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Ultra-cold Collisions and Evaporative Cooling of Caesium in a Magnetic Trap

Angharad Mair Thomas

Published Jan 1, 2004• 4 citations
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Abstract

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

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 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.

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In this work a gas of ultra-cold chromium atoms in a magnetic trap has been prepared and its elastic and inelastic scattering properties have been investigated with regard to Bose-Einstein condensation. Bose-Einstein condensation of dilute atomic gases is achieved using different cooling and trapping techniques. Deviating from the standard way we were able to devise a continuous loading mechanism for a magnetic trap as a result of the spectroscopic properties and the large magnetic dipole moment of chromium. It not only allows us to trap more atoms but also facilitates the subsequent preparation steps. After loading, the magnetic trap is compressed to increase the atomic density. In doing so we also increases the temperature of the atomic cloud. Doppler cooling of the atoms in the compressed trap reduces the temperature and increases the density. Subsequent evaporative cooling further reduces the temperature. The efficiency of the cooling mechanism is determined by the elastic and inelastic scattering properties of atomic species. Ultra-cold collisions between ground state atoms are dominated by s-wave collisions. They are characterized by a single parameter, the scattering length a. We were able to determine the temperature dependence of the elastic collision rate for the two bosonic isotopes 52Cr and 50Cr in a relaxation experiment. Comparing our results with the effective range theory allowed us not only to extract the magnitude of the scattering length, but also its sign. The sign of the scattering length is important since only condensates with a positive scattering length are stable. Our efforts to achieve Bose-Einstein condensation in chromium by evaporative cooling in a magnetic trap resulted in a maximum phase space density of 0.04. Further cooling reduced the phase space density due to increased loss of atoms from dipolar relaxation. We were able to obtain preliminary results on the magnetic field dependence of dipolar relaxation. Our experimental data is in excellent agreement with theory. These experiments confirm the theoretical prediction that the dipolar relaxation rate is independent from the details of the interaction potential but rather scales with the magnetic offset field and the magnetic dipole moment of the atoms. The findings of this work mark an important step towards the realization of a Bose-Einstein condensate with chromium atoms. Especially the knowledge of the elastic and inelastic scattering properties allow now to devise a successful strategy.

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Collisional interaction between metastable neon atoms

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In this thesis, the study of cold gases of neon atoms in different metastable states is described. It contains measurements of the collisional parameters for both the 3s[3/2]2 and the 3s'[1/2]0 metastable state and the dependence of the inelastic loss on external fields. Furthermore, the investigation of frequency dependent laser-induced collisions, and the possibility to excite photoassociation resonances is presented. Based on previous measurements we have selected 22Ne for evaporative cooling. Although, we can experimentally achieve an increase in phase-space density with evaporative cooling, the relatively high inelastic collision parameters prevent the realization of a Bose-Einstein condensate in neon. For the measurements described here, neon atoms have been confined in a magneto-optical trap, in a magnetostatic trap, or in an optical dipole trap, respectively. By laser cooling inside the magnetic trap, atomic samples with more than 95 percent occupation of the magnetic substate m=+2 could be prepared. They have a typical temperature of 0.5 mK, central densities up to 1e11 cm^-3, and a central phase-space density of up to 2.2e-7. After loading the optical dipole trap from the magnetic trap, 2.5e6 atoms with typical temperatures of 0.1 mK, and central densities up to 5e10 cm^-3 were trapped. By evaporative cooling of the atoms in the magnetic trap we could increase the phase-space density by a factor of 200 to 5e-5. Also simulations of optimized evaporation for our experimental parameters show clearly that we are limited to a phase-space density on the order of 1e-5. From these simulations it became clear that a 5-fold increase in the good-to-bad ratio for evaporative cooling suffices to reach the quantum degenerate regime. Investigating the frequency dependence of laser-induced collisions did not reveal an experimental signature for the excitation of photoassociation resonances. For the 3D3 line a frequency dependence of laser enhanced Penning ionization was observed, which is interesting in itself. The absence of the collisional enhancement effect by laser light for the transition to the 3D2 line is intriguing and for an explanation calculations are required. Measurement of the two-body loss coefficient as function of the magnetic field showed a field dependence of the inelastic loss. These losses increase towards both small and large offset fields. In the magnetic trap, we are limited to offset fields < 50 G. In this range of fields, the two-body losses are too large to achieve a Bose-Einstein condensate of magnetically trapped metastable neon. The implementation of an optical dipole trap allowed us to trap the 3P0 metastable state. From the trap loss measurements we determined the two-body loss coefficient of the 3P0 metastable state for both bosonic isotopes 20Ne and 22Ne. For 20Ne we obtained s=6(+5,-4)e-10 cm^3/s and for 22Ne s=11(+7,-6)e-10 cm^3/s. These large two-body losses make it extremely unlikely to reach degeneracy with this metastable state. Nevertheless it is important that the 3P0 metastable state can be trapped to investigate other interesting physical effects. For example, it is essential to apply the STIRAP technique for trapped atoms and to realize the proposed coherent control of collisions. There is also a large interest in a precise determination of the lifetime of this metastable state, which is of importance for the verification of QED. We can also trap neon atoms in their energetically lowest magnetic substate 3P2(m=-2) with the perspective of reducing inelastic collisions in the energetically lowest state.

