Vertical Long-Baseline Atom Interferometer

• Vertical long-baseline atom interferometry is a method that uses extended free-fall times and meter-scale separations to achieve high phase sensitivity via Earth's gravity.
• The technique employs a three-pulse Mach–Zehnder sequence where the phase shift scales with T², enabling applications in absolute gravimetry, free-fall tests, and gravitational wave detection.
• Facility implementations range from 10 m to 800 m, integrating advanced shielding, optical delivery, and noise suppression strategies to meet diverse scientific goals.

Vertical long-baseline atom interferometry denotes ground-based atomic matter-wave interferometry on large scales in space and time, implemented in a vertical geometry so that free evolution times of several seconds and wave-packet separations at the scale of meters become accessible. In its standard light-pulse realization, the basic observable is the interferometric phase, which for uniform acceleration obeys $\Delta\phi=\vec k_{\rm eff}\cdot\vec a\,T^2$; the vertical layout uses Earth’s gravity to maximize $T$, while gradiometer and multi-gradiometer configurations suppress common-mode noise and extend the technique from absolute gravimetry to universality-of-free-fall tests, gravity-gradient and curvature sensing, ultralight-dark-matter searches, and gravitational-wave detection in the band around $10^{-2}$ to $10$ Hz (Schlippert et al., 2019, Balaz et al., 27 Mar 2025).

1. Interferometric principle in a vertical baseline

A vertical long-baseline atom interferometer is typically a light-pulse Mach–Zehnder device using a $\pi/2$–$\pi$–$\pi/2$ sequence with pulse separations $T$. In the leading approximation, the acceleration phase is

$\Delta\phi = \vec k_{\rm eff}\cdot\vec a\,T^2,$

or, in the local gravitational field,

$\Delta\phi^{(0)} = k_{\rm eff}\,g\,T^2.$

The corresponding shot-noise-limited single-shot acceleration sensitivity is

$T$0

These relations are the central reason vertical devices pursue long free-fall or fountain trajectories: the scale factor grows quadratically with $T$1 (Schlippert et al., 2019).

The vertical geometry is used for both single-interferometer accelerometry and differential configurations. For two vertically separated atom interferometers sharing the same optical interrogation, the differential phase measures the local gravitational difference, and for gravitational-wave applications the leading differential response may be written as

$T$2

with corresponding strain sensitivity

$T$3

At low frequencies, $T$4, so long baselines and long interrogation times are jointly advantageous (Balaz et al., 27 Mar 2025).

Several design rationales recur across the literature. Vertical shafts align ballistic trajectories with Earth’s gravity field, allow single-beam geometry and comparatively simple vacuum and laser-delivery systems, avoid long horizontal tunnels with tight curvature and large civil-engineering costs, and suppress tilt-coupling while simplifying multi-loop interferometer implementations. This suggests that the “long-baseline” attribute is not only a matter of linear dimension, but of exploiting a vertical free-fall geometry in which $T$5 is itself a design resource (Balaz et al., 27 Mar 2025).

2. Facility-scale realizations and representative architectures

Existing and proposed implementations span scales from about $T$6 m to the km class. The Hannover VLBAI facility is built around a vertically oriented ultra-high-vacuum tube of length $T$7 and internal diameter $T$8, with drop mode at $T$9 and fountain mode at $10^{-2}$0 (Schlippert et al., 2019). ZAIGA incorporates a $10^{-2}$1-m vertical tunnel with atom fountain and atom clocks mounted, while its present vertical interferometric concept uses two axially separated atom-interferometer fountains of nominally $10^{-2}$2 m height that are extendable to the full $10^{-2}$3 m in a later phase (Zhan et al., 2019). At CERN, the PX46 access shaft is a $10^{-2}$4 deep, $10^{-2}$5-diameter vertical shaft that has been studied as the host for a $10^{-2}$6 m atom interferometer of the “AION-100” type (Arduini et al., 13 Aug 2025). At Sedrun, two vertical shafts of nominal depth $10^{-2}$7 m have been assessed as a candidate site for a future large-scale experiment (Guinchard et al., 5 Mar 2026).

