Table-top nanodiamond interferometer enabling quantum gravity tests

Unifying quantum theory and general relativity is the holy grail of contemporary physics. Nonetheless, the lack of experimental evidence driving this process led to a plethora of mathematical models with a substantial impossibility of discriminating among them or even establishing if gravity really needs to be quantized or if, vice versa, quantum mechanics must be “gravitized” at some scale. Recently, it has been proposed that the observation of the generation of entanglement by gravitational interaction, could represent a breakthrough demonstrating the quantum nature of gravity. A few experimental proposals have been advanced in this sense, but the extreme technological requirements (e.g., the need for free-falling gravitationally-interacting masses in a quantum superposition state) make their implementation still far ahead. Here we present a feasibility study for a table-top nanodiamond-based interferometer eventually enabling easier and less resource-demanding quantum gravity tests. With respect to the aforementioned proposals, by relying on quantum superpositions of steady massive (mesoscopic) objects our interferometer may allow exploiting just small-range electromagnetic fields (much easier to implement and control) and, at the same time, the re-utilization of the massive quantum probes exploited, inevitably lost in free-falling interferometric schemes.

💡 Research Summary

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The paper proposes a tabletop interferometer based on nanodiamonds (NDs) with single nitrogen‑vacancy (NV) centers to test quantum aspects of gravity without the demanding requirements of free‑fall experiments. Instead of letting massive particles fall over several meters, the authors confine two NDs in a two‑dimensional magnetic trap (confining the y and z directions) while leaving them free to move along the x‑axis. A linear magnetic field gradient B′ = dB/dx together with a small bias field B₀ creates spin‑dependent equilibrium positions: the |+1⟩ and |−1⟩ spin components experience opposite forces, leading to spatially separated coherent states |α₊(t)⟩ and |α₋(t)⟩.

The system Hamiltonian (Eqs. 1‑3) maps onto a displaced harmonic oscillator coupled to the NV spin via a Lamb‑type interaction λ(a + a†)Sₓ. Preparing the spin in the superposition (|−1⟩+|+1⟩)/√2 yields a superposition of two spatial wave packets whose separation can be tuned by the gradient strength. By tilting the whole apparatus by a small angle θ_g in the x‑z plane, a differential gravitational potential is introduced between the two branches, generating a measurable phase shift Δϑ = −4π(μ₀ m χ V)^{3/2} γₑ g B′² sin θ_g after a full oscillation period. This phase can be read out with a Ramsey‑type interferometric sequence on the NV spin, providing a direct signature of gravity‑mediated entanglement.

A major obstacle is the long interaction time required for appreciable entanglement (∼1 s to several minutes). Current NV coherence times (∼ms) are far too short, so the authors introduce a dynamical decoupling (DD) protocol: a train of microwave π‑pulses at frequency ω_DD = N ω flips the spin sign while simultaneously inverting the signs of B₀ and B′ using an anti‑Helmholtz coil configuration. This keeps the Hamiltonian effectively time‑independent and extends the coherence to ≈150 s in simulations, making the entanglement generation feasible.

To avoid spurious Casimir‑Polder forces overwhelming the tiny gravitational interaction, the experiment is designed so that the CP potential is at least an order of magnitude smaller than the gravitational potential. This is achieved by operating at 4 K, pressures below 10⁻¹⁰ mbar, and ensuring a minimum ND‑ND separation d_min = Δx + Δ_CP, where Δ_CP is calculated from the dielectric properties of diamond. Residual charges are neutralized by a radioactive source or UV illumination.

The experimental sequence consists of: (a) loading two NV‑doped NDs into the same magnetic trap; (b) applying B′ to create spatial superpositions conditioned on spin; (c) switching off B′ at a motion turning point so that the superposed branches evolve solely under mutual gravity for a chosen interaction time; (d) re‑applying B′ to recombine the branches; (e) turning B′ off and performing a joint spin measurement to detect entanglement. Because the NDs remain trapped throughout, they can be re‑initialized and reused, dramatically reducing acquisition time compared with free‑fall schemes that discard the particles after each run.

Overall, the proposal offers three key advantages: (1) a compact, centimeter‑scale apparatus; (2) reliance only on controllable electromagnetic fields rather than large‑scale free‑fall; (3) reusability of massive quantum probes, improving data‑rate and precision. Remaining technical challenges include implementing fast, synchronized magnetic field inversions for DD, maintaining ultra‑low temperature and pressure, and achieving the required NV spin coherence. If these hurdles are overcome, the tabletop nanodiamond interferometer could become a practical platform for probing quantum gravity effects in the laboratory.