Effect of the Gaussian distribution of both atomic cloud and laser intensity in an atom gravimeter

The mechanism of light-shift-related uncertainty in an atom-interferometry gravimeter is investigated systematically, which arises from the inhomogeneous intensity of Raman beams and the Gaussian distribution of an atomic cloud. Experiments using atom interferometry are performed to verify this systematic error by directly modulating the integration time $T$ and the intensity ratio of Raman laser beams. Using our method, the uncertainty of gravity measurements contributed by the single-photon light shift in an atom gravimeter can be corrected to a $\mathrm{sub}-\mu \mathrm{Gal}(1\mu \mathrm{Gal}=1\times {10}^{-8}\mathrm{m}/{\mathrm{s}}^2)$ level.

Figure 1

(a) The Raman beams geometry, (b) the expansion of atomic cloud, and (c) the $\mathrm{\Lambda }$-type structure of stimulated Raman transition.

Figure 2

The simulations of the ac Stark effect for different interrogation times $T$. The Raman beams' intensity ratio is set to $I_1/I_2=1.07\left(15\mathrm{kHz}\right)$ and $3.49(-15\mathrm{kHz})$. The Gaussian radius $(1/e)$ of the Raman beams is 4.6 mm. The Gaussian radius of the ballistically expanded cloud is about 2 mm at $t=45\mathrm{ms}$.

Figure 3

Experimental setup of the Raman laser optics: Beams of the master and slave lasers are overlapped by a polarized beam splitter (PBS) and amplified by a tapered amplifier (TA). The half-wave plate before the TA is used to adjust the intensity ratio of the Raman beams, the photodiode (PD) is used to monitor the power of the recoupling Raman beams reflected by the Raman mirror, and the microwave is for the measurement of the LS.

Figure 4

The transition probability of an atom stimulated by a microwave. (a) Without Raman beams (black squares). (b) With Raman beams and the LS is negative (red closed circles). (c) With Raman beams and the LS is positive (blue triangles).

Figure 5

The LS versus the angle of the half-wave plate, which is used to adjust the intensity ratio of the Raman beams. The dots are the measured results, and the dashed line is the fitting curve. The power of the Raman beams when we measure the LS is 7 mW, about five times smaller than the one when we measure $g$.

Figure 6

The phase shifts induced by the LS under the condition of the total Raman-beams' power at 35 mW. The measured data (dots) and the theoretical predictions (lines) shown here are in the condition of the light shift at about 15 kHz (black squares and solid line) and $-15\mathrm{kHz}$ (red circles and dashed line), respectively, which related to $I_1/I_2=1.07$ and 3.49. When measuring the LS, we turn on the microwave at $t_0=45\mathrm{ms}$, and the total power of the Raman beams is 7 mW.

Figure 7

The contributions of the LS to the $g$ value at $T=200\mathrm{ms}$ in the $+k$ configuration (black squares), in the $-k$ configuration (red circles), and the average value (green triangles). The dashed lines are the fitting curves. The transients of the two $\pi$/2 pulses are at $t=178$ and $t=578\mathrm{ms}$ after launch. From the linear relation of $f_{\mathrm{LS}}$ and $\mathrm{\Delta }{g}_{+k}^{\mathrm{LS}}$, we get the slope $\beta =-2.68\left(1\right)\mu \mathrm{Gal}/\mathrm{kHz}$.

Figure 8

The linear dependence relation of $\mathrm{\Delta }{g}_{+k}^{\mathrm{LS}}$ and $\mathrm{\Delta }{g}_{-k}^{\mathrm{LS}}$. The points are the measured data, and the dashed line is the linear fitting curve. The slope of the fitting result is $-0.96\left(6\right)$, which indicates $\alpha =-0.02\left(3\right)$.

Figure 9

The long-time performance of LSs and room temperature $\left(T\right)$. The black line displays the LS, and the red dashed line represents temperature.