Demonstration of a State-Insensitive, Compensated Nanofiber Trap

We report the experimental realization of an optical trap that localizes single Cs atoms $\simeq 215\mathrm{nm}$ from the surface of a dielectric nanofiber. By operating at magic wavelengths for pairs of counterpropagating red- and blue-detuned trapping beams, differential scalar light shifts are eliminated, and vector shifts are suppressed by $\approx 250$. We thereby measure an absorption linewidth $\Gamma /2\pi =5.7\pm 0.1\mathrm{MHz}$ for the Cs $6S_{1/2}$, $F=4\to 6P_{3/2}$, $F^{\prime }=5$ transition, where ${\Gamma }_0/2\pi =5.2\mathrm{MHz}$ in free space. An optical depth $d\simeq 66$ is observed, corresponding to an optical depth per atom $d_1\simeq 0.08$. These advances provide an important capability for the implementation of functional quantum optical networks and precision atomic spectroscopy near dielectric surfaces.

Figure 1

Adiabatic trapping potential $U_{\mathrm{trap}}$ for a state-insensitive, compensated nanofiber trap for the $6S_{1/2}$, $F=4$ states in atomic Cs outside of a cylindrical waveguide of radius $a=215\mathrm{nm}$ [10]. $U_{\mathrm{trap}}$ values for the substates of the ground level $F=4$ of $6S_{1/2}$ (excited level $F^{\prime }=5$ of $6P_{3/2}$) are shown as black (red-dashed) curves. Due to the complex polarizations of the trapping fields, the energy levels are not the eigenstates of the angular momentum operators, but rather superposition states of the Zeeman sublevels (see the Supplemental Material [26]). (a)(i) azimuthal $U_{\mathrm{trap}}(\varphi )$, (ii) axial $U_{\mathrm{trap}}(z)$; and (b) radial $U_{\mathrm{trap}}(r-a)$ trapping potentials. Input polarizations for the trapping beams are denoted by the red and blue arrows in the inset in (b).

Figure 2

(a) Schematic of the setup for a state-insensitive, compensated nanofiber trap. VBG: volume Bragg grating. DM: dichroic mirror. PBS: polarizing beam splitter. APD: avalanche photodetector. The inset shows a SEM image of the nanofiber for atom trapping. (b) Angular distribution of the Rayleigh scattering intensity from the nanofiber as a function of the angle $\theta$ of the polarization for the incident probe field and of distance $z$ along the fiber axis [36] (see Supplemental Material [26]). (c) Spatially resolved visibility $V$ as a function of axial position $z$.

Figure 3

(a) Probe transmission spectra $T^{(N)}(\delta )$ for $N$ trapped atoms as a function of detuning $\delta$ from the $6S_{1/2}$, $F=4\to 6P_{3/2}$, $F^{\prime }=5$ transition in Cs for $x$-polarized input. From fits to $T^{(N)}(\delta )$ (full curves), we obtain the optical depths $d_N$ at $\delta =0$ and linewidths $\Gamma$ from a model that incorporates the polarization measurements in Figs. 2b, 2c. $T^{(N)}(\delta )$ (i) at $\tau =299\mathrm{ms}$ with $d_N=1.2\pm 0.1$ and $\Gamma /2\pi =5.8\pm 0.5\mathrm{MHz}$ and (ii) at $\tau =1\mathrm{ms}$ with $d_N=66\pm 17$. (b) Measurement of the power $P_{\mathrm{abs}}$ absorbed by the trapped atoms as a function of input power $P_{\mathrm{in}}$, together with the associated optical depth $d_N=18\pm 2$ from curve (ii) (red line) of the inset, allows an inference of $N=224\pm 10$ [21]. The linewidth $\Gamma /2\pi =5.5\pm 0.4\mathrm{MHz}$ and $d_N=1.1\pm 0.1$ are determined from curve (i) (black line) of the inset.

Figure 4

(a) Normalized reflection spectra $R_N(\delta )/R_N(0)$ from the 1D atomic array with $N=14\pm 2$ atoms (green points), $N=79\pm 13$ atoms (blue points), and $N=224\pm 10$ atoms (red points) randomly distributed across $n_{\mathrm{site}}\simeq 4000$ sites. The solid lines are the spectra obtained from Monte Carlo simulations for $N\ll n_{\mathrm{site}}$. (b) Simulated linewidth ${\Gamma }_R$ of the reflection spectrum as a function of entropy $\mathcal{S}$. The error bars for the red, blue, and green data points include both statistical and systematic uncertainties. The black points are the results of a simulation with error bars representing numerical uncertainties. The solid line is a linear fit to the simulation points.