The Bose/Fermi oscillators in a new supersymmetric representation

Mordechai Kornbluth, Fredy R. Zypman

Willi-Hans Steeb, Yorick Hardy

We study the entanglement of Fermi particles of a supersymmetric Hamilton operator given by a simple Fermi-Bose system

FRANCESCO IACHELLO, P. Van Isacker

Tao Shi, Yue Yu, C. P. Sun

We study supersymmetric (SUSY) responses to a photoassociation (PA) process in a mixture of Bose molecules $b$ and Fermi atoms $f$ which turn to mutual superpartners for a set of proper parameters. We consider the molecule $b$ to be a bound state of the atom $f$ and another Fermi atom $F$ with different species. The $b$-$f$ mixture and a free $F$ atom gas are loaded in an optical lattice. The SUSY nature of the mixture can be signaled in the response to a photon-induced atom-molecule transition: While two new types of fermionic excitations, an individual $b$ particle--$f$ hole pair continuum and the Nambu-Goldstone-fermion-like (or ``goldstino-like'') collective mode, are concomitant for a generic $b$-$f$ mixture, the former is completely suppressed in the SUSY $b$-$f$ mixture and the zero-momentum mode of the latter approaches an exact eigenstate. This SUSY response can be detected by means of the spectroscopy method, for example, the PA spectrum which displays the molecular formation rate of $\mathit{Ff}\ensuremath{\rightarrow}b$.

R. J. Cova

In the Fock space of two Bose operators all the irreducible representations of both the 1-D para-Bose and para-Fermi oscillators are constructed. Bose states of the form |p + k–1, kn > (|p – k, kn), n = 1,2, are shown to stand for states of k-parabosons (k-parafermions) of order p. For n = 1 or n = 2 the various subspaces may be visualized in the plane as either straight-lines or parabolae, respectively.