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arXiv:1205.0690 · Physical Review A

Phase shift in an atom interferometer induced by the additional laser lines of a Raman laser generated by modulation

Olivier Carraz, Renée Charrière, Malo Cadoret, Nassim Zahzam, Yannick Bidel, Alexandre Bresson

Published Sep 5, 2012• 79 citations
arXivHTMLPDF

Abstract

The use of a Raman laser generated by modulation for a light-pulse atom interferometer allows for a laser system that is compact and robust. However, the additional laser frequencies generated can perturb the atom interferometer. In this article, we present a precise calculation of the phase shift induced by the additional laser frequencies. The model is validated by comparison with experimental measurements on an atom gravimeter. The uncertainty of the phase-shift determination limits the accuracy of our compact gravimeter to $8\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}8}\phantom{\rule{0.28em}{0ex}}\text{m}/{\text{s}}^{2}$. We show that it is possible to reduce this inaccuracy considerably with a better control of experimental parameters or with particular interferometer configurations.

DOI
10.1103/physreva.86.033605

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The use of a Raman laser generated by modulation for a light-pulse atom interferometer allows for a laser system that is compact and robust. However, the additional laser frequencies generated can perturb the atom interferometer. In this article, we present a precise calculation of the phase shift induced by the additional laser frequencies. The model is validated by comparison with experimental measurements on an atom gravimeter. The uncertainty of the phase-shift determination limits the accuracy of our compact gravimeter to 8\ifmmode×\else\texttimes\fi10\ensuremath−8m/s28\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}8}\phantom{\rule{0.28em}{0ex}}\text{m}/{\text{s}}^{2}8\ifmmode×\else\texttimes\fi10\ensuremath−8m/s2. We show that it is possible to reduce this inaccuracy considerably with a better control of experimental parameters or with particular interferometer configurations.
The additional sidebands (ASBs) in a Raman laser will have a significant effect on the performance of atom gravimeters (AGs) based on phase-modulated Raman lasers. We propose a method of modulating the sideband-to-carrier ratio in Raman lasers to determine the magic time intervals where the phase shift induced by the ASB effect is minimized, and this method is demonstrated by experiments. Among these magic time intervals, some noise-immunity points are predicted. Based on the prediction and the result of the ASB effect changing with the interval time T between adjacent Raman pulses, an optimal magic time interval is selected. Therefore, the uncertainty to the gravity measurement induced by the ASB effect when the AG works at the magic time interval is reduced to 0.5 μGal. Furthermore, the ASB effect and its zero-phase points in four-pulse atom interferometers are also discussed. This work provides a clear way to eliminate the phase shift induced by the ASB effect in high-precision AGs employing phase-modulated Raman lasers.
Light-pulse atom gravimetry has emerged as a powerful technique for precisely measuring absolute gravitational acceleration. Raman lasers are commonly used in this technique to coherently manipulate the atomic wave packet, of which the effective frequency is chirped continuously to compensate for the Doppler shift. In this study we investigate an additional phase shift in the Raman lasers that arises due to the frequency chirp. We directly measure this phase shift by recording the beat signal of the Raman lasers with a high-speed oscilloscope, providing an independent evaluation of the resultant error in atom gravimeters caused by this phase shift. Concurrently, we detect the influence of the additional phase shift on gravity measurements using our atom gravimeter, and the results are in good agreement with the independent evaluation. Notably, there may still be a residual error at the microgal level when performing differential measurements by reversing the direction of the effective wave vector of the Raman lasers. We propose that this residual error can in principle be eliminated by selecting the same chirp frequency range for both directions in the differential measurement.
