Superconducting Vortex Lattices for Ultracold Atoms

We propose and analyze a nanoengineered vortex array in a thin-film type-II superconductor as a magnetic lattice for ultracold atoms. This proposal addresses several of the key questions in the development of atomic quantum simulators. By trapping atoms close to the surface, tools of nanofabrication and structuring of lattices on the scale of few tens of nanometers become available with a corresponding benefit in energy scales and temperature requirements. This can be combined with the possibility of magnetic single site addressing and manipulation together with a favorable scaling of superconducting surface-induced decoherence.

Figure 1

(a) Schematic illustration of the superconducting vortex lattice for ultracold atoms. (b) Applied field $B_1$ as a function of $\Delta$. Inset: $|{\mathbf{B}}_{\mathrm{lat}}(x,y,z_0){|}^2$ for a square lattice, $\Delta =2$, and $B_1>B_0$ (deep wells) and $B_1<B_0$ (sharp peaks). (c) $|{\mathbf{B}}_{\mathrm{lat}}(x,0,z_0{|}^2$ in units of $B_{\max }^2\equiv |{\mathbf{B}}_{\mathrm{lat}}(x=a/2,0,z_0){|}^2$ as a function of $x/a$ for a square lattice for different $\Delta$.

Figure 2

(a) A contour plot of $|{\mathbf{B}}_{\mathrm{lat}}{|}^2$ at $y=0$ is shown for an infinite square lattice as a function of $x/a$ and ${\Delta }_z$ for $\Delta =\pi$ using Eq. (1). (b) The same plot as (a) is shown with a set of $3\times 3$ localized vortices located on a squared lattice in a thin superconductor (the borders of the plane are at $x/a=\pm 2.45$) by numerically solving the London equation [30] and using $\Lambda \approx a$.

Figure 3

(a) Tunneling rate $t$ (left axis), decoherence rate (right axis) $\Gamma ={\Gamma }_{ML}+{\Gamma }_{\mathrm{sf}}+{\Gamma }_{0\to 1}$, and $V_0/E_R$ (inset) as a function of the trapping position $z_0$ in units of $\Lambda$ for a square lattice at sufficiently large $\Delta$. The range of the plot is limited to the values of $z_0/\Lambda$ for which $50>V_0/E_R>1$. We used the atomic parameters of lithium, $a=3\Lambda /2$, $\Lambda =100\mathrm{nm}$ (solid lines) and $\Lambda =20\mathrm{nm}$ (dahsed lines), $B_M$ such that ${\omega }_{ML}=5{\omega }_T$, and $\eta /\Lambda ={10}^{-7}\mathrm{Kg}/(\mathrm{sm})$ [44]. (b) The ratio $B_d^z/B_{d,0}^z$ as a function of $\lambda /d$ for $L=1$, 2, 4.