[Paper Review] Velocity-dependent phase shift in a light-pulse atom interferometer

Léo Morel, Zhibin Yao+2 more|arXiv (Cornell University)|Jun 25, 2020

Cold Atom Physics and Bose-Einstein Condensates4 citations

TL;DR

This paper identifies and models a velocity-dependent phase shift in light-pulse atom interferometers caused by intensity variations during Raman pulses, which displaces atomic wavepackets due to asymmetric laser intensity perception. By applying tailored laser power ramps, the authors experimentally suppress this systematic bias, reducing sensitivity to atomic velocity distribution by 80%, enabling improved accuracy in precision measurements like $h/m$ and tests of the equivalence principle.

ABSTRACT

Atom interferometry relies on the separation and recombination of atom wavepackets. When the two paths overlap perfectly at the end of the interferometer, the phase is insensitive to the atomic velocity distribution. Here, we show that, when the separation and recombination is performed using a Raman transition there is a displacement of the atomic wavepacket due to a phase shift during light pulses. Because of the variation of the laser intensity seen by the atoms, there is an imperfect cancellation of these displacements. The observation of a velocity-dependent phase shift on the interferometer is the signature of this effect, which has been modeled. Thanks to the signature we have identified, we are able to compensate for this effect by applying laser power ramps during the interferometer to mitigate intensity variations.

Motivation & Objective

• To identify and model a previously unaccounted velocity-dependent phase shift in Raman-based atom interferometers arising from wavepacket displacement due to intensity variations during light pulses.
• To quantify how this phase shift arises from the imperfect cancellation of displacements caused by spatially varying laser intensity and atomic transverse velocity.
• To develop and experimentally validate a compensation method using laser power ramps to mitigate the sensitivity of the interferometer to the initial atomic velocity distribution.
• To extend the applicability of this model to other interferometer geometries and precision experiments, including $h/m$ measurements and tests of the equivalence principle.

Proposed method

• Theoretical modeling of wavepacket displacement using a general formula for phase shift in Raman transitions, accounting for time-varying Rabi frequency and differential light shifts.
• Derivation of a phase shift formula (equation 15) that includes both wavepacket displacement and light shift contributions, enabling analytical prediction of velocity-dependent phase shifts.
• Experimental implementation using a Ramsey-Bordé interferometer with 87Rb atoms in a thermal cloud (2 cm/s $1/e$ width), incorporating a 500 BOs pulse for transverse velocity selection.
• Application of linear laser power ramps (10% and 20% increase from first to last pulse) to counteract the decreasing average intensity perceived by atoms during the interferometer sequence.
• Scanning the mean Doppler detuning to map the phase response and observe the dispersive signature of the velocity-dependent phase shift.
• Calibration of power ramps without prior knowledge of the velocity distribution, enabling practical compensation in real-world interferometer setups.

Experimental results

Research questions

• RQ1 What causes a velocity-dependent phase shift in Raman-based atom interferometers despite symmetric pulse sequences?
• RQ2 How does the spatial intensity profile of Raman lasers and atomic transverse velocity combine to induce a net phase shift?
• RQ3 Can the phase shift arising from wavepacket displacement be modeled analytically and verified experimentally?
• RQ4 To what extent can laser power ramps reduce the sensitivity of the interferometer to the initial atomic velocity distribution?
• RQ5 How does this effect impact the accuracy of precision measurements such as $h/m$ and tests of the equivalence principle?

Key findings

• The velocity-dependent phase shift arises from uncancelled wavepacket displacements due to time-varying laser intensity perceived by atoms with different transverse velocities.
• Theoretical modeling yields a general phase shift formula that accounts for both Rabi frequency variation and differential light shifts, matching experimental observations.
• Experimental measurements show that the phase shifts as a function of initial velocity follow a dispersive signature, confirming the presence of the effect.
• Applying a 10% linear power ramp from first to last Raman pulse reduces the sensitivity of the interferometer to the initial velocity distribution by approximately 80%.
• The compensation method works without prior knowledge of the atomic velocity distribution and is experimentally calibrated, making it practical for real interferometer systems.
• The approach is generalizable to other Raman-based interferometer geometries and relevant for dual-species tests of the equivalence principle and high-accuracy $h/m$ measurements.