Phase-modulator-generated laser for Raman transition is widely used in atom gravimeters to simplify a system and improve robustness. However, the induced additional sidebands (ASBs) lead to systematic errors in gravity measurement. This work presents a novel, to our knowledge, method to generate an optical single-sideband (OSSB) laser for Raman transition through phase modulation based on a Faraday anomalous dispersion atomic filter (FADOF). The experimental result indicates that it can reduce the additional sidebands with a signal-to-noise ratio (SNR, the intensity ratio of carrier and unwanted sidebands) of better than 50 dB, and the phase shift caused by ASBs is demonstrated to be effectively suppressed from 358.8 to 2.2 mrad. Furthermore, this system has already been applied on an atom gravimeter to achieve a primary gravity measurement. It shows that the FADOF-based Raman laser system is a new scheme for a compact atom absolute gravimeter.
We present here an analysis of the influence of the frequency dependence of the Raman laser light shifts on the phase of a Raman-type atom gravimeter. Frequency chirps are applied to the Raman lasers in order to compensate gravity and ensure the resonance of the Raman pulses during the interferometer. We show that the change in the Raman light shift when this chirp is applied only to one of the two Raman lasers is enough to bias the gravity measurement by a fraction of $\ensuremath{\mu}\mathrm{Gal}$ ($1\phantom{\rule{0.16em}{0ex}}\ensuremath{\mu}\mathrm{Gal}\phantom{\rule{0.28em}{0ex}}=\phantom{\rule{0.28em}{0ex}}{10}^{\ensuremath{-}8}\phantom{\rule{0.28em}{0ex}}\mathrm{m}/{\mathrm{s}}^{2}$). We also show that this effect is not compensated when averaging over the two directions of the Raman wave vector kkk. This thus constitutes a limit to the rejection efficiency of the kkk-reversal technique. Our analysis allows us to separate this effect from the effect of the finite speed of light, which we find in perfect agreement with expected values. This study highlights the benefit of chirping symmetrically the two Raman lasers.
Using the electro-optical modulation method to generate Raman beams for cold atom interference is one of the better methods for constructing a more compact and robust laser system. But this way will generate some residual sidebands resulting in the additional interference phase shift, which can affect the measurement accuracy of cold atom interferometer. In order to weaken the effect of laser modulation sidebands on the phase shift of cold atom interference, a double-sideband suppressed-carrier modulation laser system for cold atom interference is constructed. Based on the designed laser system, the principle of double-sideband generation and suppression is analyzed in detail, and some residual sidebands are adjusted and controlled. Moreover, some important optical parameters that affect the phase shift of cold atomic interference, such as the initial distance between the Raman retro-reflection mirror and the atomic cloud, the interrogation time between two adjacent Raman pulses, the laser modulation depth and the initial velocity of the atomic cloud, are discussed and optimized. By optimizing these relevant parameters, the influence of residual modulation sidebands on the phase shift of cold atomic interference is weakened drastically. The research results indicate, making use of the method of double-sideband suppression, the phase shift of cold atomic interference can be optimized to 0.7 mrad when the initial distance between the Raman retro-reflection mirror and the atomic cloud is 105 mm, and the interrogation time between two adjacent Raman pulses is 82 ms. More importantly, this work can provide a method for weakening the influence of Raman sideband effect on the phase shift of cold atom interferometer, and the corresponding laser system can be applied to other inertial sensors such as atomic gravimeter or atomic gravity gradiometer.
A compact laser system for a portable 87Rb atom interferometry gravimeter has been demonstrated in this work. This laser system is based on frequency doubling of a single seed laser at the wavelength of 1560 nm. The frequency of the seed laser is controlled by a digital unit with an analog feedback circuit. By using this frequency control method, the frequency of the laser system can be shifted over 1 GHz. Based on this method, the Raman frequency can be locked on the F = 3 → F′ = 4 transition of 85Rb atoms. Moreover, the Raman sideband and the repumping laser are generated by a phase modulator, and it can generate different laser frequencies to meet the requirements of a typical atom interferometer. Additional sidebands in the Raman beam produced from the phase modulator are optimized and reduced, allowing us to observe atom interference with a free evolution time of 320 ms. The control unit including the laser system has been integrated into a box with a volume of 1.5 m × 0.6 m × 0.6 m, and the weight of which is only 150 kg. Using this compact optical scheme, our atomic gravimeter has achieved a sensitivity of 53 μGal/Hz1/2 and a resolution of better than 1 μGal (1 μGal = 1 × 10−8 m/s2) in an integration time of 3000 s.