Figure 1

Energy level structure for TPA in Rb. $\Delta$ is the detuning from the intermediate level. We observe degenerate TPA at 778.1 nm.Reuse & Permissions

Figure 2

Experimental setup: The pump laser is split into two counter-propagating beams using a 50:50 beam splitter (BS). Polarizations are made identical using polarization beam-splitter (PBS) cubes, and the beams are then coupled through the hollow-core photonic-band-gap fiber (PBGF). A blue-colored glass is used to filter the fluorescence from the excited $6P_{3/2}$ state and then detected on a photomultiplier tube (PMT). An acousto-optic modulator (AOM-1) is used to modulate the pump beams as a triangular wave at a 1-kHz frequency to vary linearly the intensity of the counter-propagating beams simultaneously. For lock-in detection of the TPA through the PBGF, one of the counter-propagating beams is modulated using AOM-2 as a square wave at 25 kHz. The signal is detected on a photodiode (PD) using a pick-off beam at one end and sent to a lock-in amplifier, the ouput of which is subsequently monitored using an oscilloscope.Reuse & Permissions

Figure 3

Blue fluorescence signal detected by the PMT. Fluorescence peaks corresponding to each of the hyperfine ground states of ${}^{85}\mathrm{Rb}$ and ${}^{87}\mathrm{Rb}$ are observed as the pump laser is scanned in frequency. Since the two beams are perfectly counter-propagating in the fiber, all the peaks are Doppler-free. Peaks are homogeneously broadened due to the short transit time ($~5$ ns) of the Rb atoms across the 6-$\mu$m core of the fiber.Reuse & Permissions

Figure 4

Blue fluorescence signal [(black) squares] detected by the PMT as the pump laser power is varied using AOM-1 when the laser is tuned to the $5S_{1/2}\to 5D_{5/2}$ $(F=3$ to $F^{\prime })$ two-photon transition of ${}^{85}\mathrm{Rb}$. The solid (red) line shows the expected square dependence of two-photon absorption on intensity.Reuse & Permissions

Figure 5

Circles (blue) show data from the direct measurement of two-photon absorption from one of the pump beams using a lock-in detector as the pump laser is scanned across the $5S_{1/2}\to 5D_{5/2}$, $F_g=3$ to $F_e$ (778.1055-nm) two-photon transition of ${}^{85}\mathrm{Rb}$. The solid (black) line shows the fit of a sum of five Lorentzians which correspond to each of the hyperfine lines. The homogeneous linewidth is estimated to be $73\pm 10$ MHz.Reuse & Permissions

Figure 6

On-resonance nondegenerate two-photon-absorption energy level scheme in Rb.Reuse & Permissions