MIGA Atom Interferometer Experiment

• Atom interferometry is a precision measurement technique that employs coherent matter-wave manipulation to detect inertial and gravitational effects.
• The experiment utilizes laser-cooled rubidium atoms in a Mach-Zehnder configuration with Bragg diffraction to record phase shifts from environmental perturbations.
• Large-scale implementations like MIGA enable detection of gravitational waves and detailed geophysical monitoring in a low-frequency operational band.

An atom interferometer (AI) experiment utilizes coherent manipulation of atomic matter waves to implement interference phenomena analogous to those in optical systems, but with enhanced sensitivity to inertial, gravitational, and potential effects due to the properties of atoms. High-precision AI experiments leverage laser-cooled atomic ensembles, controlled optical interactions (such as Bragg diffraction), and state-of-the-art detection schemes to probe fundamental physics, developing new measurement standards and enabling searches for phenomena such as gravitational waves and ultralight dark matter. The following sections detail large-scale, networked AI systems for precision geophysics and gravitational wave detection, focusing on the MIGA experiment at Laboratoire Souterrain à Bas Bruit (LSBB).

1. Measurement Principle of Large-Scale Atom Interferometry

The measurement principle in MIGA is based on an in-cavity atom interferometer configuration. Multiple AI sensors are simultaneously interrogated by the resonant field of a long, ultra-stable optical cavity. Cold rubidium atoms are launched in free fall and subjected to a three-pulse (π/2–π–π/2) Mach–Zehnder sequence in the Bragg regime. Each AI records a phase shift, Δφ_AT, imparted by the laser pulses as a function of the local inertial environment and external perturbations: $P = \frac{1}{2}[1 - \cos(\Delta\phi_{\rm AT})]$ The response function, incorporating the Bragg diffraction order $n$, is given via the sensitivity function formalism by: $$\Delta \phi_{\rm AT}(t) = n \int_{-\infty}^{\infty} s(T - t) \frac{d}{dT}\Delta \varphi(T)\, dT = n [\Delta \varphi(t) * \frac{ds(t)}{dt}]$$ where $s(t)$ is the interferometer sensitivity function and $*$ denotes convolution. The phase imprint $\Delta\varphi(t)$ is determined by the instantaneous frequency of the intracavity field, which is modulated by the input laser frequency noise, cavity mirror vibrations, and gravitational wave strain $h(t)$. Specifically,

$\Delta\varphi(t) = 2\pi \Delta t_r \nu(t)$

where $\nu(t)$ is the carrier frequency and $\Delta t_r$ the effective time delay.

2. Gravitational Wave Signal Extraction

Extraction of the gravitational wave (GW) signal involves a differential comparison of the phases recorded by atom interferometers positioned at different locations along the cavity. The differential gradiometer observable is: $$\Gamma(t) = \Delta \phi_{\rm AT}(0, t) - \Delta \phi_{\rm AT}(L, t)$$ Noise sources—including input laser frequency fluctuations, mirror vibrations, detection projection noise, and Newtonian (gravity gradient) noise—are modeled in the power spectral density of $\Gamma(t)$. The GW-induced strain contribution, after filtering by the cavity response, appears in the spectrum as proportional to $S_h(\omega)$: $$S_\Gamma(\omega) = \left[4 n \pi \nu_0 L/c \right]^2 \left\{ [1 + (\omega^2/\omega_p^2)] (S_{\delta\nu}(\omega)/\nu_0^2 + S_h(\omega)/4) + \cdots \right\}| \omega G(\omega)|^2 + 2 S_\alpha(\omega)$$ where $\omega_p$ is the cavity frequency pole, $S_{\delta\nu}(\omega)$ the laser frequency noise, and $S_\alpha(\omega)$ the detection (projection) noise. The signal-to-noise ratio (SNR) is constructed from the ratio of the GW-induced term to total noise, and the strain sensitivity $S_h(\omega)$ is determined via the SNR $=1$ criterion.

