TVLBAI: Terrestrial VL Atom Interferometer

• TVLBAI is a quantum sensor that uses matter-wave interferometry across tens to hundreds of meters, enabling precise tests of gravity and inertial effects.
• It utilizes controlled light pulses and ultracold atomic ensembles to amplify phase shifts, with sensitivity scaling quadratically with interrogation time and baseline length.
• Advanced TVLBAI designs leverage multi-species atom sources, long free-fall trajectories, and state-of-the-art noise mitigation techniques to achieve sub-nm/s² measurement precision.

A Terrestrial Very Long Baseline Atom Interferometer (TVLBAI) is a quantum sensor employing matter-wave interferometry over macroscopic distances, typically from tens to hundreds of meters, to achieve high sensitivity in probing inertial effects, gravity gradients, gravitational waves, dark matter couplings, and to test fundamental principles such as the Universality of Free Fall and Einstein’s Equivalence Principle. These devices utilize precisely controlled pulses of coherent light to manipulate ultracold atomic ensembles over extended free-fall or ballistic trajectories, exploiting long interrogation times with phase readouts that scale quadratically or cubically with both baseline length and interaction duration. TVLBAI projects are conceived as a networked global programme, integrating novel atom-optics technologies, quantum state control, and advanced environmental mitigation strategies, targeting sensitivities not accessible to conventional detectors.

1. Fundamental Principles and Motivation

TVLBAI exploits the quantum interference of matter waves—specifically, ultracold atomic ensembles manipulated via sequences of light pulses—in architectures designed for extended free evolution times and macroscopic spatial separation between measurement regions. The fundamental phase shift in a Mach–Zehnder–type atom interferometer is given by:

$\Delta\phi = k_\text{eff} \cdot a \cdot T^2$

where $k_\text{eff}$ is the effective momentum imparted by laser pulses, $a$ is the acceleration, and $T$ is the time between pulses. Sensitivity to inertial effects and gravitational fields is thus greatly enhanced by maximizing $T$, which, in turn, requires a large baseline. Gravitational wave detection leverages this quadratic scaling with interrogation time and linear scaling with baseline $L$:

$$\Delta\phi_{\mathrm{GW}} \sim h \cdot k_\text{eff} \cdot L$$

where $h$ is the strain amplitude of the incident gravitational wave (Schlippert et al., 2019, Abend et al., 2023, Balaz et al., 27 Mar 2025). The quantum nature of the atom-light interaction enables direct probing of matter-wave phase evolution, providing exceptional precision for tests of gravity, fundamental constants, and searches for ultralight fields.

2. Experimental Architectures and Baseline Scaling

TVLBAI systems are realized in vertical shafts or horizontal tunnels accommodating ultra-high vacuum tubes extending from 10 to 100 meters (current prototypes) and up to kilometers (future roadmap). Exemplary facilities include the Hannover VLBAI (10 m), ZAIGA (up to 3 km planned), MAGIS (100 m at Fermilab), and candidate projects in PX46 at CERN and Boulby mine (Hartwig et al., 2015, Zhan et al., 2019, Arduini et al., 2023, Balaz et al., 27 Mar 2025, Baynham et al., 15 Sep 2025).

The general architecture is:

• Dual or Multi-Species Sources: Independent atomic sources (e.g., ^87Rb, ^87Sr, ^170Yb) cooled and trapped, loaded into a common optical dipole trap.
• Baseline and Trajectory: Atoms are launched or dropped into the long vacuum tube, where interrogation times (up to several seconds) are achieved. The baseline determines both maximum T and spatial resolution for inertial and gravitational sensing.
• Interferometric Sequence: Light-pulse beam splitters (Bragg or clock transitions) impart momentum kicks proportional to photon recoil, optimizing scale factor matching for multi-species UFF tests and large-momentum-transfer (LMT) enhancement ($n$ up to $10^4$ photons) (Abend et al., 2023, Schach et al., 11 Jun 2025).
• Reference and Readout: Retroreflecting mirror systems and advanced seismic isolation (e.g., geometric anti-spring filters) provide a phase reference. Fluorescence or absorption imaging of output ports reads out population differences and phase.

