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Unformatted text preview: Journal of the Korean Physical Society, Vol. 46, No. 6, June 2005, pp. 1336 ∼ 1341 Energy per Particle in BEC for 87 Rb and 7 Li Dooyoung Kim , Guanghao Jin and JinHee Yoon * Department of Physics, Inha University, Incheon 402751 (Received 4 January 2005, in final form 14 April 2005) We test the validity of the equivalent linear twobody(ELTB) equation by calculating the energies per particle and the wave functions for 87 Rb gas and for 7 Li gas. For this, we use the quantum mechanical variational method for the BoseEinstein condensate energy. Our result for 87 Rb gas agrees with a numerical calculation based on the GrossPitaevskii equation, with a relative error of 12 % over a wide range of N from 100 to 10000, and the result for a 7 Li gas shows a behavior consistent with that observed in experiments. Therefore, we can conclude that the ELTB equation describes quite well the behavior of an Nboson system in its BEC state. PACS numbers: 31.15.Ja, 31.15.Pf, 31.15.Qg Keywords: BoseEinstein condensation I. INTRODUCTION The initial success in the laboratory of BoseEinstein condensation (BEC) with 87 Rb atoms [1] has been fol lowed by many serial successes with other alkalimetal atoms [2–6]. BEC was theoretically predicted by Bose and Einstein in the mid 1920’s [7–9], and since then superfluidity in liquid helium has been studied inten sively as a resulting property of BEC [10]. However, the relatively strong interaction between He atoms and the relatively short lifetime (10 9 sec) make its study difficult. Alkalimetal atoms have relatively weak inter actions compared to He atoms, so they may be good candidates for detailed investigations of BEC. When the temperature of the alkalimetal gas is low ered to the order of nanokelvin, the de Broglie wave length of atoms gets larger than the distance between them and the wave function of each atom overlaps with those of other atoms. Then, the atoms dominantly pop ulate the ground state, and a quantumstatistical phase transition to BEC occurs. Besides the ultralow temper ature, the total number of atoms must reach a certain value for a transition. Due to the difficulty in trapping the gas in a confined space, success in obtaining BEC had to wait until 1995. Following the success of the JILA group at Colorado University with a supercold 87 Rb di lute gas [1], groups at Rice University and MIT have succeeded in making BECs with lowtemperature dilute 7 Li gas [2] and Na gas [5], respectively. Also, BEC was observed in hydrogen gas in 2001 [6]. Theoretically, a purely attractive interaction is predicted to support no bound state, and an attractive system such as 7 Li gas cannot transition to BEC [11]. However, a spintriplet * Email: jinyoon@inha.ac.kr interaction is known to be able to support a bound state [12,13], so finally BEC was observed in 7 Li gas in the laboratory in 1995 [2]....
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