•Jul 29, 2008•1 citation
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 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.
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 (< 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.
 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.
In this work a gas of ultra-cold chromium atoms in a magnetic trap has been prepared and its elastic and inelastic scattering properties have been investigated with regard to Bose-Einstein condensation. Bose-Einstein condensation of dilute atomic gases is achieved using different cooling and trapping techniques. Deviating from the standard way we were able to devise a continuous loading mechanism for a magnetic trap as a result of the spectroscopic properties and the large magnetic dipole moment of chromium. It not only allows us to trap more atoms but also facilitates the subsequent preparation steps. After loading, the magnetic trap is compressed to increase the atomic density. In doing so we also increases the temperature of the atomic cloud. Doppler cooling of the atoms in the compressed trap reduces the temperature and increases the density. Subsequent evaporative cooling further reduces the temperature. The efficiency of the cooling mechanism is determined by the elastic and inelastic scattering properties of atomic species. Ultra-cold collisions between ground state atoms are dominated by s-wave collisions. They are characterized by a single parameter, the scattering length a. We were able to determine the temperature dependence of the elastic collision rate for the two bosonic isotopes 52Cr and 50Cr in a relaxation experiment. Comparing our results with the effective range theory allowed us not only to extract the magnitude of the scattering length, but also its sign. The sign of the scattering length is important since only condensates with a positive scattering length are stable. Our efforts to achieve Bose-Einstein condensation in chromium by evaporative cooling in a magnetic trap resulted in a maximum phase space density of 0.04. Further cooling reduced the phase space density due to increased loss of atoms from dipolar relaxation. We were able to obtain preliminary results on the magnetic field dependence of dipolar relaxation. Our experimental data is in excellent agreement with theory. These experiments confirm the theoretical prediction that the dipolar relaxation rate is independent from the details of the interaction potential but rather scales with the magnetic offset field and the magnetic dipole moment of the atoms. The findings of this work mark an important step towards the realization of a Bose-Einstein condensate with chromium atoms. Especially the knowledge of the elastic and inelastic scattering properties allow now to devise a successful strategy.
In this thesis, the study of cold gases of neon atoms in different metastable states is described. It contains measurements of the collisional parameters for both the 3s[3/2]2 and the 3s'[1/2]0 metastable state and the dependence of the inelastic loss on external fields. Furthermore, the investigation of frequency dependent laser-induced collisions, and the possibility to excite photoassociation resonances is presented. Based on previous measurements we have selected 22Ne for evaporative cooling. Although, we can experimentally achieve an increase in phase-space density with evaporative cooling, the relatively high inelastic collision parameters prevent the realization of a Bose-Einstein condensate in neon. For the measurements described here, neon atoms have been confined in a magneto-optical trap, in a magnetostatic trap, or in an optical dipole trap, respectively. By laser cooling inside the magnetic trap, atomic samples with more than 95 percent occupation of the magnetic substate m=+2 could be prepared. They have a typical temperature of 0.5 mK, central densities up to 1e11 cm^-3, and a central phase-space density of up to 2.2e-7. After loading the optical dipole trap from the magnetic trap, 2.5e6 atoms with typical temperatures of 0.1 mK, and central densities up to 5e10 cm^-3 were trapped. By evaporative cooling of the atoms in the magnetic trap we could increase the phase-space density by a factor of 200 to 5e-5. Also simulations of optimized evaporation for our experimental parameters show clearly that we are limited to a phase-space density on the order of 1e-5. From these simulations it became clear that a 5-fold increase in the good-to-bad ratio for evaporative cooling suffices to reach the quantum degenerate regime. Investigating the frequency dependence of laser-induced collisions did not reveal an experimental signature for the excitation of photoassociation resonances. For the 3D3 line a frequency dependence of laser enhanced Penning ionization was observed, which is interesting in itself. The absence of the collisional enhancement effect by laser light for the transition to the 3D2 line is intriguing and for an explanation calculations are required. Measurement of the two-body loss coefficient as function of the magnetic field showed a field dependence of the inelastic loss. These losses increase towards both small and large offset fields. In the magnetic trap, we are limited to offset fields < 50 G. In this range of fields, the two-body losses are too large to achieve a Bose-Einstein condensate of magnetically trapped metastable neon. The implementation of an optical dipole trap allowed us to trap the 3P0 metastable state. From the trap loss measurements we determined the two-body loss coefficient of the 3P0 metastable state for both bosonic isotopes 20Ne and 22Ne. For 20Ne we obtained s=6(+5,-4)e-10 cm^3/s and for 22Ne s=11(+7,-6)e-10 cm^3/s. These large two-body losses make it extremely unlikely to reach degeneracy with this metastable state. Nevertheless it is important that the 3P0 metastable state can be trapped to investigate other interesting physical effects. For example, it is essential to apply the STIRAP technique for trapped atoms and to realize the proposed coherent control of collisions. There is also a large interest in a precise determination of the lifetime of this metastable state, which is of importance for the verification of QED. We can also trap neon atoms in their energetically lowest magnetic substate 3P2(m=-2) with the perspective of reducing inelastic collisions in the energetically lowest state.