Usually optical lattice could be obtained using an arrangement of crisscrossed laser beams that creates a periodic two-dimensional array of standing waves. Ultracold atoms are drawn into the minima of this field pattern, whose hills and valleys resemble an egg carton. There is a limitation for the separation of the atoms in relation to the wavelength of light involved—~ 800 nanometers. To trap atoms more closely together, Romero-Isart and his colleagues—a team led by Juan Ignacio Cirac of the Max Planck Institute for Quantum Optics in Garching, Germany—propose using purely magnetic fields. They start by imagining a sheet, some tens of nanometers thick, made of a type II superconductor. An applied magnetic field can penetrate such a material only in the form of so-called vortices that pass through the sheet at a set of isolated locations.
Do you think this method could be achieved experimentally?
http://physics.aps.org/articles/v6/108#sthash.X7un9K3z.dpuf
To create the votices you have to have already a superconducting material. So this method requires a superconducting material rather than creating one. Usually defects in the underlying thin film distort the lattice significantly.
You can indeed create a periodically varying magnetic field with a type-II superconductor. Such periodic fields can be created and measured experimentally.
The magnitude of field variation depends on magnetic penetration depth and can reach in the best case ~1000G (with periodicity of few tenth of nanometers). Outside of the superconductor such field creates periodic stray fields which decreases
on the length-scale of the intervortex distance (few tenth of nanometers).
If you like to have a stronger field variation (of the order of Tesla) it is better to use a skyrmion lattice (see e.g. MnSi or Cu2OSeO3).
Perhaps one of the solutions: http://www.lightsources.org/press-release/2013/10/09/x-rays-reveal-first-designer-superconductor
A. Maisuradze has it right. The problem with using a SC vortex lattice to make a field grid in hard vacuum (which you certainly need for cold atoms) is that the field distribution flattens out within roughly the scale of the penetration depth. I doubt that this is compatible with the procedure of atom-trapping. As for MnSi skyrmion lattices, I gather the lattice constant is around 18 nm, which is pretty short; also they have the same problem with trapping atoms next to a surface.
Maybe you can begin your study with known sc (YBCO, MgB2, etc) and with low magnetic field, but you must keep in your mind, as J. Brewer said, check data about penetration depth, Hc's too
Instead of using a complex system involving superconductors, a bias magnetic field plus a time-varying magnetic field, to avoid Majorana spin-flip transitions, there is a simple way to create a magnetic lattice. A 2D permanent magnetic lattice can be created by, for example, two arrays of rectangular permanent magnetic slabs or just by a 2D array of square magnets plus a bias magnetic field (see, for instance, http://iopscience.iop.org/0953-4075/39/4/009 and http://iopscience.iop.org/0953-4075/40/6/018?rel=sem&relno=2). Period of the lattice depends on the current thin film technology and, off course, the van der Waals' interaction should be taken into account when the micro- or nano-traps are very close to surfaces.
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