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Supersymmetric Response of Bose-Fermi Mixture to Photoassociation

We study supersymmetric (SUSY) responses to a photoassociation 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 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 to an exact eigenstate. This SUSY response can be detected by means of the spectroscopy method, e.g., the photoassociation spectrum which displays the molecular formation rate of $% Ff\to b$.