Electro-Optical Nanotraps for Neutral Atoms

We propose a new class of nanoscale electro-optical traps for neutral atoms. A prototype is the toroidal trap created by a suspended, charged carbon nanotube decorated with a silver nanosphere dimer. An illuminating laser field, blue detuned from an atomic resonance frequency, is strongly focused by plasmons induced in the dimer and generates both a repulsive potential barrier near the nanostructure surface and a large viscous damping force that facilitates trap loading. Atoms with velocities of several meters per second may be loaded directly into the trap via spontaneous emission of just two photons.

Figure 1

The nanotrap. A suspended carbon nanotube, attached at each end to an electrode, supports two Ag nanospheres across a gap in a silicon nitride membrane. An illuminating laser field excites plasma oscillations in the spheres, and large electric fields near the structures are generated. In addition, a dc voltage is applied to the electrodes to create a toroidal trapping region (red). The radius of the toroid can be controlled with nanometer precision and the trap may be loaded directly from an incident atom beam.

Figure 2

The trap potential (1). The $z$ axis is parallel to the nanotube, and $r$ is the distance from the tube. Incident laser light of wavelength $\lambda =475\mathrm{nm}$ is polarized along the $z$ axis connecting two Ag spheres of diameter 90 nm and separation 2 nm. The plasmon resonance of this dimer is at 457 nm. The detuning between the laser frequency $\omega$ and the bare atomic resonance ${\omega }_0$ is picked to be $\Delta =\omega -{\omega }_0=500\Gamma$, where $\Gamma =q^2{\omega }_0^2/6\pi {\epsilon }_0{m}_e{c}^3$ is the decay rate of the excited atomic state in free space. The incident laser intensity is $I^{\mathrm{inc}}=4.6\times {10}^3\mathrm{W}/{\mathrm{cm}}^2$, and the nanospheres are charged to a voltage of $V=3.5\mathrm{V}$ (relative to a macroscopic grounding surface). With these parameters, the saturation parameter $s=0.09$ at the trap minimum. For contrast, the color scale has a lower limit corresponding to the minimum value of $U_{\mathrm{trap}}$ in the trapping region and a range equal to the equilibrium temperature. The low energy area near the surface of the nanospheres is the region where the attractive van der Waals force dominates, and is not part of the trapping region. The trapping potential has cylindrical symmetry in the quasistatic limit. When the voltage is turned off, a trapping potential persists due to a minimum in the laser field amplitude at $r=94\mathrm{nm}$, but the barrier for escape is reduced in this case from 48 to 29 mK.

Figure 3

Atom trajectories studied with Monte Carlo simulations. In (a) we show a typical capture process for an atom launched along the $z=0$ symmetry axis with velocity $1\mathrm{m}/\mathrm{s}$ at $r=500\mathrm{nm}$ (corresponding to a launch velocity of $5.5\mathrm{m}/\mathrm{s}$ from infinity). The dressed state energies are plotted as gray curves (top curve is for $|1⟩$ and bottom curve for $|2⟩$), and the state actually occupied by the atom is marked in red (and labeled I, III, V). [In the limit of vanishing laser field $|1⟩$ ($|2⟩$) is simply $|g⟩$ ($|e⟩$) but for nonzero field, the dressed states are superpositions of $|g⟩$ and $|e⟩$ [10].] In regions I and V the atom is in dressed state $|1⟩$, in region III it is in state $|2⟩$, and after transitions II and IV the particle has suffered a net energy loss. The energy dissipation in such processes is provided by loss in the nanoparticle and by emission of fluorescence photons with frequencies upshifted or downshifted relative to the laser frequency by amounts given by the energy differences between the dressed states. In (b) the same atomic motion is followed further, for up to $10\mu \mathrm{s}$. The successive stages, corresponding to different energies reached after each pair of transitions, are labeled 1–4 in both (a) and (b). In (c), Monte Carlo trajectories are plotted for both uncaptured (blue) and captured (red) atoms launched with velocity $1\mathrm{m}/\mathrm{s}$ from $(r,z)=(500,200)\mathrm{nm}$. [The paths are followed for 734 ns and $1.1\mu \mathrm{s}$, respectively.] The captured atom undergoes a pair of spontaneous transitions in the region indicated by a separate arrow (green).