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arXiv:cond-mat/9402041 · Physical Review A

Atomic Bose gas with a negative scattering length

Henk T. C. Stoof

Published May 1, 1994• 128 citations
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Abstract

We derive the equation of state of a dilute atomic Bose gas with an interatomic interaction that has a negative scattering length and argue that two continuous phase transitions, occurring in the gas due to quantum degeneracy effects, are preempted by a first-order gas-liquid or gas-solid transition, depending on the details of the interaction potential. We also discuss the consequences of this result for future experiments with magnetically trapped spin-polarized atomic gases such as lithium and cesium.

DOI
10.1103/physreva.49.3824

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We derive the equation of state of a dilute atomic Bose gas with an interatomic interaction that has a negative scattering length and argue that two continuous phase transitions, occurring in the gas due to quantum degeneracy effects, are preempted by a first-order gas-liquid or gas-solid transition, depending on the details of the interaction potential. We also discuss the consequences of this result for future experiments with magnetically trapped spin-polarized atomic gases such as lithium and cesium.
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We study necessary conditions for the observation of Bose–Einstein condensation in a magnetically trapped sample of atomic cesium gas. These constraints are due to interatomic collisions in the sample. We show that 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. An interesting aspect of the calculations is that the scattering length for this f = 3, m f = −3 hyperfine state shows pronounced resonance structures as a function of applied magnetic field leading to variations of two orders of magnitude. Most importantly, the scattering length can change sign near the resonances. This suggests a controllable means to change the behavior of the Bose condensate because for negative values a condensate is unstable and other (quantum-)collective effects might be observed. The origin of the resonances is understood from the bound singlet and triplet rovibrational Cs 2 states which are perturbed due to the hyperfine and Zeeman interactions. It is a long standing goal to achieve quantum-collective effects in atomic Fermi- or Bose gases. The prominent reasons are that for a relatively simple system with low density, a microscopic theoretical treatment of the phase transition is still feasible, and to have an experimental testing ground for more complicated quantum-coherent effects such as superfluidity in 4 He and superconductivity in metals. Here, we focus on atomic species which behave as (composite) bosons.
We study properties of the ground state of a bosonic gas of atoms in a tight trap. The atoms interact via model molecular potentials that may have either positive or negative scattering lengths. We discuss the possibility of Bose-Einstein condensation in such a system. We show that when the size of the trap becomes comparable to the correlation length of the condensate, stable Bose-Einstein condensation might occur independent of the sign of the scattering length. \textcopyright{} 1996 The American Physical Society.
Evidence for Bose-Einstein condensation of a gas of spin-polarized 7{}^{7}7Li atoms is reported. Atoms confined to a permanent-magnet trap are laser cooled to 200 \ensuremath{\mu}K and are then evaporatively cooled to lower temperatures. Phase-space densities consistent with quantum degeneracy are measured for temperatures in the range of 100 to 400 nK. At these high phase-space densities, diffraction of a probe laser beam is observed. Modeling shows that this diffraction is a sensitive indicator of the presence of a spatially localized condensate. Although measurements of the number of condensate atoms have not been performed, the measured phase-space densities are consistent with a majority of the atoms being in the condensate, for total trap numbers as high as $2\ifmmode\times\else\texttimes\fi{}{10}^{5}$ atoms. For 7{}^{7}7Li, the spin-triplet sss-wave scattering length is known to be negative, corresponding to an attractive interatomic interaction. Previously, Bose-Einstein condensation was predicted not to occur in such a system.
Dilute Fermi systems with large sss-wave scattering length as{a}_{s}as​ exhibit universal properties if the interparticle spacing r0{r}_{0}r0​ greatly exceeds the range of the underlying two-body interaction potential. In this regime, r0{r}_{0}r0​ is the only relevant length scale and observables such as the energy per particle depend only on r0{r}_{0}r0​ (or, equivalently, the energy EFG{E}_{\mathrm{FG}}EFG​ of the free Fermi gas). This paper investigates Bose and Fermi systems with nonvanishing angular momentum lll using the lowest order constrained variational method. We focus on the regime where the generalized scattering length becomes large and determine the relevant length scales. For Bose gases with large generalized scattering lengths, we obtain simple expressions for the energy per particle in terms of an lll-dependent length scale ${\ensuremath{\xi}}_{l}$, which depends on the range of the underlying two-body potential and the average interparticle spacing. We discuss possible implications for dilute two-component Fermi systems with finite lll. Furthermore, we determine the equation of state of liquid and gaseous bosonic helium.