Test of Equivalence Principle at $10^{-8}$ Level by a Dual-Species Double-Diffraction Raman Atom Interferometer

We report an improved test of the weak equivalence principle by using a simultaneous ${}^{85}\mathrm{Rb}\text{−}{}^{87}\mathrm{Rb}$ dual-species atom interferometer. We propose and implement a four-wave double-diffraction Raman transition scheme for the interferometer, and demonstrate its ability in suppressing common-mode phase noise of Raman lasers after their frequencies and intensity ratios are optimized. The statistical uncertainty of the experimental data for Eötvös parameter $\eta$ is $0.8\times 10^{-8}$ at 3200 s. With various systematic errors corrected, the final value is $\eta =(2.8\pm 3.0)\times 10^{-8}$. The major uncertainty is attributed to the Coriolis effect.

Figure 1

Schematic diagram of the 4WDR scheme. (a) ac Stark shift spectrum of rubidium atoms. (b) Lasers with frequencies of ${\omega }_i(i=1–4)$ are used as Raman beams for ${}^{85}\mathrm{Rb}\text{−}{}^{87}\mathrm{Rb}$ dual-species AI; ${\delta }_1$ is the detuning of ${\omega }_1$, ${\delta }_2$ is the detuning of ${\omega }_2$. ${\omega }_1$ and ${\omega }_2$ are detuned to the blue side of transitions $F=3$ to $F^{\prime }=4$ of ${}^{85}\mathrm{Rb}$ and $F=2$ to $F^{\prime }=3$ of ${}^{87}\mathrm{Rb}$. (c) Diagram of a double-diffraction Raman AI using $k_1,k_2$, and $k_3$. The internal states of atoms don’t change during the double diffraction Raman interferometric process, but the states are $\pm k_{\text{eff}}$ shifted in momentum.

Figure 2

Schematic diagram of experimental setup. Cold atoms trapped in MOT are launched up by moving molasses to form fountains. Raman beams and blow away beam are transited to interference area via single-mode polarization maintain fibers. Population signal of atoms are detected at window A and window B, simultaneously. HWP, half-wave plate; QWP, quarter-wave plate; PBS, polarization beam splitter; PM, polarization maintain; MOT, magneto-optical trap; AOM, acousto-optic modulator; PD, photon detector.

Figure 3

Phase noise suppression by the 4WDR method. A rapid phase modulation is applied to ${}^{85}\mathrm{Rb}$ atoms. (a) Simultaneous ${}^{85}\mathrm{Rb}\text{−}{}^{87}\mathrm{Rb}$ interference fringes obtained by single-diffraction Raman transition method and (b) simultaneous ${}^{85}\mathrm{Rb}\text{−}{}^{87}\mathrm{Rb}$ interference fringes by the 4WDR scheme. The red triangles are experimental data points of ${}^{85}\mathrm{Rb}$ atoms, and the red dotted line is a sine curve fitting. The blue dots are experimental data points of ${}^{87}\mathrm{Rb}$ atoms, and the blue solid line is a sine curve fitting.

Figure 4

Population of ${}^{87}\mathrm{Rb}$ in $F=2$ state vs population of ${}^{85}\mathrm{Rb}$ in $F=3$ state (a) and data for gravity differential measurements (b). The systematical error caused by the difference of effective wave vectors of ${}^{85}\mathrm{Rb}$ and ${}^{87}\mathrm{Rb}$ is corrected. Data A are obtained by probing ${}^{87}\mathrm{Rb}$ atoms at window A while probing ${}^{85}\mathrm{Rb}$ atoms at window B; data B are obtained by altering the probe position. The black line and the blue line are the average values of data A and data B, respectively. The average of data A and data B is $2.8\times 10^{-8}g$ shown as a red line.

Figure 5

Allan deviation of differential gravity measurement data of ${}^{85}\mathrm{Rb}$ and ${}^{87}\mathrm{Rb}$ atoms. The deviation of averaging 3200 s is $0.8\times 10^{-8}$.