[Paper Review] Measuring the Earth's gravity field with cold atom interferometers

Olivier Carraz, Christian Siemes+3 more|arXiv (Cornell University)|Jun 12, 2015

Cold Atom Physics and Bose-Einstein Condensates15 references3 citations

TL;DR

This paper proposes a cold atom interferometer (CAI)-based gravity gradiometer for future Earth observation missions, enabling high-precision measurement of the gravity gradient tensor and spacecraft angular velocity with ultra-low, flat white noise. The instrument achieves 4.7 mE/Hz^1/2 sensitivity and sub-35 prad/s/Hz^1/2 rotation accuracy, offering improved static gravity field resolution over GOCE and potential for hybrid calibration of electrostatic accelerometers to mitigate low-frequency noise.

ABSTRACT

The scope of the paper is to propose different concepts for future space gravity missions using Cold Atom Interferometers (CAI) for measuring the diagonal elements of the gravity gradient tensor, the spacecraft angular velocity and the spacecraft acceleration. The aim is to achieve better performance than previous space gravity missions due to a very low white noise spectral behaviour of the CAI instrument and a very high common mode rejection, with the ultimate goals of determining the fine structures of the gravity field with higher accuracy than GOCE and detecting time-variable signals in the gravity field.

Motivation & Objective

• To develop a spaceborne cold atom interferometer (CAI) gravity gradiometer that outperforms GOCE in static gravity field resolution.
• To measure all diagonal elements of the gravity gradient tensor and full angular velocity vector using a single CAI instrument.
• To achieve flat, white noise spectral density down to low frequencies, enabling better detection of time-variable gravity signals.
• To explore hybridization with electrostatic accelerometers to correct colored noise in low-frequency bands.
• To evaluate the feasibility of CAI-based gravity missions for monitoring fine structures and temporal changes in Earth's gravity field.

Proposed method

• Utilizes a Chu-Bordé interferometer with three equally spaced Raman laser pulses to drive stimulated Raman transitions between hyperfine states of cold atoms.
• Employs a double diffraction scheme to enhance sensitivity by a factor of two and suppress first-order parasitic effects like light shifts and magnetic fields.
• Uses four spatially separated atom interferometers to simultaneously measure gravity gradients and rotation rates via the Coriolis effect on atomic clouds.
• Relies on high common-mode rejection by combining phase measurements from multiple interferometers to cancel vibration and non-gravitational noise.
• Applies precise knowledge of inter-atomic cloud separation and velocity to extract gravity gradient components (Vxx, Vyy, Vzz) and angular rates (ωx, ωy, ωz).
• Proposes hybridization by mounting the Raman mirror on the proof mass, enabling direct comparison and calibration of CAI and electrostatic accelerometer signals.

Experimental results

Research questions

• RQ1 Can a CAI-based gravity gradiometer achieve sub-5 mE/Hz^1/2 sensitivity with flat, white noise power spectral density at low frequencies?
• RQ2 To what extent can CAI measurements improve the resolution of fine structures in Earth's static gravity field compared to GOCE?
• RQ3 Can CAI measurements detect time-variable gravity signals with sufficient sensitivity, or is a GRACE-type mission more suitable?
• RQ4 How effective is hybridization between CAI and electrostatic accelerometers in correcting spectrally colored noise in low-frequency bands?
• RQ5 What system-level parameters (altitude, orbit, mission duration, attitude control) most significantly affect the performance of a CAI gravity gradiometer mission?

Key findings

• The CAI gravity gradiometer achieves a sensitivity of 4.7 mE/Hz^1/2, with a flat noise power spectral density extending into the low-frequency range.
• Rotation rate measurements reach an accuracy of below 35 prad/s/Hz^1/2, enabling precise determination of spacecraft angular velocity.
• High common-mode rejection allows for relaxation of drag-free control requirements compared to GOCE, as non-gravitational forces can be measured directly.
• Estimation of Earth gravity field models shows improved static field resolution, but significant sensitivity improvements are needed to detect time-variable signals effectively.
• Hybridization with electrostatic accelerometers is feasible and effective, as demonstrated on ground, enabling correction of colored noise in low-frequency bands while preserving short-term sensitivity.
• Future enhancements via squeezed states or information-recycling beam splitters could improve SNR by up to three orders of magnitude, approaching the Heisenberg limit.