Bose-Einstein Condensation of Lithium: Observation of Limited Condensate Number

Abstract

Bose-Einstein condensation of7 Li has been studied in a magnetically trapped gas. Because of the effectively attractive interactions between 7 Li atoms, many-body quantum theory predicts that the occupation number of the condensate is limited to about 1400 atoms. We observe the condensate number to be limited to a maximum value between 650 and 1300 atoms. The measurements were made using a versatile phase-contrast imaging technique. [S0031-9007(97) 7 Li atoms have a negative s-wave scattering length a, indicating that for a sufficiently cold and dilute gas the interatomic interactions are effectively attractive. Attractive interactions are thought to prevent BEC from occurring at all in a spatially homogeneous (i.e., untrapped) gas [3,4], and as recently as 1994, these interactions were believed to preclude BEC in a trap as well. Current theories predict that BEC can occur in a trap such as ours, but with no more than about 1400 condensate atoms [5][6][7][8][9][10][11]. Verification of this prediction would provide a sensitive test of many-body quantum theory. In our previous work [1], the condensate could not be directly observed, and the number of condensate atoms suggested by the measurements was overestimated. In this Letter we report quantitative measurements of the condensate number, which are consistent with the theoretical limit.The effects of interactions on a trapped condensate are studied using mean-field theory. For densities n such that na 3 ø 1, the mean-field interaction energy is given by U 4ph 2 an͞m, where m is the atomic mass. For 7 Li, a ͑214.5 6 0.4͒ Å [12]. Because a , 0, the interaction energy decreases with increasing n, so the condensate tends to collapse upon itself. When the confining potential is included in the theory, it is found that if U is sufficiently small compared to the trap energy-level spacing, the destabilizing influence of the interactions is balanced by the kinetic pressure of the gas, and a metastable condensate can form. This requirement for U leads to the prediction that the number of condensate atoms N 0 is limited. As the maximum N 0 is approached, the rate for inelastic collisions increases and the gas becomes progressively less stable with respect to thermal and quantum mechanical fluctuations [7][8][9][10].

Spontaneous Symmetry Breaking, Self-Trapping, and Josephson Oscillations

“…Importantly, the presence of trapping can support metastable, non-collapsing states, although these existence of the metastable state depends on the atom number, interaction strength and shape and strength of the trapping potential. The collapse instability has been investigated experimentally [15,[26][27][28]. Numerous theoretical studies have focused on identifying the parameters associated with the onset of collapse in condensates of various geometries, using variational [43,44,61,62,64], perturbative [24], and numerical [16,17,23,43,61,62,66] methods.…”

“…The first experimental insights into BECs with attractive interactions were made using 7 Li [26]. Here the negative scattering length of a s = (−27.4 ± 0.8) a 0 , where a 0 = 5.29 × 10 −11 m is the Bohr radius, means that the condensate atom number N grows until it reaches N c and the condensate collapses.…”

Quantum entanglement and phase transition in a two-dimensional photon–photon pair model

“…Obviously, atoms aren't the only option for a Email address: ruoshui789@gmail.com (Jian-Jun Zhang) BEC. In recent years, with the development of techniques, the phenomenon of BEC was observed in several physical system [1][2][3][4][5][6][7][8][9], including exciton polaritions, solid-state quasiparticles and so on. We know that photons are the simplest of bosons, so that it would seem that they could in principle undergo this kind of condensation.…”

Stability of trapless Bose–Einstein condensates with two- and three-body interactions

“…Bose-Einstein condensates (BECs) first realized experimentally in 1995 for rubidium [1], lithium [2,3], and sodium [4], provide unique opportunities for exploring quantum phenomena on a macroscopic scale. The properties of a condensate at absolute zero temperature are usually described by the time-dependent, nonlinear, mean-field GrossPitaevskii (GP) equation [5].…”