Bounds on Collapse Models from Matter-Wave Interferometry: Calculational details

We present a simple derivation of the interference pattern in matter-wave interferometry as predicted by a class of master equations, by using the density matrix formalism. We apply the obtained formulae to the most relevant collapse models, namely the Ghirardi-Rimini-Weber (GRW) model, the continuous spontaneous localization (CSL) model together with its dissipative (dCSL) and non-markovian generalizations (cCSL), the quantum mechanics with universal position localization (QMUPL) and the Di\'{o}si-Penrose (DP) model. We discuss the separability of the collapse models dynamics along the 3 spatial directions, the validity of the paraxial approximation and the amplification mechanism. We obtain analytical expressions both in the far field and near field limits. These results agree with those already derived in the Wigner function formalism. We compare the theoretical predictions with the experimental data from two relevant matter-wave experiments: the 2012 far-field experiment and the 2013 Kapitza Dirac Talbot Lau (KDTL) near-field experiment of Arndt's group. We show the region of the parameter space for each collapse model, which is excluded by these experiments. We show that matter-wave experiments provide model insensitive bounds, valid for a wide family of dissipative and non-markovian generalizations.Comment: 49 pages,16 figure

Wigner Function Reconstruction in Levitated Optomechanics

We demonstrate the reconstruction of the Wigner function from marginal distributions of the motion of a single trapped particle using homodyne detection. We show that it is possible to generate quantum states of levitated optomechanical systems even under the effect of continuous measurement by the trapping laser light. We describe the opto-mechanical coupling for the case of the particle trapped by a free-space focused laser beam, explicitly for the case without an optical cavity. We use the scheme to reconstruct the Wigner function of experimental data in perfect agreement with the expected Gaussian distribution of a thermal state of motion. This opens a route for quantum state preparation in levitated optomechanics.Comment: 9 pages, 3 figure

Bohmian Mechanics, Collapse Models and the emergence of Classicality

We discuss the emergence of classical trajectories in Bohmian Mechanics (BM), when a macroscopic object interacts with an external environment. We show that in such a case the conditional wave function of the system follows a dynamics which, under reasonable assumptions, corresponds to that of the Ghirardi-Rimini-Weber (GRW) collapse model. As a consequence, Bohmian trajectories evolve classically. Our analysis also shows how the GRW (istantaneous) collapse process can be derived by an underlying continuous interaction of a quantum system with an external agent, thus throwing a light on how collapses can emerge from a deeper level theory.Comment: 19 pages, 2 figure

Loss of coherence of matter-wave interferometer from fluctuating graviton bath

In this paper we consider non-relativistic matter-wave interferometer coupled with a quantum graviton bath $\mathord{-}$ and discuss the loss of coherence in the matter sector due to the matter-graviton vertex. First of all, such a process does not lead to any entanglement, but nonetheless the on-shell scattering diagram can lead to loss of coherence as we will show. Importantly, we will show that graviton emission is the only one-vertex Feynman-diagram $\sim\sqrt{G}$ which is consistent with the conservation of energy and momentum at the dominant order $\sim\mathcal{O}(c^{-2})$. We will find that the resulting dephasing is extremely mild and hardly places any constraints on matter-wave interferometers in the mesoscopic regime. In particular, the show that the corresponding loss of coherence in the recently proposed experiment which would test quantum aspects of graviton $\mathord{-}$ via entanglement of two matter-wave interferometers $\mathord{-}$ is completely negligible.Comment: 10 pages, 2 figure

Precession Motion in Levitated Optomechanics

We investigate experimentally the dynamics of a non-spherical levitated nanoparticle in 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 $1.9 \pm 0.5 \times 10^{-23}$ Nm at $1 \times 10^{-1}$ mbar, with an estimated torque sensitivity of $3.6 \pm 1.1 \times 10^{-31}$ Nm/$\sqrt{\text{Hz}}$ at $1 \times 10^{-7}$ mbar.Comment: 10 pages, 4 figure

