Photon-correlation measurements of atomic-cloud temperature using an optical nanofiber

We develop a temperature measurement of an atomic cloud based on the temporal correlations of fluorescence photons evanescently coupled into an optical nanofiber. We measure the temporal width of the intensity-intensity correlation function due to atomic transit time and use it to determine the most probable atomic velocity, hence the temperature. This technique agrees well with standard time-of-flight temperature measurements. We confirm our results with trajectory simulations.

Figure 1

Experimental schematic. A MOT is spatially overlapped with a nanofiber, and the MOT beams drive resonance fluorescence that couples into the guided mode. This signal is filtered by a volume Bragg grating (VBG), bandpass (BP) filter, and long-pass filter before being split by a 50:50 beamsplitter (BS) and sent to two SPCMs. TTL pulses from the SPCMs are time-tagged by a field-programmable gate array and correlated by software.

Figure 2

Second-order correlation function $g^{\left(2\right)}\left(\tau \right)$ for light scattered into the fiber as a function of delay time $\tau$. Curves show data for low (blue) and high (red) Rb dispenser currents, illustrating antibunching and bunching, respectively.

Figure 3

Second-order correlation function $g^{\left(2\right)}\left(\tau \right)$ as a function of delay time $\tau$ for an atom temperature of $460 \mu \mathrm{K}$. Data [(blue) circles] are fit [solid (red) line] to $1+f\left(\tau \right)$ using Eq. (10), with the residuals displayed in the lower plot.

Figure 4

Extracted ${\tau }_0$ vs temperature $T$, measured via TOF. Filled (blue) circles are experimental data. Vertical error bars indicate the standard error in the fit of Eq. (10), and horizontal error bars arise from the systematic uncertainty in the magnification of the imaging system. The solid (purple) line is a fit to Eq. (8), and the shaded region is the 95% $\left(2\sigma \right)$ confidence bands considering both the vertical and the horizontal error bars. The reduced ${\chi }^2$ is 1.67. Open (red) squares are the results of the trajectory simulation, with a single scale parameter of 0.77.

Figure 5

Simulated correlation time ${\tau }_0$ vs sampling angle range $\mathrm{\Delta }\theta$ for an atomic temperature of $90 \mu \mathrm{K}$. The dashed line indicates the critical angle $arctan(53/300)$ in the simulation at which not all atoms hit the fiber.