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Journal of the Optical Society of America B

Radiation force in the magneto-optical trap

Andrew M. Steane, M. Chowdhury, Christopher J. Foot

Published Dec 1, 1992• 194 citations
Publisher

Abstract

An overview of the theory of the magneto-optical trap is presented, along with measurements of the effect of an imbalance in the intensities of the trapping beams. This investigation tests the theory of the spring constant of the trap and confirms that the confining force at the center of the trap results from an induced orientation of the atomic ground state. The experimental results give the magnitude of this force, which has not yet been calculated accurately. We calculate the radiation field in the three-dimensional molasses, finding that the relative time phase of the orthogonal standing waves is significant, and we give some insight into the phenomenon of interference fringes when the beams are misaligned. We also discuss the limitation of the trapped atomic density resulting from photon scattering within the cloud, predicting that densities above 1013 atoms/cm3 could be achieved in a trap operating at low saturation of the atomic transition. Finally, we briefly consider collisional loss at low densities, finding an especially large contribution from resonant dipole–dipole scattering.

DOI
10.1364/josab.9.002142

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An overview of the theory of the magneto-optical trap is presented, along with measurements of the effect of an imbalance in the intensities of the trapping beams. This investigation tests the theory of the spring constant of the trap and confirms that the confining force at the center of the trap results from an induced orientation of the atomic ground state. The experimental results give the magnitude of this force, which has not yet been calculated accurately. We calculate the radiation field in the three-dimensional molasses, finding that the relative time phase of the orthogonal standing waves is significant, and we give some insight into the phenomenon of interference fringes when the beams are misaligned. We also discuss the limitation of the trapped atomic density resulting from photon scattering within the cloud, predicting that densities above 1013 atoms/cm3 could be achieved in a trap operating at low saturation of the atomic transition. Finally, we briefly consider collisional loss at low densities, finding an especially large contribution from resonant dipole–dipole scattering.
In this thesis, the effect of radiation trapping on the photon statistics of the light scattered from optical molasses is experimentally investigated.It is demonstrated that the intensity correlation function is sensitive to the presence of radiation trapping at an on-resonance optical depth, OD, as low as 0.1.It is also shown that it is possible by introducing a mild anisotropy in the trapped cloud to change the number density of a trapped sample of laser-cooled atoms in a dilute magnetooptical trap by over an order of magnitude, from 1.9 × 10 9 /cm 3 to 1.6 × 10 8 /cm 3 , while keeping the temperature constant.
A cloud of ultracold atoms confined in a magneto-optical trap (MOT) has a temperature greater than that of a low-density vapour in the same light field. It has been observed (Drewsen M. et al., Appl. Phys. B , 59 (1994) 283) that this temperature excess is proportional to the cube root of the total number of trapped atoms ( N 1/3 ). We present an explanation for this effect in terms of the scattering which arises when photons spontaneously emitted by atoms have an appreciable probability of being reabsorbed within the cloud. This hypothesis has been tested by time-of-flight measurements of the temperature of clouds of atoms released from a MOT into 1-dimensional and 3-dimensional optical molasses in the σ + -σ - and lin ⊥ lin configuration.
Using three orthogonal pairs of counterpropagating red-detuned lasers and a magnetic field gradient, we have constructed a trap of 85 Rb atoms at temperatures reduced to the order of 100 microKelvins and densities of 10 9 atoms/cm 3 .When the atoms interact with the light, they are absorbing and spontaneously emitting photons.The emitted photons from atoms can be absorbed by neighboring atoms.This phenomenon, called radiation trapping, limits the density and temperature of the trap and also destroys the atomic coherence.We can noninvasively measure the effects of radiation trapping by measuring the intensity correlation function of the light radiated from the trap.We have found that theoretically, the effects of radiation trapping can be detected in dilute atomic samples with an on-resonance optical depth as low as 0.1, more than an order of magnitude less than seen before.Experimental progress is reported.
