Can quantum probes satisfy the weak equivalence principle?

Abstract

We address the question whether quantum probes in a gravitational field can be considered as test particles obeying the weak equivalence principle (WEP). A formulation of the WEP is proposed which applies also in the quantum regime, while maintaining the physical content of its classical counterpart. Such formulation requires the introduction of a gravitational field not to modify the Fisher information about the mass of a freely-falling probe, extractable through measurements of its position. We discover that, while in a uniform field quantum probes satisfy our formulation of the WEP exactly, gravity gradients can encode nontrivial information about the particle's mass in its wavefunction, leading to violations of the WEP.Comment: close to published versio

Fisher information and the weak equivalence principle of a quantum particle in a gravitational wave

“…The uniform gravitational field induces a mass-dependent phase factor in Eq. (17). This mass-dependent phase factor however, is not present in the probability distribution, |ψ g (x, t)| 2 = |ψ free (x − gt 2 /2, t)| 2 .…”

“…The evolution of a quantum particle is governed by the time-evolution operator U = e −i Ht . Taking the Baker-Campbell-Hausdorff expansion of U to second-order, the time-evolution operator in a Schwarzschild field is (h = 1) [17] U ≈ exp imt 3 3…”

“…The WEP's notion that free-falling trajectories should be independent of mass, can be reformulated as the statement that the Fisher information of a free-falling object is invariant with mass [17]. In this information-theoretic framework, violation of the WEP means that one may extract information about an object's mass in free-fall.…”

Quantum Sensing of Curvature

“…By free, we mean that the particle is affected only by the constraining potential that forces it to stay on the surface. The rationale behind this approach is that quantum systems are inherently sensitive to the parameters of their Hamiltonians, which may be exploited to precisely estimate the values of those parameters by performing suitable measurements on them [23][24][25][26][27][28][29][30][31][32]. This idea has been recently exploited to develop a new approach to probe macroscopic systems, based on the quantification and optimisation of the information that can be extracted by an interacting quantum probe as opposed to a classical one.…”

Lorentz-violating scalar Hamiltonian and the equivalence principle in a static metric

“…In this sense, it is better to view UFF as a classical manifestation of WEP. On the contrary, WEP can still be safely guaranteed in quantum realm, especially constrained to NR region reduced [20][21] [43] from GR. Actually, WEP provides a key to "gauge away" the gravitational analogy of gauge potential, the first derivatives of metric tensor, i.e., ∂ ρ g µν ∼ Γ ρµν , thus is an essential ingredient to glue quantum matter (neglecting spin-gravity couplings) to the classical gravitational background.…”