Trapping ultracold atoms in a sub-micron-period triangular magnetic lattice

We report the trapping of ultracold ${}^{87}\mathrm{Rb}$ atoms in a 0.7-$\mu \text{m}$-period two-dimensional triangular magnetic lattice on an atom chip. The magnetic lattice is created by a lithographically patterned magnetic Co/Pd multilayer film plus bias fields. Rubidium atoms in the $|F=1,m_F=-1\rangle$ low-field seeking state are trapped at estimated distances down to about $100\mathrm{nm}$ from the chip surface and with calculated mean trapping frequencies up to about $800\mathrm{kHz}$. The measured lifetimes of the atoms trapped in the magnetic lattice are in the range 0.4–$1.7\mathrm{ms}$, depending on distance from the chip surface. Model calculations suggest the trap lifetimes are currently limited mainly by losses due to one-dimensional thermal evaporation following loading of the atoms from the $Z$-wire trap into the very tight magnetic lattice traps, rather than by fundamental loss processes such as surface interactions, three-body recombination, or spin flips due to Johnson magnetic noise. The trapping of atoms in a $0.7\text{−}\mu \mathrm{m}$-period magnetic lattice represents a significant step toward using magnetic lattices for quantum tunneling experiments and to simulate condensed matter and many-body phenomena in nontrivial lattice geometries.

Figure 1

(a) Magnetic film pattern designed to create a triangular magnetic lattice optimized for a trap distance $z=z_{\text{min}}=a/2$ from the surface of the magnetic film, where $a$ is the lattice period. Blue regions represent the magnetic film and arrows represent virtual currents circulating around the edges of the film structure. (b) Contour plot of the optimized triangular magnetic lattice potential with bias fields $B_x=0.5\mathrm{G},B_y=4.5\mathrm{G}$; $a=0.7\mu \mathrm{m}$; and $z_{\text{min}}=a/2=350\mathrm{nm}$. Dark regions are trap minima. (c) Contour plot of a triangular magnetic lattice potential with bias fields $B_x=52\mathrm{G},B_y=0\mathrm{G}$; $a=0.7\mu \mathrm{m}$; and $z_{\text{min}}=139\mathrm{nm}$. (d)–(f) Calculated trapping potentials for ${}^{87}\mathrm{Rb}$ $|F=1,m_F=-1\rangle$ atoms trapped in a $0.7\text{−}\mu \mathrm{m}$-period triangular magnetic lattice for bias fields $B_x=$ (d) $7\mathrm{G}$, (e) $26\mathrm{G}$, and (f) $52\mathrm{G}$. Black dashed lines are the magnetic lattice potentials and red solid lines include the Casimir-Polder interaction with $C_4=8.2\times {10}^{-56}\text{J}{\text{m}}^4$ for a silica surface. Vertical orange lines indicate the position of the silica surface $\left(z=75\mathrm{nm}\right)$ used in the calculations. Magnetic film parameters: magnetization $4\pi M_z=5.9\mathrm{kG}$, film thickness $t_m=10.3\mathrm{nm}$.

Figure 2

(a) Schematic of the DBC atom chip. The structure includes four separated current-carrying $U$-wire and $Z$-wire structures for trapping the ultracold atom cloud and loading into the magnetic lattice traps plus two wires on either side for rf evaporative cooling or rf spectroscopy. The small green squares in the center show the positions of four magnetic lattice structures, which are located below their respective $U$ and $Z$ wires. (b) SEM image of the fabricated $0.7\text{−}\mu \mathrm{m}$-period triangular magnetic lattice structure. Light-gray regions are the unetched magnetic film and the dark-gray regions are the etched regions.

Figure 3

(a) Distance calibration of the $Z$-wire trapped atoms close to the chip surface for $B_x=52\mathrm{G}$, showing measurements of the distance $d$ from the trap center to the gold reflecting layer on the chip surface versus $Z$-wire current $I_z$. Solid line is a linear fit: $d=(38.8\pm 1.6)I_z-(718\pm 33)\mu \mathrm{m}$, where the uncertainties are $1\sigma$ statistical uncertainties. Inset: reflective absorption image of the atom cloud close $\left(31\mu \mathrm{m}\right)$ to the chip surface, showing the direct and mirror images. (b) Remaining atom fraction $\chi \left(d\right)$ versus distance $d$ of the cloud center from the chip surface for a BEC at $T\approx 200\mathrm{nK}$ [blue (top) points] and for a thermal cloud at $600\mathrm{nK}$ [orange (second) points], $1\mu \mathrm{K}$ [green (third) points], and $2\mu \mathrm{K}$ [red (bottom) points], for $B_x=52\mathrm{G}$. Solid curves are theoretical fits using the simple truncation model with $T\approx 190\mathrm{nK}$ [blue (top) line], $430\mathrm{nK}$ [orange (second) line], $0.85\mu \mathrm{K}$ [green (third) line], and $1.5\mu \mathrm{K}$ [red (bottom) line]. The dashed blue curve for the BEC at $T\approx 200\mathrm{nK}$ is a theoretical fit using the 1D surface evaporation model with $T=130\mathrm{nK},{\tau }_{\text{el}}=0.6\mathrm{ms}$.

