Real-time phase control methods for cold-atom interferometry

TL;DR

This work addresses real-time inertial phase compensation (RTC) in cold-atom interferometers to suppress vibration-induced phase noise while maintaining mid-fringe sensitivity. It introduces two alternative RTC methods for retroreflected Raman/Bragg configurations—mirror-position jumps and frequency jumps—complementing the traditional Raman-laser phase-jump approach, with the underlying phase control described by $\Delta\Phi^{\pm}=\mp k_\mathrm{eff}\,\delta l$ and $\Delta\Phi^{\pm}=\mp\delta\Delta\,\tau$, respectively. Experimental results on a Cs gyroscope show state-of-the-art rotation sensitivity and an Allan deviation scaling as $\mathrm{ADEV}\propto \tau^{-1/2}$, achieving roughly a 7-fold reduction in vibrational noise. The methods are presented as complementary, all-optical or minimally mechanical options that can extend RTC applicability to spaceborne sensors and to double-diffraction schemes, broadening the operational envelope of atomic interferometers.

Abstract

We present two methods to achieve real-time inertial phase compensation in atom interferometers. Both methods, based on jumps of the position of the retroreflection mirror or frequencies of Raman lasers, demonstrate similar state-of-the-art performance on our cold atom gyroscope, comparable to that of the reference method based on optical phase jumps. These alternative approaches broaden the scope of applications for real-time inertial phase compensation methods in atomic interferometers, particularly for space applications.

Figures (6)

• Figure 1: (Left) Scheme of the experimental setup. Atomic clouds are prepared at the bottom of the chamber, launched vertically and interact with two pairs of Raman lasers in a sequence of four pulses, numbered from 1 to 4, before falling back into the detection area. M1 and M2: retroreflection Raman lasers mirrors. L: distance from the mirror M1 to the positions of the atom cloud at the fourth pulse. The Raman laser beams are slightly tilted by 4° in the vertical direction. (Right) Diagram of the space-time diagram of the interferometer sequence. Beamsplitters and mirrors are realized by a set of Raman pulses of areas $\pi/2$ and $\pi$. The real-time compensation of the vibrations is applied just at a time $t_{RTC}$ before the beginning of the last beamsplitter pulse. The laser beams at frequency $\omega_{3}$ (respectively $\omega_{4}$) are represented in red (respectively blue). $\pi/2$ pulses (respectively $\pi$ pulses) are retroflected on mirror M$_1$ (respectively M$_2$)
• Figure 2: Schematic diagram of the two alternative methods developed in order to control the output phase of the interferometer. The two Raman lasers are brought together in the experiment and retroreflected on the mirror. Real-time compensation is achieved by modifying the optical phase difference between the two counter-propagating Raman light fields at the position of the atoms before the last pulse: a) by moving the retroreflecting mirror and b) by modifying the effective wave vector of the Raman transition. Only the laser fields involved in the transition are shown.
• Figure 3: Variation of the interferometer phase as a function of the mirror displacement between the third and fourth pulses. The x-axis shows the control voltage of the nanopositioner. Dots are the experimental results average over 700 cycles. Dashed line is the linear fit with a slop of $43.08(15) \,\mathrm{rad.V}^{-1}$.
• Figure 4: Characterization of modifications to the Raman bench in order to achieve a frequency jump while keeping the Rabi frequency constant: a) post-frequency jump time evolution of error signals from the frequency and phase control system of laser L3, on the top, and L4, on the bottom, versus reference-locked to laser L1 and laser L3 respectively (see text). b) relative optimum power to preserve the $\pi$ or $\pi/2$ pulse conditions as a function of Raman detuning. The reference point is set at maximum Raman detuning for $\abs{\Delta}=1555\ \mathrm{MHz}$. Each point is deduced from the Rabi oscillations based on measurement over 30 cycles. The Dashed orange line is a linear fit of the data points with a slope of $4.6$% variation in optimum power per $100\ \mathrm{MHz}$ variation of the Raman detuning.
• Figure 5: Atom interferometer phase shift as a function of the frequency jump before the last pulse, while keeping $\Omega_\text{Rabi}$ constant. Dots are the experimental results average over 700 cycles. The dashed line represents a linear fit of the experimental data with a slope of the $3.786(6)\ \mathrm{mrad/MHz}$.