Designs of magnetic atom-trap lattices for quantum simulation experiments

We have designed and realized magnetic trapping geometries for ultracold atoms based on permanent magnetic films. Magnetic chip based experiments give a high level of control over trap barriers and geometric boundaries in a compact experimental setup. These structures can be used to study quantum spin physics in a wide range of energies and length scales. By introducing defects into a triangular lattice, kagome and hexagonal lattice structures can be created. Rectangular lattices and (quasi-)one-dimensional structures such as ladders and diamond chain trapping potentials have also been created. Quantum spin models can be studied in all these geometries with Rydberg atoms, which allow for controlled interactions over several micrometers. We also present some nonperiodic geometries where the length scales of the traps are varied over a wide range. These tapered structures offer another way to transport large numbers of atoms adiabatically into subwavelength traps and back.

Figure 1

Three-dimensional representation of the magnetic potential in arbitrary units above an out-of-plane magnetized patterned layer of FePt (gray). The potential is calculated at a height $z=0.5a$ above the surface, with $a$ the lattice constant. The external magnetic field ${\mathit{B}}_{\mathrm{ext}}$ was chosen such that a square trapping potential with equal barrier heights at $z=0.5a$ is obtained: $B_{ext}=(-10,-9.0,-5.0\times {10}^{-2})G$.

Figure 2

(a) The tile of the triangular lattice with magnetization $M$ out of plane. (b) Two loop wires that are added to the unit cell, one on each side of the unit cell, with one loop section canceling the equivalent edge current. (c) The resulting modified unit cell.

Figure 3

(a) The triangular structure with $a=$ 5 $\mu \mathrm{m}$; (b) the corresponding potential taken at $z=0.5a=$ 2.5 $\mu \mathrm{m}$. The external field is given by ${\mathit{B}}_{\mathrm{ext}}=(-5.0,2.0,-0.2)G$ and the trap bottom field is 2.2 G. (c) The kagome lattice structure. In black the magnetic pattern is shown with modified local shapes at the trap positions that needed to be raised. (d) The potential created by pattern (c) with a lattice spacing of 5 $\mu \mathrm{m}$ and trap minima at $z=0.5a$. The same external magnetic field as (b) is applied. The kagome lattice is indicated by the white dashed lines. (e) The honeycomb lattice structure. In black the magnetic pattern is shown with modified local shapes at the trap positions that needed to be raised. (f) The potential created by pattern (e) with a lattice spacing of 5 $\mu \mathrm{m}$ and trap minima at $z=0.5a$. The same external magnetic field as in (b) is applied. The hexagonal lattice is indicated by the white dashed lines.

Figure 4

SEM image of the honeycomb lattice with lattice spacing of 5 $\mu \mathrm{m}$. Lighter regions indicate magnetic material.

Figure 5

(a) Magnetic film pattern with $a=5\mu \mathrm{m}$ that can create a double-well series or two-rail ladder. The external field is here set to generate equal barriers between all ladder sites and is ${\mathit{B}}_{\mathrm{ext}}=(-10,-9.0,-5.0\times {10}^{-2})G$.

Figure 6

(a) The same magnetic film pattern as Fig. 5. (b) The potential created by the film of (a) with the reversed external field: ${\mathit{B}}_{\mathrm{ext}}=(10,9.0,5.0\times {10}^{-2})G$. A three-rail ladder is created by the same structure as Fig. 5 with reversed external field to create wells above the other edge of the magnetic structures.

Figure 7

(a) Magnetic film pattern with $a=5\mu \mathrm{m}$ where horizontal and vertical barriers have been combined to isolate a plaquette of $10\times 9$ sites. (b) The potential created by the film of (a) with the same external field as for a square lattice with periodic barriers: ${\mathit{B}}_{\mathrm{ext}}=(-10,-9.0,-5.0\times {10}^{-2})G$.

Figure 8

(a) A single diamond chain where single traps are positioned in between double wells. (b) Potential corresponding to the pattern of (a) with an external field ${\mathit{B}}_{\mathrm{ext}}=(24.4,2.05,0.13)G$ chosen such that traps are formed at $z=0.45a$. Here $a=5\mu \mathrm{m}$. By controlling the external field, trap barriers in different directions can be controlled independently.

Figure 9

(a) Example of a straight taper of 11 lines shrinking by a factor of 2 (5% per line). (b) Example of a rounded taper. The unit cells are now also rotated such that the lattice locally keeps its original shape. The traps along the two red lines are similar but the traps along the blue lines differ due to the different transformation.

Figure 10

(a) Section of the tapered lattice structure for which the potential is presented. The taper has a slope of 5% per line and the largest lattice spacing is 5 $\mu \mathrm{m}$. (b) The potential cross section taken at height $z=0.35a$ such that it cuts through the trap bottom of the horizontal array at $y=2a$. The white lines show points where possible trap positions can be created. Using a time-varying external field, atoms can be moved along those lines. The external field is ${\mathit{B}}_{\mathrm{ext}}=(-11,-4.2,0.20)G$.