Sagnac interferometry in a slow-light medium

We use a Sagnac interferometer to measure the dispersive and absorptive properties of room temperature Rubidium vapor on the $D_2$ line at $780.2\mathrm{nm}$. We apply a pump beam such that the resulting $\Lambda$ system exhibits electromagnetically induced transparency. Using a “biased alignment” technique we demonstrate a direct and robust method of measuring the rapid variation in the refractive index. Such a “slow-light” Sagnac interferometer is ideally suited to precision measurement applications such as magnetometry and inertial sensing.

Figure 1

(Color online) (i) Sagnac interferometer experimental setup. The probe beam (red or dark grey) passes around the Sagnac interferometer in both clockwise and anticlockwise directions, however the orthogonally polarized pump beam (orange or light grey) only passes through the rubidium vapor cell in the clockwise direction. BS, 50:50 beam splitter; ND, neutral-density filter; PD, photodiode; PBS, polarization beam spitting cube; BD, beam dump; and $\lambda ∕4$, quarter-wave plate. (ii) The $\Lambda$ system investigated in this paper: $\Delta$ is the single-photon detuning of the pump field from the atomic resonance; and $\delta$ is the detuning of the probe from the two-photon Raman resonance. (iii) Output beam profiles for “perfect” alignment (upper) and “biased” alignment (lower), see text. The shaded rectangles show the positions of two mechanical slits.

Figure 2

(Color online) Sum (i) and difference (ii) of the output arms of the Sagnac interferometer. The orange (light grey) trace shows unsmoothed data, the blue (dark grey) trace shows the data with a 19 point running average. The probe beam power is $4\mu \mathrm{W}$, the pump beam power is $26\mu \mathrm{W}$. The piezo is used to scan both pump and probe fields over a range of $1.3\mathrm{GHz}$ while the AOM scans the probe field 12 times, over a range of $1.8\mathrm{MHz}$, about the two-photon Raman resonance. The frequency scale applies only to the piezo scan, with 0 defined as the frequency of the $F=1\to F^{\prime }=2$ hyperfine transition. When the Raman resonance condition is met, there is a sharp increase in transmission and a concomitant rapid change in the refractive index. The signals in both plots are normalized such that the sum of the signals in the two arms, away from the Doppler resonance, is equal to one. The Doppler broadened background has been subtracted from both signals.

Figure 3

(Color online) The EIT feature as measured in the Sagnac interferometer, as a function of $\delta ∕2\pi$. The probe power is $3\mu \mathrm{W}$ and the pump power is $28\mu \mathrm{W}$. The signal size is normalized to the sum of the off-resonance signal in both arms. The background signal has been subtracted from each arm after normalization. (i) shows the individual signals from the two output arms of the Sagnac interferometer: A, blue (dark grey) and B, green (light grey). (ii) shows the difference signal between the two arms $\mathrm{A}-\mathrm{B}$. (iii) shows the sum signal of the two arms (green or light-grey solid line), with least-square fits of a Lorentzian function (red or mid-grey dashed line) and a cusp function (blue or dark-grey solid line).

Figure 4

Plot of the FWHM of a Lorentzian dispersion fit to the difference signal for a range of pump powers. Experimental data (circles) with a linear fit (solid line).