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arXiv:cond-mat/0208581

Bose-Einstein-Young condensates

I. E. Mazets

Published Aug 29, 2002• 0 citations
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Abstract

We demonstrate a possibility to create a new state of ultracold atoms which we call a Bose-Einstein-Young condensate. Atoms are supposed to be in different hyperfine state of the same isotope. The wave function of such a state, although totally symmetric with respect to simultaneous permutation of co-ordinates and spins of any pair of atoms, has more complicated structure than a simple product of totally symmetric co-ordinate and spin parts. Its properties with respect to permutations of only co-ordinates or only spins are characterized by a particular Young diagram, a symbol denoting an irreducible representation of the permutation group.

DOI
10.48550/arxiv.cond-mat/0208581

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We demonstrate a possibility to create a new state of ultracold atoms which we call a Bose-Einstein-Young condensate. Atoms are supposed to be in different hyperfine state of the same isotope. The wave function of such a state, although totally symmetric with respect to simultaneous permutation of co-ordinates and spins of any pair of atoms, has more complicated structure than a simple product of totally symmetric co-ordinate and spin parts. Its properties with respect to permutations of only co-ordinates or only spins are characterized by a particular Young diagram, a symbol denoting an irreducible representation of the permutation group.
We could recently achieve the Bose Einstein condensation (BEC) of Yb atoms. Yb differs from most of the elements that have previously been condensed, because it is a two‐electron atom with the singlet S ground state. Furthermore the Bosonic isotopes of Yb, like 174Yb which we succeeded to condensate, has no nuclear spin, so that the ground state is completely spin‐less state and hence insensitive to magnetic fields. Thus a new type of atom could join the group of atoms for BEC studies. We would like to report how we could achieve the BEC of Yb atoms.
The symmetry properties of the N-particle multilevel system are studied. For indistinguishable particles, the total wave function must be either symmetric or antisymmetric in the exchange of any two particles. The internal states of the multilevel system are combined with suitable spatial wave functions to produce a totally symmetric or antisymmetric wave function. The problem of degeneracy and the method of combining a given permutational symmetry of the internal wave function with the same or the conjugate symmetry for the spatial part are described. It is found that Young’s diagram corresponding to the given irreducible representation of the permutation group plays an important role.