Extensive magnetic shielding is employed (residual fields < 4 nT, gradients < 2.5 nT/m), vital for suppressing Zeeman-induced biases to sub-picometer/s² levels (Wodey et al., 2019, Lezeik et al., 2022).

3. Measurement Strategies and Sensitivity Optimization

Three primary strategies enhance sensitivity in TVLBAI:

• Very-long baseline (baseline $L$): Larger separation increases the GW-induced phase shift. Differential configurations (spatially separated interferometers) isolate signals from gravitational waves and gradients.
• Resonant Multi-Diamond Geometries ($Q$): Coherent accumulation of phase across repeated interferometric loops amplifies GW and signal response (e.g., vertically-stacked fountains).
• Large-momentum-transfer Pulse Techniques ($N$): Multiple photon recoil pulses increase wave packet separation and phase shift amplitude. However, high pulse numbers demand extreme pulse fidelity to minimize atom loss ($\lambda$ per pulse), with optimal pulse numbers bounded by the exponential atom loss formula:

$N_\text{at} = N_0 (1-\lambda)^{N_P}$

where $N_P$ is the total number of pulses (Schach et al., 11 Jun 2025).

Delta-kick cooling and double-lens schemes achieve expansion energies down to the picoKelvin regime, critical for maintaining coherence over multi-second free-fall (Hartwig et al., 2015).

Sensitive gradiometric and curvature measurement protocols (e.g., co-located Mach–Zehnder and symmetric double diffraction sequences) allow local extraction of gravitational curvature with phase scaling as $T^3$ (Werner et al., 5 Sep 2024).

4. Applications: Fundamental Physics, Metrology, and Astrophysics

TVLBAI enables diverse applications:

• Universality of Free Fall and Equivalence Principle Tests: By comparing ultracold atomic species with distinct nucleonic compositions (e.g., Rb vs. Yb), TVLBAI can measure the Eötvös ratio to $7\times10^{-13}$ accuracy, probing composition-dependent violations parameterized by effective charges $\Delta Q'_A,B$ (Hartwig et al., 2015).
• Absolute Gravimetry and Reference Standards: Gravity measurements with sub-nm/s² sensitivity (uncertainty < 10 nm/s²) enable applications in geodesy, hydrology, and calibration of mobile gravimeters (Schilling et al., 2020, Lezeik et al., 2022).
• Gravitational Wave Detection: TVLBAI covers the “mid-frequency” band (0.1–10 Hz) inaccessible to LIGO/Virgo (10–1000 Hz) and LISA (mHz). Configurations such as ZAIGA–GW (kilometer-scale equilateral triangle) enable detection of intermediate-mass black-hole mergers and stochastic backgrounds. Joint operation with conventional interferometers significantly tightens bounds on dipole radiation parameters in alternative gravity models ($|B|\lesssim10^{-10}$) (Zhao et al., 2021).
• Search for Ultralight Dark Matter (ULDM): By monitoring modulations of atomic transition frequencies and phase, TVLBAI experiments probe coherent bosonic fields and new couplings, with vertical side-arm layouts facilitating differential measurements (Baynham et al., 15 Sep 2025).
• Quantum Fundamental Tests: Large baseline and long coherence times allow exploration of quantum decoherence, gravity-induced phase shifts, and tests of quantum mechanics at macroscopic scales (Schlippert et al., 2019).