Facility or programme	Vertical scale	Distinguishing feature
Hannover VLBAI	$10^{-2}$8 m	Drop and fountain modes for gravimetry and UFF
CERN PX46 / AION-100 type	$10^{-2}$9 m scale	Two launch zones separated by $10$0 m
ZAIGA vertical shaft	$10$1 m shaft	Two vertically separated fountains, extendable to full shaft
Sedrun candidate	$10$2 m shaft	Environmental measurements for a future large-baseline AI

For the CERN implementation study, the indicative benchmark parameters for a $10$3 m AI are explicit: $10$4, $10$5, $10$6 $10$7 pulses, $10$8, $10$9 atoms, $\pi/2$0, phase noise $\pi/2$1, and $\pi/2$2; strontium is envisaged as the atomic species, following the AION-100 design (Arduini et al., 13 Aug 2025). The TVLBAI Proto-Collaboration has organized these scales into a staged programme: prototype and precursor devices at $\pi/2$3, Stage I instruments in $\pi/2$4 vertical shafts, and Stage II plans at $\pi/2$5 (Balaz et al., 27 Mar 2025).

The coexistence of these architectures reflects differing scientific priorities. Ten-metre systems emphasize precision gravimetry, calibration, and dual-species tests, whereas $\pi/2$6-m and longer shafts are aimed at ULDM and mid-band GW sensitivity. A plausible implication is that vertical long-baseline atom interferometry is developing as a tiered infrastructure rather than a single canonical instrument class.

3. Atomic sources, interrogation topologies, and optical delivery

Atomic-source choices in vertical long-baseline interferometry are diverse. Hannover combines dual-species sources at the top and bottom ends of the tube, including $\pi/2$7 and bosonic and fermionic ytterbium isotopes, prepared by magneto-optical trapping, evaporative cooling, and delta-kick collimation to reach $\pi/2$8 temperatures (Schlippert et al., 2019). The rubidium–ytterbium equivalence-principle proposal at HITec Hanover specifies a $\pi/2$9 m vertical tube, two independent source chambers, Bose–Einstein-condensate atom numbers $\pi$0 and $\pi$1 in a $\pi$2 s cycle, and operation in both drop mode and fountain mode (Hartwig et al., 2015). For long-baseline strontium at CERN, two launch zones are envisaged, one near the bottom of the tube and a second vertically displaced by $\pi$3 m, with common-laser-link gradiometers and state-selective fluorescence detection (Arduini et al., 13 Aug 2025).

Vertical fountain operation has also been developed as a source-engineering problem in its own right. In ytterbium Bose–Einstein-condensate experiments, Bloch oscillations in vertical lattice beams have been used to launch a $\pi$4-atom $\pi$5Yb BEC with typical parameters $\pi$6 and $\pi$7, leading to a fountain height of about $\pi$8 mm. The same work demonstrated a shaped optical potential for gravity compensation and a pulsed optical matter-wave lens; the latter reduced velocity spread by more than a factor of five, with Ramsey coherence time increasing from $\pi$9 to $\pi/2$0 (Gochnauer et al., 2021). Although this implementation is not itself a hundred-metre device, it provides enabling techniques for vertical fountain interferometry.

Topologically, vertical devices use several related geometries. The standard form is the three-pulse Mach–Zehnder. Differential gravity-gradient sensing can be implemented as a double Mach–Zehnder, as in the ytterbium fountain work, where the differential phase is dominated by $\pi/2$1 (Gochnauer et al., 2021). A co-located gradiometric interferometer combines an upper standard Mach–Zehnder interferometer and a lower Symmetric Double-Diffraction Interferometer so that their differential signal isolates the curvature of the gravitational potential, with

$\pi/2$2

for a purely quadratic field (Werner et al., 2024).

Optical delivery over long vertical baselines creates its own constraints. For MAGIS-100, Coriolis-force compensation is performed by adjusting the angle of the interferometer beam prior to a magnifying telescope so that the beam pivots about a tunable point along the baseline. The telescope design uses $\pi/2$3, $\pi/2$4, a separation of $\pi/2$5, and magnification $\pi/2$6, producing an output waist of about $\pi/2$7 cm with Rayleigh range $\pi/2$8 m. The associated free-space plus short-fiber laser transport system maintained single-mode coupling $\pi/2$9 continuously over $T$0 h with no realignment, RMS power-coupling fluctuations of about $T$1, and long-term drift $T$2 per day (Glick et al., 2023). In the CERN study, a single master oscillator seeds two fibre amplifiers, upward and downward delivery paths, and active fibre-noise cancellation referenced to an ultra-stable cavity (Arduini et al., 13 Aug 2025).

4. Environmental control, magnetic shielding, and dominant systematics

Magnetic and gravitational environment control is a defining requirement of the vertical long-baseline format. A dedicated $T$3 m-long magnetic shield for Very Long Baseline Atom Interferometry has been built as two concentric octagonal-prism shells surrounding the vacuum tube. It achieves residual fields below $T$4 and longitudinal inhomogeneities below $T$5 over $T$6 m, with a modular design that can be extended to longer baselines without compromising shielding performance. In the magnetostatic regime the measured transverse shielding factor satisfies $T$7, while the longitudinal shielding is $T$8 lower because of the large length-to-diameter ratio $T$9 (Wodey et al., 2019).

