Quantum mechanics is an extremely successful theory that agrees with every experimental test. However, the principle of linear superposition, a central tenet of the theory, apparently contradicts a commonplace observation: macroscopic objects are never found in a linear superposition of position states. Moreover, the theory does not explain why during a quantum measurement, deterministic evolution is replaced by probabilistic evolution, whose random outcomes obey the Born probability rule. In this article a review is given of an experimentally falsifiable phenomenological proposal, known as continuous spontaneous collapse: a stochastic nonlinear modification of the Schr\"odinger equation, which resolves these problems, while giving the same experimental results as quantum theory in the microscopic regime. Two underlying theories for this phenomenology are reviewed: trace dynamics and gravity-induced collapse. As the macroscopic scale is approached, predictions of this proposal begin to differ appreciably from those of quantum theory and are being confronted by ongoing laboratory experiments that include molecular interferometry and optomechanics. These experiments, which test the validity of linear superposition for large systems, are reviewed here, and their technical challenges, current results, and future prospects summarized. It is likely that over the next two decades or so, these experiments can verify or rule out the proposed stochastic modification of quantum theory.

Levitated optomechanics, a new experimental physics platform, holds promise for fundamental science and quantum technological sensing applications. We demonstrate a simple and robust geometry for optical trapping in vacuum of a single nanoparticle based on a parabolic mirror and the optical gradient force. We demonstrate parametric feedback cooling of all three motional degrees of freedom from room temperature to a few millikelvin. A single laser at 1550 nm and a single photodiode are used for trapping, position detection, and cooling for all three dimensions. Particles with diameters from 26 to 160 nm are trapped without feedback to ${10}^{-5}\mathrm{mbar}$, and with feedback-engaged, the pressure is reduced to ${10}^{-6}\mathrm{mbar}$. Modifications to the harmonic motion in the presence of noise and feedback are studied, and an experimental mechanical quality factor in excess of $4\times {10}^7$ is evaluated. This particle manipulation is key to building a nanoparticle matter-wave interferometer in order to test the quantum superposition principle in the macroscopic domain.

We experimentally squeeze the thermal motional state of an optically levitated nanosphere by fast switching between two trapping frequencies. The measured phase-space distribution of the center of mass of our particle shows the typical shape of a squeezed thermal state, from which we infer up to 2.7 dB of squeezing along one motional direction. In these experiments the average thermal occupancy is high and, even after squeezing, the motional state remains in the remit of classical statistical mechanics. Nevertheless, we argue that the manipulation scheme described here could be used to achieve squeezing in the quantum regime if preceded by cooling of the levitated mechanical oscillator. Additionally, a higher degree of squeezing could, in principle, be achieved by repeating the frequency-switching protocol multiple times.

Levitated nanoparticles and microparticles are excellent candidates for the realization of extremely isolated mechanical systems, with a huge potential impact in sensing applications and in quantum physics. Magnetic levitation based on static fields is a particularly interesting approach, owing to the unique property of being completely passive and compatible with low temperatures. Here, we show experimentally that micromagnets levitated above type-I superconductors feature very low damping at low frequency and low temperature. In our experiment, we detect five out of six rigid body mechanical modes of a levitated ferromagnetic microsphere, using a dc superconducting quantum interference device with a single pick-up coil. The measured frequencies are in agreement with a finite-element simulation based on an ideal Meissner effect. For two specific modes, we find further substantial agreement with analytical predictions based on the image method. We measure damping times $\tau$ exceeding ${10}^4\mathrm{s}$ and quality factors $Q$ beyond ${10}^7$, an improvement of 2–3 orders of magnitude over previous experiments based on the same principle. We investigate the possible residual loss mechanisms besides gas collisions, and argue that a much longer damping time can be achieved with further effort and optimization. Our results open the way towards the development of ultrasensitive magnetomechanical sensors with potential applications to magnetometry and gravimetry, as well as to fundamental and quantum physics.

What gravitational field is generated by a massive quantum system in a spatial superposition? Despite decades of intensive theoretical and experimental research, we still do not know the answer. On the experimental side, the difficulty lies in the fact that gravity is weak and requires large masses to be detectable. However, it becomes increasingly difficult to generate spatial quantum superpositions for increasingly large masses, in light of the stronger environmental effects on such systems. Clearly, a delicate balance between the need for strong gravitational effects and weak decoherence should be found. We show that such a trade off could be achieved in an optomechanics scenario that allows to witness whether the gravitational field generated by a quantum system in a spatial superposition is in a coherent superposition or not. We estimate the magnitude of the effect and show that it offers perspectives for observability.