Understanding gravity in the framework of quantum mechanics is one of the great challenges in modern physics. However, the lack of empirical evidence has lead to a debate on whether gravity is a quantum entity. Despite varied proposed probes for quantum gravity, it is fair to say that there are no feasible ideas yet to test its quantum coherent behavior directly in a laboratory experiment. Here, we introduce an idea for such a test based on the principle that two objects cannot be entangled without a quantum mediator. We show that despite the weakness of gravity, the phase evolution induced by the gravitational interaction of two micron size test masses in adjacent matter-wave interferometers can detectably entangle them even when they are placed far apart enough to keep Casimir-Polder forces at bay. We provide a prescription for witnessing this entanglement, which certifies gravity as a quantum coherent mediator, through simple spin correlation measurements.

Levitated optomechanics is showing potential for precise force measurements. Here, we report a case study to show experimentally the capacity of such a force sensor, using an electric field as a tool to detect a Coulomb force applied onto a levitated nanosphere. We experimentally observe the spatial displacement of up to 6.6 nm of the levitated nanosphere by imposing a DC field. We further apply an AC field and demonstrate resonant enhancement of force sensing when a driving frequency, ω_AC, and the frequency of the levitated mechanical oscillator, ω₀, converge. We directly measure a force of 3.0 ± 1.5 × 10^–20N with 10 s integration time, at a centre of mass temperature of 3 K and at a pressure of 1.6 × 10^–5 mbar.

This paper points out the importance of the quantum nature of the gravitational interaction with matter in a linearized theory of quantum gravity induced entanglement of masses. We will show how the quantum interaction entangles the steady states of a closed system (eigenstates) of two test masses placed in the harmonic traps, and how such a quantum matter-matter interaction emerges from an underlying quantum gravitational field. We will rely upon quantum perturbation theory highlighting the critical assumptions for generating a quantum matter-matter interaction and showing that a classical gravitational field does not render such an entanglement. We will consider two distinct examples: one where the two harmonic oscillators are static, and the other where the harmonic oscillators are nonstatic. In both cases it is the quantum nature of the gravitons interacting with the harmonic oscillators that are responsible for creating an entangled state with the ground and the excited states of harmonic oscillators as the Schmidt basis. We will compute the concurrence as a criterion for the above entanglement and compare the two ways of entangling the two harmonic oscillators.

Matter-wave interferometers with large momentum transfers, irrespective of specific implementations, will face a universal dephasing due to relative accelerations between the interferometric mass and the associated apparatus. Here we propose a solution that works even without actively tracking the relative accelerations: putting both the interfering mass and its associated apparatus in a freely falling capsule, so that the strongest inertial noise components vanish due to the equivalence principle. In this setting, we investigate two of the most important remaining noise sources: (a) the noninertial jitter of the experimental setup and (b) the gravity-gradient noise. We show that the former can be reduced below desired values by appropriate pressures and temperatures, while the latter can be fully mitigated in a controlled environment. We finally apply the analysis to a recent proposal for testing the quantum nature of gravity [S. Bose et al., Phys. Rev. Lett. 119, 240401 (2017)] through the entanglement of two masses undergoing interferometry. We show that the relevant entanglement witnessing is feasible with achievable levels of relative acceleration noise.

We investigate experimentally the dynamics of a nonspherical levitated nanoparticle in a vacuum. In addition to translation and rotation motion, we observe the light torque-induced precession and nutation of the trapped particle. We provide a theoretical model, which we numerically simulate and from which we derive approximate expressions for the motional frequencies. Both the simulation and approximate expressions we find in good agreement with experiments. We measure a torque of $1.9\pm 0.5\times {10}^{-23}\mathrm{N}\mathrm{m}$ at $1\times {10}^{-1}\mathrm{mbar}$, with an estimated torque sensitivity of $3.6\pm 1.1\times {10}^{-31}\mathrm{N}\mathrm{m}/\sqrt{\mathrm{Hz}}$ at $1\times {10}^{-7}\mathrm{mbar}$.