Geiger and Trupke (Phys. Rev. Lett. 120, 043602, 2018) proposed testing the weak equivalence principle (WEP) with a test mass consisting of two entangled atoms of different species, noting that no theoretical model predicts whether such entanglement leads to a WEP violation at any level, so that the experiment would be a discovery-driven search. The problem is to design and analyze the entangled dual-species atom-interferometric differential gravity measurement with systematics controlled so that the entangled-atom result can be compared with classically independent atoms at the 5×10−85\times 10^{-8} level of the Eötvös parameter, isolating any entanglement contribution from mass-dependent systematics.

Background

The weak equivalence principle (WEP) states that the free fall of a body is independent of its composition and internal structure; in Newtonian language it is the equality of inertial and gravitational mass. Its experimental figure of merit is the Eötvös parameter η=2∣aA−aB∣/(aA+aB)\eta = 2|a_A - a_B|/(a_A + a_B), comparing the accelerations of two test masses AA and BB; space-based tests with macroscopic masses constrain η\eta to about one part in 101510^{15}. A complementary line of tests uses light-pulse atom interferometers, in which laser pulses split and recombine the atomic wave packet so that the interferometer phase is proportional to the atom's acceleration; the differential phase ΔΦ∝kT2(gA−gB)\Delta\Phi \propto k T^2 (g_A - g_B) (with kk the laser wave number, TT the pulse separation, and gAg_A, gBg_B the accelerations of the two species) constrains η\eta. In all existing dual-species atom-interferometric WEP tests the two test masses are classically independent: each species interferes in its own interferometer and the two are compared only at the data-analysis level. The question of how the equivalence principle should be formulated for genuinely quantum systems is itself under development: Zych and Brukner introduced a quantum formulation of the Einstein equivalence principle (the umbrella principle comprising the WEP, local Lorentz invariance, and local position invariance) in which the rest, inertial, and gravitational internal energies of a system are quantum operators, showed that the validity of the classical principle does not imply the quantum one, and parameterized possible violations by operator-valued quantities; Rosi and co-workers tested the internal-energy aspect experimentally with single atoms in coherent superpositions of internal states (energy splitting of order 30 µeV), constraining violations at the 5×10−85\times 10^{-8} level. None of these involves entanglement between two different masses. Geiger and Trupke's proposal makes the two test masses non-classically correlated. Two atoms of different species (85^{85}Rb and 87^{87}Rb, differing by about 2 GeV in mass-energy) are entangled at the first beam splitter of a dual-species interferometer by detecting a single photon emitted by either atom inside a high-finesse optical cavity: because the detected photon does not reveal which atom emitted it, the two atoms are projected into an entangled state. The entangling event is produced by vacuum-stimulated stimulated Raman adiabatic passage (vSTIRAP), a cavity quantum-electrodynamics technique that coherently transfers an excitation between the atoms and a single cavity photon. The subsequent differential gravity measurement then probes the free fall of a genuinely two-particle entangled state, whose interference occurs at the total center of mass rather than at the independent centers of mass of each species — a nonlocal feature with no analogue in standard dual-species interferometers. Simulations give a heralding success probability PS≈7%P_S \approx 7\% and a false-positive probability PF≈0.26%P_F \approx 0.26\%, and a projected Eötvös sensitivity of 5×10−85\times 10^{-8} for 10410^4 successful shots at T=50T = 50 ms, requiring control of isotope-dependent systematics — for example, the differential magnetic-field response, which produces a phase shift of order 500 mrad per 1 mG/cm gradient and must be controlled at the 2% level. The authors emphasize that, to their knowledge, no theoretical model addresses whether the presence of entanglement in a system would result in a WEP violation at any given level of accuracy: within ordinary quantum mechanics on a classical spacetime the expected answer is null (the mean acceleration of each species is independent of the joint state), so any observed deviation would point to new physics at the quantum-gravity interface, and the experiment is discovery-driven. The same apparatus was noted to enable a Bell test — a correlation test that no local hidden-variable theory can reproduce — with free-falling massive particles of different species, whose locality and detection-efficiency requirements were not analyzed.

Problem Statement

The research question is whether quantum entanglement between two atoms of different species affects their free fall — that is, whether the weak equivalence principle holds for an entangled test mass. The task is resolved by a single deliverable: produce a design and a quantified systematics budget for the entangled dual-species atom-interferometric differential gravity measurement, not a laboratory realization of it; the heralded-entanglement scheme with 85^{85}Rb and 87^{87}Rb proposed by Geiger and Trupke is a concrete instance whose completion suffices. This requires deriving, rather than restating, both the predicted differential free-fall signal of the entangled test mass and a systematics budget characterizing the heralding statistics (vSTIRAP success and false-positive rates) and the isotope-dependent systematics — magnetic-field gradients, gravity gradients, differential recoil — well enough that the differential gravitational acceleration measured with entangled atoms can be compared with that measured with classically independent atoms at the 5×10−85\times 10^{-8} level of the Eötvös parameter, so that any entanglement-specific effect is separated from mass-dependent systematics. Because no consensual theoretical model predicts whether entanglement leads to a WEP violation at any level — the differential signal predicted by ordinary quantum mechanics on a classical background is null, a baseline rather than the answer — the measurement is a discovery-driven search: any observed deviation would point to new physics at the quantum-gravity interface, and a null result at the 5×10−85\times 10^{-8} level would constrain such deviations in a regime inaccessible to tests with classically independent test masses.

References

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