5. Technical Challenges and Innovations

Scaling TVLBAI systems involves overcoming significant challenges:

• Pulse Fidelity and Atom Loss: Requirements for atom-light interaction loss per pulse ($\lambda \lesssim 10^{-5}$) are unmet in current experiments ($\lambda \sim 10^{-3}$), necessitating advances in pulse-shaping, optimal control, and dichroic mirror technology (Schach et al., 11 Jun 2025).
• Environmental Noise Mitigation: Seismic and Newtonian gravity gradient noise (GGN) pose fundamental sensitivity limits. Underground sites (mountains, mines, tunnels) and multi-sensor noise subtraction with Wiener filtering are essential (Abend et al., 2023, Abdalla et al., 19 Dec 2024).
• Magnetic Shielding: Modular, high-performance shields achieve residual field budgets needed for Zeeman bias suppression. Designs offer scalability to kilometer class (Wodey et al., 2019).
• Beam Delivery and Alignment: Over long baselines, Coriolis compensation and robust laser delivery (pivot point tuning, relay imaging systems) maintain overlap between atom trajectories and beam center, ensuring high pulse efficiency and phase accuracy (Glick et al., 2023).
• Gravity Gradient and Local Environment Modeling: Precise building and site modeling enables correction for gravitational non-linearities (bias shifts $\delta g \sim 2.6$ nm/s²) necessary for metrological standards (Schilling et al., 2020, Lezeik et al., 2022).
• Atom Source and Quantum State Control: High-flux, ultracold sources (with EIT cooling and squeezing) deliver large atom numbers and reduced shot noise, supporting advanced quantum metrology (Abdalla et al., 19 Dec 2024).

6. Roadmap, Collaboration, and Future Directions

An international proto-collaboration under the TVLBAI initiative (signed by over 50 institutions (Abdalla et al., 19 Dec 2024)) is coordinating the staged deployment and technological advancement of long-baseline atom interferometers:

• Prototyping and Demonstrator Experiments: 10-m scale devices (e.g., Hannover, Magis, Wuhan) serve as testbeds for techniques and environmental isolation (Schlippert et al., 2019).
• 100-m Scale Devices: The PX46 shaft at CERN and Boulby mine are prime sites for larger vertical systems (with feasibility, safety, and cost studies completed), integrating advanced access, shielding, and evacuation apparatus for concurrent operation with accelerator facilities (Arduini et al., 2023, Arduini et al., 13 Aug 2025, Baynham et al., 15 Sep 2025).
• km-Class Detectors: Conceptual designs and site selection studies for kilometer-baseline detectors (SURF, LSBB, Gotthard Tunnel) are ongoing, aiming for mid-2030s operation (Abend et al., 2023, Abdalla et al., 19 Dec 2024, Balaz et al., 27 Mar 2025).
• Networked Operation and Fundamental Science: TVLBAI’s future vision includes networked, multi-site operation for GW triangulation and beyond-standard-model physics searches, employing advanced quantum metrology (entanglement-enhanced sensing, cavity squeezing) and precision calibration standards.

The collaborative framework facilitates multi-disciplinary expertise, rapid R&D cycles, and rigorous environmental modeling, targeting technological milestones such as momentum transfer at $10^4$ photon recoils, robust atom source engineering, and real-time noise cancellation. Integration with existing GW detector networks and geodetic infrastructures further amplifies impact across physics and applied science.

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This comprehensive overview reflects the technical depth, architectural diversity, methodological advances, and strategic vision inherent to Terrestrial Very Long Baseline Atom Interferometry, as documented in recent international collaborations, workshop proceedings, and implementation studies (Hartwig et al., 2015, Zhan et al., 2019, Schlippert et al., 2019, Wodey et al., 2019, Schilling et al., 2020, Zhao et al., 2021, Lezeik et al., 2022, Arduini et al., 2023, Abend et al., 2023, Glick et al., 2023, Werner et al., 5 Sep 2024, Abdalla et al., 19 Dec 2024, Balaz et al., 27 Mar 2025, Baynham et al., 12 Apr 2025, Schach et al., 11 Jun 2025, Arduini et al., 13 Aug 2025, Baynham et al., 15 Sep 2025).