Within the Hannover VLBAI facility, the measured residual magnetic-field gradients in the region of interest imply a bias acceleration of only $\Delta\phi = \vec k_{\rm eff}\cdot\vec a\,T^2,$0, whereas the evaluated bias shift due to the facility’s non-linear gravity gradient is $\Delta\phi = \vec k_{\rm eff}\cdot\vec a\,T^2,$1. The same modelling framework supports use of the instrument as a reference for calibration of mobile devices with uncertainty below the $\Delta\phi = \vec k_{\rm eff}\cdot\vec a\,T^2,$2 level (Lezeik et al., 2022). These numbers illustrate a recurrent asymmetry in vertical instruments: magnetic biases can often be engineered to a negligible level, while gravity-field modelling remains a metrological limitation.

Noise budgets in long shafts are not restricted to internal apparatus terms. Atmospheric gravity-gradient noise from pressure and temperature fluctuations is comparable to seismic noise in its impact in the $\Delta\phi = \vec k_{\rm eff}\cdot\vec a\,T^2,$3–$\Delta\phi = \vec k_{\rm eff}\cdot\vec a\,T^2,$4 Hz band. Underground placement is an effective but selective passive mitigation strategy: at $\Delta\phi = \vec k_{\rm eff}\cdot\vec a\,T^2,$5 and depth $\Delta\phi = \vec k_{\rm eff}\cdot\vec a\,T^2,$6, infrasound attenuation gives only about a $\Delta\phi = \vec k_{\rm eff}\cdot\vec a\,T^2,$7 reduction, whereas temperature-induced noise can be reduced by about $\Delta\phi = \vec k_{\rm eff}\cdot\vec a\,T^2,$8 (Carlton et al., 2024). This directly addresses a common misconception: depth does not uniformly suppress all forms of gravity-gradient noise.

Site characterizations at large shafts reinforce this point. In the Sedrun access shaft, long-term acceleration ASD mode curves at $\Delta\phi = \vec k_{\rm eff}\cdot\vec a\,T^2,$9, $\Delta\phi^{(0)} = k_{\rm eff}\,g\,T^2.$0, and $\Delta\phi^{(0)} = k_{\rm eff}\,g\,T^2.$1 Hz were all below the AION-100 requirement of $\Delta\phi^{(0)} = k_{\rm eff}\,g\,T^2.$2, while low-frequency magnetic spectra showed dominant lines at $\Delta\phi^{(0)} = k_{\rm eff}\,g\,T^2.$3 Hz and $\Delta\phi^{(0)} = k_{\rm eff}\,g\,T^2.$4 Hz. For $\Delta\phi^{(0)} = k_{\rm eff}\,g\,T^2.$5Rb with $\Delta\phi^{(0)} = k_{\rm eff}\,g\,T^2.$6, keeping magnetic phase noise below $\Delta\phi^{(0)} = k_{\rm eff}\,g\,T^2.$7 requires $\Delta\phi^{(0)} = k_{\rm eff}\,g\,T^2.$8, implying a $\Delta\phi^{(0)} = k_{\rm eff}\,g\,T^2.$9-metal rejection factor $T$00–$T$01 across $T$02–$T$03 Hz (Guinchard et al., 5 Mar 2026). At CERN PX46, the conceptual feasibility study reports low-frequency magnetic-field noise around $T$04 at $T$05 Hz and seismic acceleration PSD below $T$06 above $T$07 Hz (Arduini et al., 2023).

Coriolis systematics are likewise amplified by long lever arms. The pivot-point beam-rotation method proposed for MAGIS-100 is explicitly motivated by the fact that beam-rotation-induced atom–beam misalignment is magnified by the long baseline length, and simulations indicate suppression of contrast loss below $T$08 for $T$09, $T$10 while residual Coriolis phase is measured to $T$11 accuracy (Glick et al., 2023).

5. Measurement modes and scientific uses

Vertical long-baseline atom interferometers were first developed as inertial sensors, and absolute gravimetry remains a core application. The Hannover VLBAI programme projected shot-noise-limited instabilities better than $T$12 at $T$13 s at the horizon, and the facility-specific performance summary gives $T$14 in fountain mode for $T$15 and $T$16 (Schlippert et al., 2019). Because the measurement is absolute rather than relative, such instruments occupy a distinct metrological role relative to superconducting gravimeters.