Gravitational decoherence by the apparatus in the quantum-gravity induced entanglement of masses

One of the outstanding questions in modern physics is how to test whether gravity is classical or quantum in a laboratory. Recently there has been a proposal to test the quantum nature of gravity by creating quantum superpositions of two nearby neutral masses, close enough that the quantum nature of gravity can entangle the two quantum systems, but still sufficiently far away that all other known Standard Model interactions remain negligible. However, the mere process of preparing superposition states of a neutral mass (the light system), requires the vicinity of laboratory apparatus (the heavy system). We will suppose that such a heavy system can be modelled as another quantum system; since gravity is universal, the lighter system can get entangled with the heavier system, providing an inherent source of gravitational decoherence. In this paper, we will consider two light and two heavy quantum oscillators, forming pairs of probe-detector systems, and study under what conditions the entanglement between two light systems evades the decoherence induced by the heavy systems. We conclude by estimating the magnitude of the decoherence in the proposed experiment for testing the quantum nature of gravity.Comment: 14 pages, 4 figure

Quantum Gravitational Sensor for Space Debris

Matter-wave interferometers have fundamental applications for gravity experiments such as testing the equivalence principle and the quantum nature of gravity. In addition, matter-wave interferometers can be used as quantum sensors to measure the local gravitational acceleration caused by external massive moving objects, thus lending itself for technological applications. In this paper, we will establish a three dimensional model to describe the gravity gradient signal from an external moving object, and theoretically investigate the achievable sensitivities using the matter-wave interferometer based on the Stern-Gerlach set-up. As an application we will consider the Mesoscopic Interference for Metric and Curvature (MIMAC) and Gravitational wave detection scheme [New J. Phys. 22, 083012 (2020)] and quantify its sensitivity to gravity gradients using frequency-space analysis. We will consider objects near Earth-based experiments and space debris in proximity of satellites and estimate the minimum detectable mass of the object as a function of their distance, velocity, and orientation.Comment: 13 pages, 8 figure

Optimal Superpositions for Particle Detection via Quantum Phase

Exploiting quantum mechanics for sensing offers unprecedented possibilities. State of the art proposals for novel quantum sensors often rely on the creation of large superpositions and generally detect a field. However, what is the optimal superposition size for detecting an incident particle (or an incident stream of particles) from a specific direction? This question is nontrivial as, in general, this incident particle will scatter off with varied momenta, imparting varied recoils to the sensor, resulting in decoherence rather than a well defined measurable phase. By considering scattering interactions of directional particulate environments with a system in a quantum superposition, we find that there is an "optimal superposition" size for measuring incoming particles via a relative phase. As a consequence of the anisotropy of the environment, we observe a novel feature in the limiting behaviour of the real and imaginary parts of the system's density matrix, linking the optimality of the superposition size to the wavelength of the scatterer.Comment: 6 page

Real-Time Kalman Filter: Cooling of an Optically Levitated Nanoparticle

We demonstrate that a Kalman filter applied to estimate the position of an optically levitated nanoparticle, and operated in real-time within a Field Programmable Gate Array (FPGA), is sufficient to perform closed-loop parametric feedback cooling of the centre of mass motion to sub-Kelvin temperatures. The translational centre of mass motion along the optical axis of the trapped nanoparticle has been cooled by three orders of magnitude, from a temperature of 300K to a temperature of 162 +/- 15mK

Measurement of single nanoparticle anisotropy by laser induced optical alignment and Rayleigh scattering for determining particle morphology

We demonstrate the measurement of nanoparticle anisotropy by angularly resolved Rayleigh scattering of single optical levitated particles that are oriented in space via the trapping light in vacuum. This technique is applied to a range of particle geometries from perfect spherical nanodroplets to octahedral nanocrystals. We show that this method can resolve shape differences down to a few nanometers and be applied in both low-damping environments, as demonstrated here, and in traditional overdamped fluids used in optical tweezers