Alignment-dependent decay rate of an atomic dipole near an optical nanofiber

We study the modification of the atomic spontaneous emission rate, i.e., the Purcell effect, of ${}^{87}\mathrm{Rb}$ in the vicinity of an optical nanofiber ($\sim 500$ nm diameter). We observe enhancement and inhibition of the atomic decay rate depending on the alignment of the induced atomic dipole relative to the nanofiber. We present calculations with two different methods that qualitatively agree with some of the results; the calculations that best agree consider the atoms as simple oscillating dipoles. This is surprising since the multilevel nature of the atoms should produce a different radiation pattern, predicting different modification of the lifetime than the measured ones. This work is a step towards characterizing and controlling atomic properties near optical waveguides, fundamental tools for the development of quantum photonics.

Figure 1

(a) Sketch of the experimental configuration where a dilute ensemble of cold atoms spontaneously emit photons at a rate ${\gamma }_0$ or $\gamma$ when they are placed far away or close to the fiber, respectively. (b), (c) Sketch of the orientation of the induced atomic dipoles relative to the nanofiber for horizontal and vertical probe beam polarization, respectively. A coordinate system considering the $z$ axis along the ONF is used throughout the paper.

Figure 2

(a) Schematic of the experimental setup. A train of pulses generated from a Pockels cell is directed to an ensemble of cold ${}^{87}\mathrm{Rb}$ atoms placed near an optical nanofiber. The spontaneously emitted photons into the nanofiber are collected and time tagged to obtain the atomic radiative lifetime. Photons emitted into free space are also measured to verify possible systematic errors. (b) Experimental sequence of light pulses to cool, repump, and probe the atoms.

Figure 3

Normalized time distribution of the collected photon count rate in logarithmic scale with a time bin of 1.5 ns. (a), (c) Represent the decay signal for atoms near the ONF excited with vertical and horizontal polarization, respectively. (b) Represents the decay signal for atoms in free space far from the ONF. The inset in (b) shows the excitation pulse (note the different vertical axis). The noise floor in the pulse reaches is down from the excitation by 2.5 orders of magnitude 30 ns after the pulse turns off. The black solid lines are fits to exponential decays, and their residuals normalized to the standard deviation are displayed below the plots. The fits correspond to decay rates normalized by the free-space decay rate of $1.090\pm 0.013$, $1.003\pm 0.006$, $0.932\pm 0.025$, respectively. Each individual reduced ${\chi }^2$ is 1.22, 1.14, and 0.70, respectively, with an uncertainty of $\pm 0.26$ in all three cases. For more details of the data analysis, see the main text.

Figure 4

Modification of the atomic spontaneous emission rate due to the presence of the ONF normalized by the free-space decay rate. The results are displayed as function of the distance between the atom and the fiber surface, and the ONF radius. The three possible atomic dipole orientations can be along $\widehat{z}$, $\widehat{\varphi }$, and $\widehat{r}$. (a)–(c) Show the result of FDTD calculation. (d), (e) Show the result of a mode expansion calculation.

Figure 5

Plot of the spatial dependence of $\rho \left(r\right)$ (dotted blue line), $p_{\text{abs}}\left(r\right)$ (dashed green line), and $\alpha \left(r\right)$ (dotted-dashed red line) in arbitrary units as a function of the atom-surface distance. The black solid line is the direct multiplication of these functions and it represents the distribution over which the spatial average is taken in a realistic experiment, as stated in Eq. (11).

Figure 6

Normalized decay rates for different polarizations of the probe with respect to the nanofiber. The red circle (blue square) corresponds to the measured modified lifetime of atoms driven by vertically (horizontally) polarized probe light. The green diamonds are the simultaneously measured free space decay time for each configuration. The solid green line is the expected decay rate in free space. The dashed blue and red lines are the calculated values from the two-level atom FDTD calculation for a horizontal polarized probe and a vertically polarized probe respectively. The dotted lines are the calculated values from the two-level atom mode expansion calculation. Both calculation are done considering the spatial average in Eq. (11).