Figure 1

(a) Artist’s impression of the setup. The disks represent the bosonic condensate density and the balls (blue online) in the vortex core represent the fermionic density. The black line is a guide to the eye to see the wiggling of the vortex line that corresponds to a Kelvin mode. (b) Schematic of the setup. Here $r$ is the radial distance in the $xy$ plane. The larger oval (pink online) and smaller circular (blue online) blobs represent the bosonic and fermionic densities, respectively. Moreover, $\lambda$ is the wavelength of the laser. The lower (blue online) and upper (red online) solid lines indicate the strength of the optical potential, respectively, for the bosons and fermions as a function of the $z$ coordinate. (c) Schematic fine structure level scheme of the bosonic and fermionic atomic species. Because we consider only sufficiently large detunings the hyperfine level structure is not resolved.Reuse & Permissions

Figure 2

Tuning of the lattice laser to obtain supersymmetry for 1000 bosonic atoms per lattice site: Rabi frequency for the bosonic atoms versus wavelength for ${}^{87}\mathrm{Rb}\mathrm{\text{−}}{}^{40}\mathrm{K}$ (solid line) and ${}^{23}\mathrm{Na}\mathrm{\text{−}}{}^6\mathrm{Li}$ (dotted line). Note that for the blue-detuned part, i.e., $\lambda <760\mathrm{nm}$ for the ${}^{87}\mathrm{Rb}\mathrm{\text{−}}{}^{40}\mathrm{K}$ mixture extra radial trapping is needed, either magnetically, or by using an extra running laser as discussed later in the text and shown in Fig. 3. In Fig. 3 we display how to tune the running laser to obtain also supersymmetric interactions. The numbers (1)–(4) indicate the parameters for which this is calculated. The inset shows the average number of fermions per lattice site. This depends linearly on the ratio of the harmonic lengths in the axial and radial directions. This ratio should be sufficiently small to be radially in the Thomas-Fermi limit. For this plot a ratio of $1/5$ is chosen.Reuse & Permissions

Figure 3

Tuning of the additional laser to obtain supersymmetric interactions for 1000 bosonic atoms per lattice site. The Rabi frequency versus the wavelength of the running laser for different wavelengths of the lattice laser beam: (1) 400 nm, (2) 740 nm, (3) 850 nm, and (4) 1200 nm. See Fig. 2 for the corresponding Rabi frequencies of the lattice laser beam.Reuse & Permissions

Figure 4

The second-order Feynman diagrams describing the dissipation processes due to the creation of (a) additional pairs of bosonic and (b) fermionic excitations. The full lines correspond to bosons and the dotted lines to fermions. Because the right diagram contains a fermionic loop, it comes with an additional minus sign and the two diagrams thus cancel exactly in the supersymmetric case.Reuse & Permissions