Resolving closely spaced levels for Doppler mismatched double resonance

In this paper, we present experimental techniques to resolve the closely spaced hyperfine levels of a weak transition by eliminating the residual or partial two-photon Doppler broadening and crossover resonances in a wavelength-mismatched double-resonance spectroscopy. The elimination of the partial Doppler broadening is based on velocity-induced population oscillation (VIPO) and velocity-selective saturation (VSS) effects followed by the subtraction of the broad background of the two-photon spectrum. Since the VIPO and VSS effects are the phenomena for near-zero-velocity group atoms, the subtraction gives rise to Doppler-free peaks and the closely spaced hyperfine levels of the $6P_{3/2}$ state in Rb are well resolved. The double-resonance experiment is conducted on the $5S_{1/2}\to 5P_{3/2}$ strong transition (at 780 nm) and $5S_{1/2}\to 6P_{3/2}$ weak transition (at 420 nm) at room temperature.

Figure 1

Energy levels (${}^{85}\mathrm{Rb}$) with hyperfine splitting (in MHz) and the various transitions in different configurations for EIT. (a) V-type open system, (b) V-type open system with the VIPO effect at IR transition, and (c) V-type open system with the VIPO effect at the IR transition and VSS effect at the blue transition. ${\mathrm{\Pi }}_g\approx 40$ kHz [3] is the ground-state mixing rate.

Figure 2

Energy levels (${}^{85}\mathrm{Rb}$) with hyperfine splitting (in MHz) and the various transitions in different configurations for the enhanced absorption scheme. (a) Optical pumping system, (b) optical pumping system with the VIPO effect at the IR transition, and (c) optical pumping system with the VIPO effect at the IR transition and VSS effect at the blue transition.

Figure 3

The experimental setup for resolving the closely spaced hyperfine levels of the $6P_{3/2}$ state in the Rb atom using the VIPO and VSS effects.

Figure 4

Numerically calculated thermal averaged probe absorption vs detuning of 420-nm pump laser for the V-type open system with various configurations shown in Fig. 1 (where ${\mathrm{\Omega }}_p=\sqrt{0.0005}{\mathrm{\Gamma }}_2$). The blue curve corresponds to Fig. 1 with ${\mathrm{\Omega }}_{c2}=\sqrt{1.5}{\mathrm{\Gamma }}_3$. The red curve marked by circles corresponds to Fig. 1 with ${\mathrm{\Omega }}_{c1}={\mathrm{\Gamma }}_2$ and ${\mathrm{\Omega }}_{c2}=\sqrt{1.5}{\mathrm{\Gamma }}_3$. The green curve marked with dots corresponds to Fig. 1 with ${\mathrm{\Omega }}_{c1}=\sqrt{0.5}{\mathrm{\Gamma }}_2, {\mathrm{\Omega }}_{c2}=\sqrt{1.5}{\mathrm{\Gamma }}_3, {\mathrm{\Gamma }}_2=2\pi \times 6.065$ MHz, and ${\mathrm{\Gamma }}_3=2\pi \times 1.32$ MHz. The vertical axis of the blue trace is on the left and the red trace marked by circles and the green trace marked with dots are on the right.

Figure 5

Numerically calculated thermal averaged probe absorption vs detuning of 420-nm pump laser for optical system with various configurations shown in Fig. 2 (where ${\mathrm{\Omega }}_{\text{p}}=\sqrt{0.0005}{\mathrm{\Gamma }}_2$). The blue curve corresponds to Fig. 2 with ${\mathrm{\Omega }}_{\text{c2}}=\sqrt{1.5}{\mathrm{\Gamma }}_3$. The red curve marked by circles corresponds to Fig. 2 with ${\mathrm{\Omega }}_{\text{c1}}={\mathrm{\Gamma }}_2$ and ${\mathrm{\Omega }}_{\text{c2}}=\sqrt{1.5}{\mathrm{\Gamma }}_3$. The green curve marked with dots corresponds to Fig. 2 with ${\mathrm{\Omega }}_{\text{c1}}=\sqrt{0.5}{\mathrm{\Gamma }}_2, {\mathrm{\Omega }}_{\text{c2}}=\sqrt{1.5}{\mathrm{\Gamma }}_3, {\mathrm{\Gamma }}_2=2\pi \times 6.065$ MHz, and ${\mathrm{\Gamma }}_3=2\pi \times 1.32$ MHz. The vertical axis of the blue trace is on the left and the red trace marked by circles and the green trace marked with dots are on the right.

