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, ωAC , and the frequency of the levitated mechanical oscillator, ω0, converge. We directly measure a force of 3.0 ± 1.5 × 10 −20 N with 10 second integration time, at a centre of mass temperature of 3 K and at a pressure of 1.6 × 10 −5 mbar.The ability to detect forces with increasing sensitivity, is of paramount importance for many fields of study, from detecting gravitational waves [1] to molecular force microscopy of cell structures and their dynamics [2]. In the case of a mechanical oscillator, the force sensitivity limit arises from the classical thermal noise, as given by,Where, k b is the Boltzmann constant, T is the temperature of the thermal environment, m, the mass of the object, ω 0 is the oscillator angular frequency, Q m = ω 0 /Γ 0 is the mechanical quality factor and Γ 0 is the damping factor. In recent decades, systems, such as cold-atoms traps, have pushed the boundaries of force sensitivities down to 1 × 10 [3,35]. The control of charges on nanoparticles is essential for experiments to prepare non-classical states of motion of the particle [30,36]. In addition, force detection at 1.63 × 10 −18 N/ √ Hz in levitated nanospheres has already been demonstrated [20] by experiment.Here, we take a detailed look at the interaction of an optically levitated dielectric charged particle with an external electric field as a case study for force sensing. We measure the effect of the Coulomb interaction on the motion of a single nanoparticle, at high vacuum (10 −5 mbar) by applying a DC and an AC electric field to a metallic needle positioned near the trapped particle. These particles can carry multiple elementary electric charges (e = 1.6 × 10 −19 C), and we use the Coulomb interaction to determine the number of elementary charges attached to the particle.The charge at the needle tip, q t , for a given applied voltage is according to Gauss's Law, s E·ds t = qt 0 , where s t is the surface of the needle tip, 0 is the vacuum permittivity, and E is the electric field. The electric field at any point in a potential, V , is given by −∇V = E. If, we approximate the needle tip as a sphere, of radius, r t , arXiv:1706.09774v3 [quant-ph]

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Levitated nano-oscillators are promising platforms for testing fundamental physics and quantum mechanics in a new high mass regime. Levitation allows extreme isolation from the environment, reducing the decoherence processes that are crucial for these sensitive experiments. A fundamental property of any oscillator is its linewidth and mechanical quality factor Q. Narrow linewidths in the microhertz regime and mechanical Q's as high as 10 12 have been predicted for levitated systems. The insufficient long-term stability of these oscillators has prevented direct measurement in high vacuum. Here we report on the measurement of an ultranarrow linewidth levitated nano-oscillator, whose width of 81 ± 23 μHz is only limited by residual gas pressure at high vacuum despite residual variations of the trapping potential. This narrow linewidth allows us to put new experimental bounds on dissipative models of wave-function collapse including continuous spontaneous localization and Diósi-Penrose and illustrates its utility for future precision experiments that aim to test the macroscopic limits of quantum mechanics.