Autler-Townes splitting via frequency up-conversion at ultralow-power levels in cold ${}^{87}\mathrm{Rb}$ atoms using an optical nanofiber

The tight confinement of the evanescent light field around the waist of an optical nanofiber makes it a suitable tool for studying nonlinear optics in atomic media. Here, we use an optical nanofiber embedded in a cloud of laser-cooled ${}^{87}\mathrm{Rb}$ for near-infrared frequency up-conversion via a resonant two-photon process. Sub-nW powers of the two-photon radiation, at 780 and 776 nm, copropagate through the optical nanofiber and the generation of 420 nm photons is observed. A measurement of the Autler-Townes splitting provides a direct measurement of the Rabi frequency of the 780 nm transition. Through this method, dephasings of the system can be studied. In this work, the optical nanofiber is used as an excitation and detection tool simultaneously, and it highlights some of the advantages of using fully fibered systems for nonlinear optics with atoms.

Figure 1

Energy-level diagram for ${}^{87}\mathrm{Rb}$ atoms showing the 780 nm coupling and 776 nm probe beams.

Figure 2

Schematic of the experimental setup. 780 and 776 nm light are copropagating in the nanofiber to generate blue photons from the cold atoms. An SPCM is used to detect the blue photons exiting from the nanofiber pigtail after filtering in free space. 780 and 776 nm light counterpropagating in a Rb vapor cell are used to obtain the reference signal for identification of the peaks in the two-photon spectrum. SPCM: single-photon counting module; ECDL: extended cavity diode laser; AOM: acousto-optic modulator; QWP: quarter waveplate; HWP: half waveplate; PMT: photomultiplier tube; MOT: magneto-optical trap; ONF: optical nanofiber; DAQ: data-acquisition card; FC: fiber coupler.

Figure 3

Transmission of 780 nm light passing through the ONF with cold ${}^{87}\mathrm{Rb}$ atoms around the waist. The laser is scanning across the $5S_{1/2} F=2$ to $5P_{3/2}$ possible transitions. This spectrum is obtained using an additional ECDL laser in scan mode. The data are fit (red curves) to Lorentzian profiles and the obtained linewidths for the relevant transitions are indicated at the peaks.

Figure 4

(a) 420 nm photon count rate (blue dots) as ${\omega }_2$ is scanned across the $5P_{3/2}$ to $5D_{5/2}$ transition. An intermediate power (1.4 nW) of ${\omega }_2$ is input into the nanofiber, whereas any 780 nm present is only from the MOT beams. The data are fitted (solid blue curve) to a Lorentzian profile. The black spectrum is the corresponding reference signal obtained from the vapor cell when the 780 and 776 nm beams are counterpropagating. The hyperfine transitions associated with each peak are indicated. (b) Maximum blue-photon count [i.e., the peak value of the curve in (a)] for different powers of ${\omega }_2$. Here, the 780 nm contribution is also only from the MOT beams. The red curve is a theoretical fit to yield the saturation power as $1.24\pm 0.12$ nW. This corresponds to $\sim 1.1$ nW of 776 nm power at the waist.

Figure 5

Blue fluorescence from the atoms collected via the ONF for different powers in ${\omega }_1$, which is 14 MHz red detuned from the $5S_{1/2} F=2$ to $5P_{3/2} F^{\prime }=3$ transition, while ${\omega }_2$ is scanned across the $5P_{3/2} F^{\prime }=3$ to $5D_{5/2}$ hyperfine levels. The power for ${\omega }_2$ is fixed at 0.5 nW. ${\delta }_p$ is the detuning of ${\omega }_2$ as indicated in Fig. 1. ${\omega }_1$ is held at the same frequency as the cooling beams. Asymmetry in the observed A-T doublet is due to the fact that ${\omega }_1$ is not on resonance. Solid lines are theoretical fits to the data using Eq. (1).

Figure 6

Measured A-T splitting as a function of the square root of the power in the 780 nm coupling beam.

Figure 7

Variation of ${\gamma }_{23}$ and ${\gamma }_{13}$ as a function of coupling power $P_{{\omega }_1}$.