Physics Letters A 373 (2009) 258–261 Contents lists available at ScienceDirect Physics Letters A www.elsevier.com/locate/pla 85 Rb Bose–Einstein condensate with tunable interaction: A quantum many body approach Tapan Kumar Das a , Anasuya Kundu a , Sylvio Canuto b , Barnali Chakrabarti c,∗ a Department of Physics, University of Calcutta, 92 A.P.C. Road, Calcutta-700009, India b Instituto de Física, Universidade de São Paulo, CP 66318, 05315-970, São Paulo, SP, Brazil c Department of Physics, Lady Brabourne College, P1/2 Suhrawardy Avenue, Calcutta-700017, India article info abstract Article history: Received 9 September 2008 Accepted 15 October 2008 Available online 21 November 2008 Communicated by V.M. Agranovich PACS: 03.75.Hh 31.15.Ja 03.65.Ge 03.75.Nt Keywords: Bose–Einstein condensation Potential harmonics Hyperspherical harmonics Two-body correlation We present a quantum many body approach with van der Waal type of interaction to achieve 85 Rb Bose–Einstein condensate with tunable interaction which has been produced by magnetic field induced Feshbach resonance in the JILA experiment.  2008 Elsevier B.V. All rights reserved. In the recent condensate experiments [1–3], one can tune the s-wave scattering length to essentially any value, including sign, simply by using Feshbach resonances. 85 Rb is chosen as the best candidate where one can effectively control the atom–atom inter- action using magnetic field to induce Feshbach resonance. After forming a stable condensate with positive scattering length (repul- sive interaction), one can tune the scattering length to a selected negative value, which causes instability and collapse of the con- densate. Thus the ability to tune the atomic interaction allows one to study the onset of instability in a controlled way. In the JILA experiment [2,3] this controlled collapse has been obtained by sudden reversal of sign of the scattering length near the reso- nance. In the mean field approximation the interatomic interaction is characterized by a contact interaction of strength proportional to the s-wave scattering length, which gives rise to the popular Gross–Pitaevskii (GP) equation. In the GP equation, the effective condensate potential is proportional to a s , it is repulsive or attrac- tive accordingly as a s is positive or negative, respectively. The gross * Corresponding author. E-mail address: chakb@rediffmail.com (B. Chakrabarti). general properties of the condensate are well understood in terms of the GP equation [4]. In spite of this success, Geltman [5] and Gao [6] pointed out that the scattering length description does not represent the true atom–atom interaction. Lack of a strong repul- sive core of the two-body contact interaction for the GP equation gives rise to an attractive essential singularity at the origin, for negative a s . This unphysical essential singularity is usually ignored and the motion of the attractive condensate with the number of atoms ( A) less than a critical number ( A cr ) is obtained by solv- ing the GP equation in the metastable region only. A complete description calls for a full many-body formalism, as the use of a realistic two-body interaction (with a strong short-range repulsion) removes the above mentioned singularity. In addition importance of two-body correlation also necessitates going beyond the mean field theory. We employ a many-body theory with a realistic two-body in- teraction, which can give rise to the correct effective condensate potential for the collective motion, both for positive and negative values of a s . The realistic interatomic interaction has a long at- tractive van der Waals type tail with a strongly repulsive core at shorter separation [7]. The repulsive part is usually represented by a hard core of radius r c . The solution of the two-body equation shows [7] that the value of a s changes from negative to positive – 0375-9601/$ – see front matter  2008 Elsevier B.V. All rights reserved. doi:10.1016/j.physleta.2008.10.092