Two-photon-excited fluorescence spectroscopy of Rb atoms in a magneto-optical trap

TL;DR

We address the challenge of observing entangled two-photon absorption (ETPA) signals at very low photon flux using ultracold rubidium in a magneto-optical trap. The authors perform two-photon excited fluorescence measurements with a $778.1$ nm laser on $^{85}$Rb and $^{87}$Rb MOTs, confirming a quadratic power dependence with slope $m\approx2$ and extracting two-photon cross-sections on the order of $\sim10^{12}$ GM. They report minimum detectable photon fluxes of $\Phi_{min}= (4.30\pm0.22)\times10^{18}$ cm$^{-2}$ s$^{-1}$ and $\Phi_{min}=(5.17\pm0.26)\times10^{18}$ cm$^{-2}$ s$^{-1}$ and provide upper bounds on the natural-width cross-sections after accounting for MOT broadening, $\delta^{(nat)}\approx(1.59-1.76)\times10^{12}$ GM. The results establish ultracold Rb in a MOT as a sensitive platform for low-flux two-photon spectroscopy and point toward future SPDC-based explorations of ETPA with potential impact on precision metrology and quantum nonlinear optics.

Abstract

We report the results of two-photon-excited fluorescence (TPEF) measurements of the $5\mathrm{S}_{1/2} \rightarrow 5\mathrm{D}_{1/2}$ transition of $^{85}$Rb and $^{87}$Rb cooled in a magneto-optical trap (MOT). We observe TPEF at excitation powers as low as 1 $μ$W or fluxes as low as $4.30 \pm 0.22 \times 10^{18}\ \text{photons}\,\text{cm}^{-2}\,\text{s}^{-1}$ ($^{85}$Rb) and $5.17 \pm 0.26 \times 10^{18}\ \text{photons}\,\text{cm}^{-2}\,\text{s}^{-1}$ ($^{87}$Rb). Our results show that Rb, with additional benefits due to its ability to be optically cooled to the point where Doppler-broadening is negligible, is a promising platform for observing sensitive two-photon spectral signatures at low photon fluxes.

Figures (9)

• Figure 1: The energy level diagram of the $5\mathrm{S}_{1/2} \rightarrow 5\mathrm{D}_{1/2}$ two-photon excitation of Rb (natural linewidth of 667 kHz). Branching ratios and radiative linewidths (calculated from the radiative lifetimes) Sheng2008 are reported. The narrow two-photon detuning (1.06 THz) between the virtual state and the nearest P state is depicted, in addition to the larger detuning (8.21 THz).
• Figure 2: Schematic for two-photon excitation of the Rb MOT. GT = Glan-Taylor polarizer.
• Figure 3: Log--log power-dependence plots for (a) $^{85}$Rb and (b) $^{87}$Rb. Linear fits of the form $y = m x + b$ in $\log_{10}$--$\log_{10}$ space give, for $^{85}$Rb: $m = 2.009 \pm 0.004$, $b = -37.740 \pm 0.840$; and for $^{87}$Rb: $m = 2.046 \pm 0.036$, $b = -38.466 \pm 0.699$. A slope consistent with $m \approx 2$ indicates fluorescence arising purely from two-photon processes. The noise floor is indicated by the solid black line; points whose error bars cross this line are not statistically significant.
• Figure 4: (a) (Top) Two-photon Doppler-free spectrum of hot ^85_Rb vapor (heated to $\approx 90^\circ C$). FWHM (the strongest hyperfine peak) is 3.8 MHz. (Bottom) Error signal (green) used for locking. The points at which the error signal is 0.00 (dashed line) represent potential lock points. (b) (Top) Two-photon Doppler-free spectrum in hot ^87_Rb vapor (heated to $\approx 90^\circ$ C). FWHM (the strongest hyperfine peak) is 2.4 MHz. (Bottom) corresponding error signal.
• Figure 5: (a) MOT absorption image with OD plotted as an intensity surface plot. (b-c) Fitting of example pixels used to produce the absorption OD plot (OD reported at the top of each figure, data shown in blue, fit shown in orange).