 A detailed experimental and theoretical investigation of a magneto-optical trap for caesium atoms is presented. Particular emphasis has been placed on achieving high spatial number densities and low temperatures. Optimizing both of these together enables efficient evaporative cooling from a conservative trap, a procedure which has recently led to the first observations of Bose-Einstein condensation in a dilute atomic vapour. The behaviour of a magneto-optical trap is nominally determined by four independent parameters: the detuning and intensity of the light field, the magnetic field gradient and the number of trapped atoms. A model is presented which incorporates previous treatments into a single description of the trap that encompasses a wide range of its behaviour. This model was tested quantitatively by measuring the temperature of the cloud and its spatial distribution as a function of the four parameters. The maximum density was found to be limited both by the reabsorption of photons scattered within the cloud and by a reduction of the confining force at small light shifts. The nonlinear variation with position of the restoring force was found to be significant in limiting the number of atoms confined to a high density. A maximum density in phase space (defined as the number of atoms in a box with sides of dimension one thermal de Broglie wavelength) of (1.5 ± 0.5) x 10-5 was observed, with a spatial density of 1.5 x 1011 atoms per cm3. Cold collision losses from a caesium magneto-optical trap have been studied with the purpose of assessing their influence on spatial densities. In contrast to previous measurements of similar quantities, these measurements did not require the use of an ultra-low ( A study is presented of a modified magneto-optical trap in which a fraction of the population is shelved into a hyperfine level that does not interact with the trapping light. In this so-called dark magneto-optical trap, improved densities of nearly 1012cm-3 have been previously reported for sodium. The application of the technique to caesium is not straightforward due to the larger excited state hyperfine splittings. A simple theory for caesium is presented and its main predictions verified by measurements of density, number and temperature. A density of nearly 1012cm,-3 was indeed obtained but at a temperature substantially higher than in the conventional magneto-optical trap.
We discuss our recent experimental demonstrations of three novel atom traps which are all based on the optical dipole force in far-detuned laser light. In the gravito-optical surface trap (GOST), Cs atoms are trapped and cooled by means of an evanescent-wave mirror very closely above a dielectric surface. This trap allows for optical cooling at very high densities and provides good starting conditions for evaporative cooling to quantum degeneracy and the realization of a 2D quantum gas. The conical atom trap (CAT) uses a hollow blue-detuned laser beam in combination with gravity to trap atoms in a dark spatial region. This trap is experimentally simple and provides high loading efficiency, tight confinement, efficient sub-Doppler cooling, and strong suppression of collisional losses. The standing-wave red-detuned (STAR) trap allows one to confine atoms in a shallow optical potential at a very low photon scattering rate, and is thus an interesting tool for studies of the atomic ground-state dynamics in external electro-magnetic fields. We have studied atomic spin polarization in this trap.
This thesis describes theoretical and experimental work concerning radiation forces on atoms, with particular reference to rubidium atoms confined in a magneto-optical trap. After a short history of the field of laser cooling, a review of the semiclassical theory of mechanical interactions between two-level atoms and electromagnetic radiation is given. Different formulations of the semiclassical theory are discussed, including a new formulation in terms of momentum transfer amongst the plane wave modes of the electromagnetic field. Two important applications of light forces on atoms, namely 'optical molasses' and the 'magneto-optical trap', are then described with emphasis on experimental parameters. Three sub-Doppler cooling mechanisms, 'sisyphus cooling', 'motion-induced orientation cooling' and the 'magnetically-assisted sisyphus effect', are described and their role in optical molasses and the magneto-optical trap is discussed. A new study of the polarisation gradients which occur in 3-D monochromatic light fields is presented and quantifies their relative presence in different light field configurations. Polarisation gradient parameters are developed and shown to be directly related to the relativistic spin tensor of the light field. Implications of this polarisation gradient study for laser cooling work are discussed. The design, construction from scratch, operation and testing of a magneto-optical trap for rubidium are described, including novel designs for two vacuum cells. Preliminary experiments to characterise the trap are described and results are presented; they primarily concern the number and distribution of atoms in the trap. Finally. the theory of time domain spectroscopy is reviewed. The construction and testing of a pulsed dye laser for study of coherent transients in samples of laser-cooled atoms and a proposed experiment to measure the temperature of cold atoms using coherent transients are described. Factors expected to influence the shape of coherent transients in cold atoms are discussed.