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Journal of Optics B Quantum and Semiclassical Optics

Strong evaporative cooling towards Bose Einstein condensation of a magnetically trapped caesium gas

A M Thomas, S. A. Hopkins, Simon L. Cornish, Christopher J. Foot

Published Apr 1, 2003• 12 citations
Publisher

Abstract

We have evaporatively cooled caesium atoms in a magnetic trap to temperatures as low as 8 nK and produced a final phase space density within a factor of four of that required for the onset of Bose–Einstein condensation. At the end of the forced radio-frequency evaporation, 1500 atoms in the F = 3, m F = −3 state remain in the magnetic trap. We observe a decrease in the one-dimensional evaporative cooling efficiency at very low temperatures as the trapped sample enters the collisionally thick (hydrodynamic) regime. To alleviate this problem we propose a modified trapping scheme where three-dimensional evaporation is possible. In addition, we report measurements of the two-body inelastic collision rates for caesium atoms as a function of magnetic field. We confirm the positions, with reduced uncertainties, of three previously identified resonances at magnetic fields of 108.87(6), 118.46(3) and 133.52(3) G.

DOI
10.1088/1464-4266/5/2/366

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Physical Review A•Sep 20, 2011•8 citations
We have evaporatively cooled caesium atoms in a magnetic trap to temperatures as low as 8 nK and produced a final phase space density within a factor of four of that required for the onset of Bose–Einstein condensation. At the end of the forced radio-frequency evaporation, 1500 atoms in the F = 3, m F = −3 state remain in the magnetic trap. We observe a decrease in the one-dimensional evaporative cooling efficiency at very low temperatures as the trapped sample enters the collisionally thick (hydrodynamic) regime. To alleviate this problem we propose a modified trapping scheme where three-dimensional evaporation is possible. In addition, we report measurements of the two-body inelastic collision rates for caesium atoms as a function of magnetic field. We confirm the positions, with reduced uncertainties, of three previously identified resonances at magnetic fields of 108.87(6), 118.46(3) and 133.52(3) G.
Ultra-cold Collisions and Evaporative Cooling of Caesium in a Magnetic Trap Angharad Mair Thomas, Jesus College, Oxford University DPhil Thesis, Hilary Term 2004 Caesium-133 atoms have been evaporatively cooled in a magnetic trap to temperatures as low as 8 nK producing a final phase-space density within a factor of 4 of that required for the onset of Bose-Einstein condensation. At the end of the forced radio-frequency evaporation, 1500 atoms in the F = 3,mF = −3 state remain in the magnetic trap. A decrease in the one-dimensional evaporative cooling efficiency at very low temperatures is observed as the trapped sample enters the collisionally thick (hydrodynamic) regime. Different evaporation trajectories are experimentally studied leading to a greater understanding of one-dimensional evaporation, inelastic collisions and the hydrodynamic regime. A theoretical simulation accurately reproduces the experimental data and indicates that the reduction in the evaporative cooling efficiency as the cloud enters the hydrodynamic regime is the main obstacle to the realization of Bose-Einstein condensation in the F = 3,mF = −3 state. In addition, we report measurements of the two-body inelastic collision rate coefficient for caesium atoms as a function of magnetic field and collision energy. The positions of three previously identified resonances are confirmed, with reduced uncertainties, at magnetic fields of 108.87(6), 118.46(3) and 133.52(3) Gauss. The resonance centred at 118.46Gauss is also investigated as a function of temperature, thus demonstrating the dependence of the inelastic Feshbach resonance on collision energy. The importance of including partial waves of a higher basis in theoretical
We study the efficiency of evaporative cooling of a trapped gas of caesium atoms in the hydrodynamic regime by the numerical solution of classical kinetic theory equations. The results of the numerical simulation are compared to our experimental observations of evaporative cooling of magnetically trapped 133 Cs atoms in the F = 3, m F = −3 state. The simulation accurately reproduces our experimental performance and indicates that the reduction in cooling efficiency as the gas enters the hydrodynamic regime is the main obstacle to the realization of Bose–Einstein condensation (BEC) in this state. The simulation is used to explore alternative routes to BEC.
 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.
The dynamics of evaporative cooling of magnetically trapped 87 Rb atoms is studied on the basis of the quantum kinetic theory of a Bose gas. The theoretical optimization of the cooling trajectory clarifies that the acceleration of evaporative cooling around the transition point of Bose-Einstein condensation is very effective against serious three-body recombination loss. The number of condensed atoms is expected to be largely enhanced by the optimization as compared with the typical value produced by the conventional evaporative cooling, where the frequency of the radio-frequency magnetic field is swept exponentially. Next, we precisely examine how the growth of a condensate depends on the experimental parameters of evaporative cooling in this inefficient exponential-sweep cooling. We find that, due to large nonlinear three-body loss, the number of condensed atoms finally becomes insensitive to the initial number of trapped atoms, the initial temperature, and the bias field of a magnetic trap. This result opens up the experimental possibility that the final number of condensed atoms can be well stabilized against the shot-to-shot fluctuations of experimental conditions in evaporative cooling.
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 (< 10-10 Torr) background vapour pressure. The dependence of the cold collision loss coefficient β on the trapping intensity was measured to permit identification of the different cold collision processes. The largest loss rates observed were those due to hyperfine structure-changing collisions, with a coefficient β = (2±1) x 10-10cm3s-1. 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 report on a highly efficient evaporative cooling optimized experimentally. We successfully created sodium Bose-Einstein condensates with 6.4\ifmmode\times\else\texttimes\fi{}107{}^{7}7 atoms starting from 6.6\ifmmode\times\else\texttimes\fi{}109{}^{9}9 thermal atoms trapped in a magnetic trap by employing a fast linear sweep of radio frequency at the final stage of evaporative cooling so as to overcome the serious three-body losses. The experimental results such as the cooling trajectory and the condensate growth quantitatively agree with the numerical simulations of evaporative cooling on the basis of the kinetic theory of a Bose gas carefully taking into account our specific experimental conditions. We further discuss theoretically a possibility of producing large condensates, more than 108{}^{8}8 sodium atoms, by simply increasing the number of initial thermal trapped atoms and the corresponding optimization of evaporative cooling.