Tests of the universality of free fall are a second major use. The rubidium–ytterbium proposal for a $T$17 m very-large-baseline atom interferometer targets an accuracy in the Eötvös ratio of $T$18, with advanced-scenario shot-noise limit $T$19 in fountain mode with higher-order Bragg splitting (Hartwig et al., 2015). More generally, VLBAI operated with several atomic states, isotopes, or species simultaneously is described as reaching parts in $T$20 and beyond (Schlippert et al., 2019).

A third measurement mode is local gravity-gradient and curvature sensing. In the co-located gradiometric scheme studied for Hannover, the differential signal of two co-located interferometers isolates a phase shift proportional to curvature, and the scale factor depends only on the photon wave number, the interferometer time, and the atomic recoil. Using the Hannover gravity profile, which varies by about $T$21 over $T$22 m, the analysis finds that for $T$23 one has $T$24, and for $T$25, $T$26, $T$27, and $T$28, the phase amplitude is $T$29 for $T$30; the estimator reproduces the true $T$31 to $T$32 for $T$33 (Werner et al., 2024).

Longer baselines reorient the science case toward ultralight dark matter and gravitational waves. The CERN conceptual study states that a vertical fountain AI can probe GWs in the band $T$34–$T$35 Hz, and that a $T$36 m AI with $T$37, $T$38 large-momentum-transfer pulses, and atom-shot-noise-limited phase could attain $T$39 around $T$40 Hz (Arduini et al., 2023). The TVLBAI review, using a different benchmark, quotes $T$41–$T$42 around $T$43 Hz for a $T$44 m device with $T$45 and $T$46 in the context of ULDM searches (Balaz et al., 27 Mar 2025). These estimates should be read in the context of different signal models and conventions, rather than as a single directly comparable sensitivity number.

The ZAIGA programme illustrates the connection between vertical atom interferometry and relativistic astrophysics. In a study of dipole radiation from binary neutron stars, combining ground-based laser interferometers with the atom-interferometer ZAIGA or its illustrative upgrade Z+ yields tighter bounds on the parameterized dipole-radiation parameter $T$47 by a few times to a few orders of magnitude relative to laser interferometers alone, reaching ultimately $T$48 with ZAIGA and $T$49 with Z+ (Zhao et al., 2021).

6. Optimization, scalability, and unresolved technical boundaries

Optimization of vertical long-baseline instruments has become a distinct theoretical topic. For resonant-mode dark-matter detectors based on multi-diamond fountain gradiometers, the shot-noise-limited optimum is achieved when the fountain height is $T$50 of the available baseline, the ultimate limit is independent of the dark-matter oscillation frequency, and doubling the baseline decreases the ultimate measurement uncertainty by approximately $T$51. The same analysis proposes a multi-diamond scheme with fewer mirror pulses in which the leading-order gravitational phase contribution is suppressed, and for even $T$52 the leading gravity-gradient phase cancels exactly (Pumpo et al., 2023). This suggests that baseline exploitation is not exhausted by simply maximizing free-fall height.

Scalability is being pursued both instrumentally and organizationally. The TVLBAI Proto-Collaboration frames the field as a coordinated programme: from 2025 to 2029, detailed design and technology maturation in $T$53–$T$54 shafts; from 2029 to 2034, construction and commissioning of one or more $T$55 vertical detectors in PX46, Boulby, and Canfranc; and from 2035 onward, km-scale vertical interferometers at sites including SURF, Gotthard, and Boulby, targeting $T$56 at $T$57 Hz (Balaz et al., 27 Mar 2025). Site studies at Sedrun conclude that both ground motion and electromagnetic backgrounds, including those due to passing trains, are low enough for successful operation of a future $T$58 m AI experiment (Guinchard et al., 5 Mar 2026).

A recurrent source of confusion concerns the relation between science-case papers and instrument-design papers. The binary-neutron-star dipole-radiation analysis that uses ZAIGA and Z+ does not provide the detailed engineering-level design of the ZAIGA vertical long-baseline atom interferometer: it does not give the mirror and laser geometry, vacuum-tube layout, atomic-source specifics, control and cooling schemes, the derivation of the GW-induced phase shift $T$59, the transfer function $T$60, or an explicit breakdown of atomic shot noise, laser-frequency noise, seismic noise, and gravity-gradient noise. What it uses is the final sensitivity curves and simple detector factors from Ref. [49], plus an ad hoc “Z+” defined by dividing ZAIGA’s noise curve by $T$61 (Zhao et al., 2021). The plausible implication is that the vertical long-baseline atom interferometer should be understood as a family of experimentally and theoretically mature subsystems whose full integration is still distributed across multiple proposal, design, and performance studies rather than fixed in a single canonical blueprint.