws, the R\ontgen term has dynamical consequences. This is established by explicit calculations of the expectation values of the mechanical momentum 〈MR\ifmmode \dot{}\else \.{}\fi{}〉 and the radiation pressure force 〈MR\ifmmode\ddot\else\textasciidieresis\fi{}〉 on a two-level atom in the dipole approximation. Results of calculations are displayed for the case of a single light beam and for counterpropagating beams. The feasibility of experimentally observing the transverse force is explored. Generalizations of the well-known friction force arising in one-dimensional optical molasses are given and discussed.

Spectrum of resonance fluorescence and cooling dynamics in quantized one-dimensional molasses: Effects of laser configuration.

We study theoretically the spectrum of resonance fluorescence and laser-cooling dynamics corresponding to quantized atomic motion in one-dimensional optical molasses. We consider an atom with a ${\mathit{J}}_{\mathit{g}}$=1\ensuremath{\rightarrow}${\mathit{J}}_{\mathit{e}}$=2 transition interacting with two counterpropagating laser beams. The laser light is assumed to be linearly polarized with an angle \ensuremath{\theta} between the polarization vectors. We discuss the spectrum of resonance fluorescence, the spectroscopy of band structure in the optical potentials, and the population of the vibrational quantum levels as a function of the angle between the polarization vectors.

Laser cooling at low intensity in a strong magnetic field.

We have studied theoretically and experimentally the effect of a relatively strong magnetic field on sub-Doppler laser cooling in a one-dimensional optical molasses. We used the operator description of laser cooling with the Larmor precession frequency ${\mathrm{\ensuremath{\omega}}}_{\mathit{Z}}$ being much higher than the optical pumping rate. We found velocity-selective resonances (VSR) in the force at velocities ${\mathit{v}}_{\mathit{r}}$=n${\mathrm{\ensuremath{\omega}}}_{\mathit{Z}}$, with n=0,\ifmmode\pm\else\textpm\fi{}1,\ifmmode\pm\else\textpm\fi{}2 for both the scattering and redistribution force operators. These depend on the relative direction of the magnetic field and the polarization vectors of the light beams. Analytical results for the force on the atom are obtained in two cases that illustrate the effect of the VSR on the force. These formulas are compared with numerical calculations of the force. We also discovered a redistribution mechanism that relies on the gradient of the eigenstates of the light-shift operator, with eigenvalues that are independent of position so that a ``Sisyphus cooling'' picture does not apply. The theory is compared with many experimental results and excellent agreement is found. We believe that all essential features of laser cooling at low intensity are well described by this operator theory.

Laser cooling and deflection of a calcium atomic beam

The thermal velocity distribution of a calcium atomic beam was compressed into a narrow velocity distribution with selectable velocities. Subsequently these slow atoms were deflected by an angle of 30° by a one-dimensional optical molasses. In the deflected beam we obtained an estimated flux of several 1010 atoms/s at mean longitudinal velocities near 35 m/s and a velocity width of approximately 13 m/s. The transverse velocities of the deflected atoms were close to the one-dimensional Doppler limit. We have observed saturated absorption signals in the deflected laser-cooled beam. The reduced transit time broadening allowed us to resolve the recoil splitting in saturated absorption.

A frequency-stabilized LNA laser at $1.083~\mu$m : application to the manipulation of helium 4 atoms

We describe a single mode LNA ring laser, which emits 60 mW at 1.083 ~m. Thanks to a high frequency F-M- saturated absorption technique, this laser is directly locked to an atomic line in a ~He discharge cell. The residual frequency jitter is 130kHz. We then present two examples of laser manipulation of helium 4 atoms in the 2~Sj metastable state, using this laser a density increase of the atomic beam by a factor of 8, with one-dimensional optical molasses, and a selective deflection of the metastable helium beam using a laser beam with curved wavefronts.

Optical molasses and multilevel atoms: theory

A theoretical analysis is given for laser cooling of a two-level atom with magnetic sublevels in the presence of polarization gradients. The optical Bloch equations for the multilevel system are solved numerically for four combinations of polarizations in one-dimensional optical molasses. The light-pressure force on the atom as given by a simple two-level theory is recovered in the absence of polarization gradients, whereas a spatial variation of the polarization is found to lead to a strong cooling force for slow atoms. The increased cooling force is responsible for the recent observations of atoms cooled in optical molasses to temperatures an order of magnitude below the Doppler limit.