3. Strain Sensitivity and Frequency Band Targeted

In its nominal configuration (cavity length $L=200\,{\rm m}$, finesse $F=100$, interrogation time $2T=500\,{\rm ms}$, first-order Bragg diffraction), the MIGA instrument achieves projected peak strain sensitivity: $$S_h^{1/2} \approx 2.2 \times 10^{-13} \, {\rm Hz}^{-1/2}\ \text{(at } 2\,\mathrm{Hz})$$ The limiting factor is quantum projection noise during fluorescence detection, with the design optimizing for the 100 mHz–1 Hz frequency range—well below that of current ground-based optical interferometers (e.g., LIGO), providing access to GW sources and geophysical phenomena inaccessible to existing observatories. This regime includes the inspiral phases of compact binaries years prior to merger and geological mass reconfigurations.

4. Instrument Architecture and Subsystem Functionality

MIGA comprises a hybridized set of atom–laser systems with the following subsystems:

• Atomic Sources: Each atomic head uses a 2D–MOT to accumulate Rb atoms, which are further cooled in a 3D–MOT to the μK scale. The atoms are launched in free fall, then state-prepared (optical pumping and Raman transitions) to the desired magnetic sublevel.
• Optical Cavities: Two horizontally oriented 200 m long cavities provide the optical pulses for Bragg diffraction. A master telecom laser (1560 nm) is frequency-doubled to 780 nm, enabling simultaneous spatial filtering and temporal modulation via the cavity.
• Stabilization Systems: The cavities are stabilized both actively (piezo actuation and feedback) and passively (vibration isolation). High mechanical and thermal stability are achieved via underground location and robust mounting.
• Vacuum and Magnetic Environments: The interrogation regions maintain pressures below $10^{-9}$ mbar; multiple μ-metal shields minimize external magnetic field fluctuations.
• Detection and Timing: Fluorescence detection is used after the trajectory apex to read out the population in output ports. The three AIs are synchronized for common-mode environmental noise rejection in differential signal processing.

This integrated architecture enables detection of minute phase shifts with reduced sensitivity to technical noise.

5. Environmental Control and Site Characteristics

MIGA's site at LSBB (Rustrel, France) offers exceptional characteristics for precision AI operation:

• Low Seismic and Electromagnetic Noise: Up to 500 m underground, the laboratory is shielded by extensive bedrock. Ambient seismic noise is among the lowest in Europe, verified by broadband seismic sensors and superconducting gravimeters, directly reducing GGN and vibrational phase noise.
• Minimal Anthropogenic Disturbance: The facility's remoteness eliminates most vibration and EM interference attributable to human activity.
• Ambient Stability: The underground gallery maintains temperature fluctuations below 0.1°C and air pressure stability, optimizing optical alignment, cavity length, and overall measurement conditions.
• Multidisciplinary Infrastructure: Other geophysical sensors (seismometers, gravimeters, strainmeters, magnetometers) are networked for correlating AI output with environmental data, and the laboratory's location in a karst aquifer provides unique opportunities for coupled hydro-geophysical studies.

Given these properties, LSBB supports long-term, high-precision AI measurements essential for GW detection and high-resolution geoscience.

6. Multidisciplinary Potential and Outlook

The MIGA experiment exemplifies the transition of AI from laboratory-scale to large-scale, multidisciplinary instrumentation. Key implications:

• Gravitational Wave Astrophysics: Sensitivity in the 0.1–1 Hz band bridges a gap between LISA (space-based, $\sim10^{-4}$–1 Hz) and ground-based optical interferometers ($\sim10$–$10^3$ Hz), potentially capturing GWs from early-inspiral binaries or exotic cosmological sources years before final merging.
• Geoscience: Fast, high-sensitivity monitoring of local gravity variations, including aquifer mass redistributions or tectonic events, is enabled by the ability to operate AIs in a coordinated, spatially distributed network.
• Measurement Science and Technology Transfer: The integration of cavity-enhanced, Bragg-based matter-wave optics with robust environmental control paves the way for portable, scalable AI networks for a variety of precision measurement tasks.

This comprehensive approach demonstrates the utility of the in-cavity AI platform not only for fundamental physics—such as GW astronomy and tests of gravity—but also for advancing precision monitoring in Earth sciences and potentially other application domains.