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Bulletin of the American Physical Society

Prospects for bose condensation in a dilute vapor of heavy alkali atoms

Eric Cornell

Published May 1, 1993• 0 citations
OpenAlex

Abstract

Evaporative cooling is a proven strategy for reaching new regimes of temperature and density in magnetically trapped vapors. The technique works, however, only if the intratrap collision rate dominates the rates of undesirable processes such as spin-flip inelastic collisions and collisions with untrapped background vapor. Our measurement of the elastic scattering cross section in Cs at temperatures down to 30 {mu}K, in combination with recent theoretical calculations of the inelastic scattering rate, shows that inelastic spin-flip collisions do not pose a significant obstacle to attaining Bose condensation. We measure the elastic scattering cross section by observing the rate of thermal equilibration in a trapped sample which is initially far from thermal equilibrium. I will discuss this work and other developments relevant to attaining Bose condensation.

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Evaporative cooling is a proven strategy for reaching new regimes of temperature and density in magnetically trapped vapors. The technique works, however, only if the intratrap collision rate dominates the rates of undesirable processes such as spin-flip inelastic collisions and collisions with untrapped background vapor. Our measurement of the elastic scattering cross section in Cs at temperatures down to 30 {mu}K, in combination with recent theoretical calculations of the inelastic scattering rate, shows that inelastic spin-flip collisions do not pose a significant obstacle to attaining Bose condensation. We measure the elastic scattering cross section by observing the rate of thermal equilibration in a trapped sample which is initially far from thermal equilibrium. I will discuss this work and other developments relevant to attaining Bose condensation.
We have measured the elastic collision cross section for spin polarized atomic cesium. Neutral cesium atoms are optically cooled, then loaded into a dc magnetic trap. We infer the scattering rate from the rate at which anisotropies in the initial energy distribution are observed to relax. The cross section for F=3, mF{\mathit{m}}_{\mathit{F}}mF​=-3 on F=3, mF{\mathit{m}}_{\mathit{F}}mF​=-3 is 1.5(4)\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}12}$ cm2{\mathrm{cm}}^{2}cm2, and is independent of temperature from 30 to 250 \ensuremath{\mu}K. This determination clarifies the technical requirements for attaining Bose-Einstein condensation in a magnetically trapped Cs vapor. We also study heating due to glancing collisions with 300 K background Cs atoms.
We study conditions necessary for the observation of Bose-Einstein condensation in a magnetically trapped sample of atomic Cs gas. These conditions are associated with the value of the elastic scattering length, the rate of elastic scattering events, and the lifetime for decay of the density due to both magnetic dipole relaxation in two-body collisions, as well as recombination to Cs2{\mathrm{Cs}}_{2}Cs2​ in three-body collisions. We find that, on the basis of these conditions, the prospects for observing Bose-Einstein condensation are favorable for a gas of ground-state Cs atoms in the highest state of the lowest hyperfine manifold. In all calculated elastic and inelastic two-body rates we find a pronounced resonance structure, which can be understood in terms of the interplay between the singlet-triplet interaction and the hyperfine, Zeeman, and magnetic dipole interactions. The experimental observation of these resonances may help to eliminate present uncertainties about interaction potentials.
Using magnetically trapped atomic hydrogen as an example, we investigate the prospects of achieving Bose–Einstein condensation in a dilute Bose gas. We show that, if the gas is quenched sufficiently far into the critical region of the phase transition, the typical time scale for the nucleation of the condensate density is short and of O(ħ/k B T c ). As a result we find that thermalizing elastic collisions act as a bottleneck for the formation of the condensate. In the case of doubly polarized atomic hydrogen these occur much more frequently than the inelastic collisions leading to decay and we are led to the conclusion that Bose–Einstein condensation can indeed be achieved within the lifetime of the gas. Introduction In the last few years it has been clearly demonstrated that not only charged ions but also neutral atoms can be conveniently trapped and cooled by means of electro-magnetic fields. Although the physics of the various ingenious scenarios developed to accomplish this is already interesting in itself [1], the opportunities offered by an atomic gas sample at very low temperatures are exciting in their own right. Examples in this respect are the performance of high-precision spectroscopy, the search for a violation of CP invariance by measuring the electric dipole moment of atomic cesium [2], the construction of an improved time standard based on an atomic fountain [3] and the achievement of Bose–Einstein condensation in a weakly interacting gas.
The calculated upper limit ${\mathcal{K}}_{i}^{\mathrm{pol}}<~{10}^{\ensuremath{-}14}{\mathrm{cm}}^{3}/\mathrm{s}$ of the rate constant for suppressed ionization in a gas of metastable Ne(3P2)\mathrm{Ne}{(}^{3}{\mathrm{P}}_{2})Ne(3P2​) atoms in the fully aligned ∣J=2,mJ=2〉|{J=2,m}_{J}=2〉∣J=2,mJ​=2〉 state is used as input to investigate the prospects for achieving Bose-Einstein condensation (BEC). The heating rate of the trap population by secondary collisions of the hot products of the process of ionization---i.e., ground-state atoms, ions, and dimer-ions---with cold trapped metastable atoms is discussed in terms of a semiclassical model. An important step lies in limiting the depth of the magnetic trap to a value of a few millikelvin, to limit the range of small-angle scattering that contributes to heating. Also, a tight radial confinement reduces the probability for secondary collisions. At a trap depth of 10 mK, a radial dimension of $3\ensuremath{\mu}\mathrm{m},$ and a density of $2\ifmmode\times\else\texttimes\fi{}{10}^{13}{\mathrm{cm}}^{\ensuremath{-}3}$ the heating rate is $1.4\ensuremath{\mu}\mathrm{K}/\mathrm{s},$ which should be compared to the transition temperature to BEC of $0.6\ensuremath{\mu}\mathrm{K}.$ The collisional heating is dominated by ion---metastable-atom collisions, due to their long-range charge-induced dipole interaction. Keeping the evaporative cooling switched on at T=TC{T=T}_{C}T=TC​ reduces the heating a hundredfold. Using a bright beam of laser cooled neon atoms, an initial population of > 1010>~{10}^{10}> 1010 atoms can be loaded into a magneto-optical trap in one second. Tight magnetic traps are easy to achieve for metastable neon atoms, due to their magnetic moment of $3{\ensuremath{\mu}}_{B}.$ We conclude that achieving BEC is feasible for metastable neon. This also holds for triplet metastable helium, once the loading rate of traps has been improved. Finally, the semiclassical model used for calculating the heating rate is applicable to a wide range of inelastic collisions in trapped alkali gases and/or collisions with background gas.
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.