Figure 6

The transparency spectrum of the $6P_{3/2}$ hyperfine levels in ${}^{85}\mathrm{Rb}$ under various configurations shown in Fig. 1. The red dashed trace is for the V-type open system [Fig. 1], the blue trace marked with dots in (a) is for the V-type open system with VIPO effect at IR transition [Fig. 1], while the blue trace marked with dots in (b) is for the V-type open system with the VIPO effect at IR and the VSS effect at the blue transition [Fig. 1]. The green trace is the final result after removing the broad transparency background and it is magnified $3\times$ for visibility purposes.

Figure 7

The EA spectrum of the $6P_{3/2}$ hyperfine levels in ${}^{85}\mathrm{Rb}$ under various configurations shown in Fig. 2. The red dashed trace is for the optical pumping system [Fig. 2], the blue trace marked with dots in (a) is for the optical pumping system with the VIPO effect at the IR transition [as shown in Fig. 2], while the blue trace marked with dots in (b) is for the optical pumping system with the VIPO effect at the IR and the VSS effect at the blue transition [Fig. 2]. The green trace is the final result after removing broad absorption background and it is magnified $3\times$ for visibility purposes.

Figure 8

The transparency spectrum of the $6P_{3/2}$ hyperfine levels in ${}^{87}\mathrm{Rb}$ recorded for similar configurations of ${}^{85}\mathrm{Rb}$ shown in Fig. 1. The red dashed trace is for the V-type open system [Fig. 1], the blue trace marked with dots is for the V-type open system with VIPO effect at the IR and VSS effect at the blue transition [Fig. 1], and the green trace is the final result after removing the broad transparency background and it is magnified $3\times$ for visibility purposes.

Figure 9

The EA spectrum of the $6P_{3/2}$ hyperfine levels in ${}^{87}\mathrm{Rb}$ recorded for similar configurations of ${}^{85}\mathrm{Rb}$ shown in Fig. 2. The red dashed trace is for the optical pumping system [Fig. 2], the blue trace marked with dots is for the optical pumping system with the VIPO effect at the IR and the VSS effect at the blue transition [Fig. 2], and the green trace is the final result after removing the broad absorption background and it is magnified $3\times$ for visibility purposes.

Figure 10

(a) The result of the final spectra of the VIPO dips of the $6P_{3/2}$ hyperfine levels in ${}^{87}\mathrm{Rb}$ recorded for various powers of IR pump laser after removing the broad absorption background. (b) The variation of the linewidth of the resolved peak $F=2$ with the power of the IR pump.

Figure 11

Comparison of the full numerical solution of the density matrix in a V-type open system with the analytical solution given in Eq. (A3). ${\mathrm{\Omega }}_{\text{c2}}=\sqrt{1.5}{\mathrm{\Gamma }}_3, {\mathrm{\Gamma }}_2=2\pi \times 6.065$ MHz, and ${\mathrm{\Gamma }}_3=2\pi \times 1.32$ MHz.

Figure 12

The graphical representation of the individual terms I, II, and III given in Eq. (4). ${\mathrm{\Omega }}_{c1}={\mathrm{\Gamma }}_2, {\mathrm{\Omega }}_{c2}=\sqrt{1.5}{\mathrm{\Gamma }}_3, {\mathrm{\Gamma }}_2=2\pi \times 6.065\text{MHz}$, and ${\mathrm{\Gamma }}_3=2\pi \times 1.32\text{MHz}$. The vertical axis of the red trace marked by circles and the blue dashed trace are on the left and the green trace marked with dots and the cyan trace are on the right.

Figure 13

Comparison of the full numerical solution of the density matrix in optical pumping system with the analytical solution given in Eq. (B3). ${\mathrm{\Omega }}_{\text{c2}}=\sqrt{1.5}{\mathrm{\Gamma }}_3, {\mathrm{\Gamma }}_2=2\pi \times 6.065$ MHz, and ${\mathrm{\Gamma }}_3=2\pi \times 1.32$ MHz.

Figure 14

The graphical representation of the individual terms I and II given in Eq. (10). ${\mathrm{\Omega }}_{\text{c1}}={\mathrm{\Gamma }}_2, {\mathrm{\Omega }}_{\text{c2}}=\sqrt{1.5}{\mathrm{\Gamma }}_3, {\mathrm{\Gamma }}_2=2\pi \times 6.065$ MHz, and ${\mathrm{\Gamma }}_3=2\pi \times 1.32$ MHz. The vertical axis of the red trace marked by circles is on the left and the blue dashed trace and the green trace marked with dots are on the right.