Quantum-Gravitational Deflection of Parallel Atomic Matter Beams ✦
It is well known that gravitational interaction between two parallel light beams is absent. In the work, a model is proposed where two spatially separated Bose-Einstein condensates are used to create parallel atomic laser beams. It is discovered that along with classical deflection, a purely quantum-gravitational tidal effect arises, leading to unavoidable noise in the geodesic separation of the beams. Based on this theoretical result, an experimental scheme is proposed for measuring the quantum-gravitational standard deviation of the distance between two parallel matter wave beams. Such an experiment could become a new test of gravity at the microscale.
Context
Quantum gravity remains one of the toughest challenges in physics. Direct unification leads to non-renormalizable divergences, and experimental data at Planck scales is out of reach. Hence, a key strategy has become the search for low-energy signatures of the quantum nature of gravity—for instance, through generating quantum entanglement between massive objects, as in the famous QGEM protocol. Back in the mid-20th century, Richard Feynman posed a fundamental question: are superposition and gravity compatible? Today's experiments with Bose–Einstein condensates allow us to approach an answer from a new angle—by using coherent atomic beams and sensitive interferometry.
Methods
The authors proposed a model where two Bose–Einstein condensates with non-interacting bosons are held in harmonic traps at a distance d. The atoms are then released by a radio-frequency outcoupler and form two parallel atomic laser beams, freely falling in Earth's gravity. Unlike photons, whose trajectories are described by null geodesics, atoms move slower than light and follow timelike trajectories—this key difference makes deflection possible. To compute the spacetime background, linearized gravity is used, but an operator addition is introduced into the stress-energy tensor via quasiparticles (phonons), as in the pioneering works of Bryce DeWitt on quantum field theory in curved space. Thus, spacetime curvature becomes an operator, and the geodesic equation for beam separation acquires quantum corrections.
Results
Classical calculation shows no mutual deflection of two parallel photon beams. For massive atomic beams, the classical solution also yields no noticeable effect. However, under quantum-mechanical treatment, when the metric fluctuation becomes operator-valued, an irreducible noise appears in the geodesic separation. The standard deviation Δx of the coordinate difference between the beams turned out to be proportional to the number of particles N₀ in the condensate and the square of the flight time τ. For realistic parameters—N₀ = 10⁶, atomic mass m ~ 10⁻²⁵ kg, trap frequency ω ~ 10³ Hz, distance d on the order of two characteristic wave function sizes—the theoretical Δx is approximately 10⁻¹⁸ τ² m. For a lab free-fall time of τ ~ 0.1–1 s, this gives a deviation from 10⁻²⁰ to 10⁻¹⁸ m. In the regime of very small gaps (d < quantum length), a 'tidal' character emerges with a dependence Δx ∝ 1/d³. The effect is interpreted as resulting from the exchange of virtual gravitational waves—gravitons—between the condensates, giving rise to quantum fluctuations of their trajectories.
Implications
Detecting such a prediction would be direct evidence of the quantum-field nature of gravity. Unlike protocols based on generating quantum entanglement, here one measures not the state of internal degrees of freedom but the spread in coordinates—this is an alternative and independent test. Confirmation of the effect would mean that vacuum fluctuations of spacetime genuinely influence the motion of quantum objects, opening a new window into Planck-scale physics through a relatively low-energy experiment. Moreover, such studies lay the groundwork for quantum measurements of the gravitational field using atomic interferometry.
Future development
A natural next step is to increase sensitivity by using condensates with up to 10⁹ particles (e.g., magnon condensates) and extending free-fall time to tens of seconds in special towers or on satellites. Enhancement techniques like large momentum transfer (LMT) can boost the phase shift by another three orders of magnitude, pushing the expected fringe shifts to values accessible to precision interferometry. In the longer term, combining with ideas of quantum superposition of geometries could lead to a unified picture of quantum spacetime.
Impact
The work will impact several cutting-edge areas: experimental quantum gravity, atomic matter-wave interferometry, and quantum sensing. The results can be used to build next-generation quantum sensors of gravity.
Next steps
The immediate task is a detailed analysis of all technical noise sources in real atom-interferometric setups and a search for optimal parameters to isolate the irreducible quantum-gravitational component. Then, a dedicated experiment with two identical condensate sets is required, where one arm serves as a low-particle-number reference.
Key open problems
The proposed experiment is directly linked to the unsolved problem of non-renormalizability of quantum gravity and to the question of whether the gravitational field can be considered quantized in the low-energy limit. Success would confirm or refute fundamental assumptions about the nature of spacetime, referred to as Feynman's mass superposition dilemma, and would complement searches for gravitational waves from astrophysical sources—but at the lab scale and from the side of vacuum fluctuations.
🎯 In the usual picture, two parallel laser beams never change their distance, even if they carry significant energy. Atomic lasers, however, due to their low speed and timelike trajectory, experience mutual influence, but only thanks to the quantum nature of gravity—it's like a 'shiver' of space caused by the exchange of invisible gravitons between the falling streams of atoms.
Key numbers
- Standard deviation Δx: 10⁻¹⁸ – 10⁻²¹ m (for N₀ = 10⁶ and τ = 0.1–1 s)
- Increase of Δx over time: ~10⁻²⁰ m per second of fall
- Phase shift in the interference pattern: ~10⁻¹³ rad (without enhancement)
- Expected shift of interference fringes: ~10⁻¹⁸ m (in a standard setup), up to 10⁻¹⁰ m with optimization
- Number of atoms in the condensate: N₀ = 10⁶ (can be increased up to 10⁹)