Trapping cold atoms using surface-grown carbon nanotubes

We present a feasibility study for loading cold atomic clouds into magnetic traps created by single-wall carbon nanotubes grown directly onto dielectric surfaces. We show that atoms may be captured for experimentally sustainable nanotube currents, generating trapped clouds whose densities and lifetimes are sufficient to enable detection by simple imaging methods. This opens the way for a different type of conductor to be used in atomchips, enabling atom trapping at submicron distances, with implications for both fundamental studies and for technological applications.

Figure 1

Atomic force microscope image of an isolated CNT fabricated and contacted for use as a $\mathrm{Z}$-shaped wire trap for atomchip experiments. This sample was produced during development of our fabrication procedures [42]. It includes a straight $1\text{−}\mu \text{m}$-long CNT grown on an ${\text{SiO}}_2$ layer and electrically connected with Pd wires ($1\mu \text{m}$ wide by 25 nm thick). The Pd/CNT junctions are shown at the arrow tips. We have verified that the currents used for the simulations described in this work are sustainable for the repeated cycling required by atomchip experiments.

Figure 2

(Color online) Schematic of the two-layer CNT atomchip chosen as the basis for our feasibility study due to its simplicity. The nanotube is grown by chemical vapor deposition directly onto an upper $100\text{−}\mu \text{m}$-thick $\text{Si}/{\text{SiO}}_2$ substrate (the substrate is not shown in the schematic for clarity). This substrate is aligned and glued to a lower atomchip on which a gold $\mathrm{Z}$ wire has already been fabricated in order to facilitate loading the CNT trap. For clarity, only the central portion of this $\mathrm{Z}$ wire is shown. The lower chip contains additional wires for generating the necessary bias fields. The trap center is located at a distance $d$ above the CNT. Current flows in the direction designated by $I$ through Pd contacts that are separated by a distance $L$. The $+z$ axis is oriented in the direction of gravity.

Figure 3

(Color online) Atomic trapping potentials and optical densities for CNT traps calculated using a current of $20\mu \text{A}$ through a $5\text{−}\mu \text{m}$-long nanotube. (a) Trapping potential directly above the nanotube $\left(x=y=0\right)$ as a function of height $z$ for different positions $d$ of the trap center. The trap center is controlled using the bias field $B_y$. (b) Isopotential surfaces viewed along the $x$ and $y$ axes at an energy of $1.05\mu \text{K}$ for a trap centered at $d=0.9\mu \text{m}$ and $1.15\mu \text{K}$ for $d=0.7\mu \text{m}$. The openings show where atoms can escape due to gravity or to the surface, respectively. (c) Trap depth (triangles) and number of trapped atoms (circles) as a function of the trap center position $d$. Inverted triangles show the energy above which atoms can reach the surface due to the Casimir-Polder force; upright triangles show the energy above which atoms can drop out of the trap due to gravity. (d) In situ optical-density maps of the trapped atoms for $d=0.85\mu \text{m}$, as viewed parallel to the nanotube and perpendicular to it, calculated using the Gross-Pitaevskii equation for a trap containing 275 interacting ground-state atoms; the chemical potential $\mu$ is 1/3 of the trap depth at this height.

Figure 4

(Color online) Trap loss rates as a function of the distance $d$ between the trap center and the surface due to Majorana spin flips, tunneling to the surface, and thermal noise-induced spin flips from the Pd contacts, assuming a 50 s lifetime due to collisions with background gases. The Majorana and tunneling loss rates are shown only for a $5\text{−}\mu \text{m}$-long CNT; the thermal spin-flip rates are for 1-, 3-, and $5\text{−}\mu \text{m}$-long CNTs. The chosen Majorana spin-flip rate limits the overall trap lifetime to 1 s for all values of $d$ considered in this feasibility study.

Figure 5

(Color online) (a) Atomic trapping potentials due to a current of 0.5 A through the gold $\mathrm{Z}$ wire only (the “loading” trap) and due to the “combined” trap, which has in addition a $20\mu \text{A}$ current flowing through a $5\text{−}\mu \text{m}$-long nanotube. Both trap minima are $0.85\mu \text{m}$ from the surface. The nanotube current creates a much higher potential barrier for the combined trap as well as generating tighter confinement. (b) Potential isosurface for the combined trap at an energy of $1.3\mu \text{K}$ using the above currents, demonstrating how the combined CNT trap pinches off the atom density directly above the nanotube contacts and isolates it from the atomchip surface.

Figure 6

(Color online) (a) Position of atoms in the cloud as a function of time of flight under the influence of external potentials. Bands correspond to the range of initial starting points $z_0$ within the cloud, whose center is located at $d=0.85\mu \text{m}$. The main graph shows the atomic positions under the influence of gravity, the Casimir-Polder force, and a magnetic gradient. The inset shows the atomic positions, at short time of flight, under the influence of only gravity and the Casimir-Polder force. Atoms at all points starting at $z_0<z_{\text{eq}}=0.76\mu \text{m}$ will crash into the chip unless a magnetic gradient is applied. (b) Evolution of the atom cloud optical density after a time of flight of 2 ms (upper) and 5 ms (lower) under the influence of external potentials and atomic collisions. The cloud becomes resolvable after 2 ms and remains detectable even after 5 ms using standard imaging systems. See text for trap release details.