Figure 4

Reflection absorption images of the time evolution of an ultracold atom cloud projected toward the magnetic lattice potential with no bias fields. Launching position of atom cloud $d_0=$ (a) $145\mu \mathrm{m}$, (b) $128\mu \mathrm{m}$, (c) $76\mu \mathrm{m}$, and (d) $67\mu \mathrm{m}$ from the chip surface. Both direct and mirror images are visible due to the reflection absorption imaging geometry. The white dashed line in (a) indicates the position of the reflecting surface. (e),(f) Time evolution of the lateral width $\left(\sigma \right)$ along $y$ and the vertical position of the ultracold atom cloud $\left(d\right)$ projected toward the magnetic lattice potential. Launching positions $d_0=67\mu \mathrm{m}$ [blue (top) points], $76\mu \mathrm{m}$ [orange (second) points], $128\mu \mathrm{m}$ [green (third) points], and $145\mu \mathrm{m}$ [red (bottom) points]. Fitted curves in (f) (with $\sigma$ and $d$ in micrometers, $t$ in milliseconds, $g=9.8\mu \mathrm{m}/{\mathrm{ms}}^2)$ are $d=-67.5+70t-0.5g{t}^2$ before reflection and $d=-82.5+60(t+8.1)-0.5g{(t+8.1)}^2$ after reflection [blue (bottom) line]; $d=-75.7+65t-0.5g{t}^2$ before reflection and $d=-82.5+60(t+7.8)-0.5g{(t+7.8)}^2$ after reflection [orange (second) line]; $d=-130+52t-0.5g{t}^2$ [green (top) line].

Figure 5

Reflection absorption images of ${}^{87}\mathrm{Rb}$ $|F=1,m_F=-1\rangle$ atoms (a) trapped in the $0.7\text{−}\mu \mathrm{m}$-period triangular magnetic lattice midway between the direct and mirror images of the $Z$-wire trapped cloud, for $B_x=52\mathrm{G}$; (b) trapped in the $0.7\text{−}\mu \mathrm{m}$-period triangular magnetic lattice only, for $B_x=14\mathrm{G}$; and (c) after launching the atom cloud vertically toward the chip surface for times of flight of $0\mathrm{ms}$ (left panel), $2\mathrm{ms}$ (center), and $3\mathrm{ms}$ (right).

Figure 6

(a) Decay curve for atoms trapped in the $0.7\text{−}\mu \mathrm{m}$-period triangular magnetic lattice for $B_x=14\mathrm{G}$. The solid line is a single exponential fit to the data corresponding to $\tau =1.24\pm 0.07\mathrm{ms}$. Time zero is chosen arbitrarily. (b) Measured lifetimes (black points) of atoms trapped in the magnetic lattice versus distance $z$ of the lattice trap center from the magnetic film surface. The $B_x$ values (in G) are shown and the error bars are $1\sigma$ statistical uncertainties. The red curve shows the calculated evaporation lifetimes ${\tau }_{ev}$ for ${\overline{N}}_{\text{site}}=1.5,\eta =4,\delta d=25\mathrm{nm}$ and the fixed parameters given in Tables 1 and 2.

Figure 7

Calculated lifetimes for evaporation ${\tau }_{\text{ev}}$ [red (second) curve], three-body recombination ${\tau }_{3b}$ [blue (top) curve], and spin flips ${\tau }_s$ (dashed orange) for ${\overline{N}}_{\text{site}}=1.5,\eta =4,\delta d=25\mathrm{nm}$ and the fixed parameters given in Tables 1 and 2. The curves for ${\tau }_{3b}$ and ${\tau }_s$ are reduced by factors of 3 and 100, respectively. The chip surface is located at $z=50\mathrm{nm}$.