The necessity of quantising the gravitational field is still subject to an open debate.In this paper we compare approach quantum gravity, with that a fundamentally semiclassical theory in weak-field non-relativistic limit.We show that, while former case Schrödinger equation stays linear, latter one ends up so-called Schrödinger-Newton equation, which involves nonlinear, non-local contribution.We further discuss does not describe collapse wave-function, although it was initially proposed for...

We discuss effects of loss coherence in low energy quantum systems caused by or related to gravitation, referred as gravitational decoherence.These effects, resulting from random metric fluctuations, for instance, promise be accessible relatively inexpensive table-top experiments, way before the scales where true gravity become important.Therefore, they can provide a first experimental view on regime.We will survey models decoherence induced both classical and fluctuations; it manifest that...

We reconsider the time-dependent Schrödinger–Newton equation as a model for self-gravitational interaction of quantum system. numerically locate onset gravitationally induced inhibitions dispersion Gaussian wave packets and find them to occur at mass values more than six orders magnitude higher reported by Salzman Carlip (Salzman 2006, arXiv:gr-qc/0606120, 2008 Class. Quantum Grav. 25 107–44), namely about 1010 u. This fits much better simple analytical estimates but unfortunately also...

In this paper we show that the Schr\"odinger-Newton equation for spherically symmetric gravitational fields can be derived in a WKB-like expansion 1/c from Einstein-Klein-Gordon and Einstein-Dirac system.

The Schr\"odinger-Newton equation has been proposed as an experimentally testable alternative to quantum gravity, accessible at low energies. It contains self-gravitational terms, which slightly modify the dynamics. Here we show that it distorts spectrum of a harmonic system. Based on this effect, propose optomechanical experiment with trapped microdisc test equation, and can be realized existing technology.

We investigate the implication of non-linear and non-local multi-particle Schroedinger-Newton equation for motion mass centre an extended object, giving self-contained comprehensible derivations. In particular, we discuss two opposite limiting cases. first case, width centre-of-mass wave packet is assumed much larger than actual extent in second case it smaller. Both cases result deviations from ordinary free Schroedinger evolution mass. On a general conceptual level include some discussion...

The nonlinear Schr\"odinger-Newton equation, a prospective semiclassical alternative to quantized theory of gravity, predicts gravitational self-force between the two trajectories corresponding $z$-spin eigenvalues for particle in Stern-Gerlach interferometer. To leading order, this force results relative phase trajectories. For experimentally relevant case spherical with localized wave function, we present rederivation that which is both rigorous its approximations and concise, allowing...

We modify the time-dependent Schrödinger–Newton equation by using a potential for solid sphere suggested Jääskeläinen (2012 Phys. Rev. A 86 052105) as well hollow-sphere potential. Compared to our recent paper (Giulini and Großardt 2011 Class. Quantum Grav. 28 195026) where single point particle, i.e. Coulomb potential, was considered, this has been be more realistic model molecule. Surprisingly, compared previous results, inhibitions of dispersion Gaussian wave packet occur at even smaller...

Experiments witnessing the entanglement between two particles interacting only via gravitational field have been proposed as a test whether gravity must be quantized. In language of quantum information, non-quantum force would modeled by local operations with classical communication (LOCC), which cannot generate in an initially unentangled state. This idea is criticized too constraining on possible alternatives to gravity. We present parametrized model for interaction matter spacetime,...

The author reviews the arguments most often raised against a fundamental coupling of classical spacetime to quantum matter. shows that an experiment by Page and Geilker does not exclude such semiclassical theory but mandates inclusion objective mechanism for wave function collapse. In this regard, presents classification models defined way in which collapse is introduced. Two related types paradoxes have been discussed context necessity quantize gravitational field can be shown constrain...

It has been proposed that quantum features of the gravitational field can be exposed experimentally by employing gravity as a mediator entanglement. We show in order to witness this type entanglement experimentally, strong limits on acceleration noise, which neglected previous work, must overcome. In case two particles similar mass, Casimir-Polder forces lead fundamental limit tenths femtometers per second squared root Hertz. Limits are between three and six orders magnitude less strict for...

Abstract The Schrödinger–Newton equation has gained attention in the recent past as a nonlinear modification of Schrödinger due to gravitational self-interaction. Such is expected from fundamentally semi-classical theory gravity and can, therefore, be considered test case for necessity quantisation field. Here we provide thorough study effects micron-sized sphere trapped harmonic oscillator potential. We discuss both effect on energy eigenstates dynamical behaviour squeezed states, covering...

The evolution of the centre-of-mass wave-function for a mesoscopic particle according to Schr\"odinger-Newton equation can be approximated by harmonic potential, if is narrow compared size particle. It was noticed Colin et al. [Phys. Rev. A, 93, 062102 (2016)] that, in regime where self-gravitational effects are weak, intermediate and wider wave-functions may potential as well, but with width dependent coupling, leading time that determined only differential Gaussian single parameter. Such...

We derive the effect of Schr\"odinger-Newton equation, which can be considered as a nonrelativistic limit classical gravity, for composite quantum system in regime high energies. Such meson-antimeson systems exhibit very unique properties, e.g., distinct masses due to strong and electroweak interactions. This raises an immediate question: what does one mean by mass gravity state that is superposition eigenstates interactions? find conceptually different physical scenarios lacking clear...

We present a detailed derivation of model to study effects self-gravitation from semi-classical gravity, described by the Schr\"odinger-Newton equation, employing spin superposition states in inhomogeneous magnetic fields, as proposed recently for experiments searching gravity induced entanglement. Approximations experimentally relevant limits are discussed. Results suggest that interferometry could provide more accessible route towards an experimental test quantum aspects than both previous...

We present an algorithm that uses a single ancilla qubit can evolve nonlinearly, and show how to use it efficiently solve generic nonlinear Schr\"odinger equations, including nonlocal Hartree equations the Navier-Stokes equation for irrotational, non-viscous flow. propose realization of such qubits via spin-spin coupling neutral atom Bose-Einstein condensate. The results suggest ancillas provide substantial speedups compared exclusively linear devices.

The prediction of non-local phenomena is a key attribute quantum mechanics that distinguishes it from classical theories. It was recently suggested state swapping one such effect fundamentally gravitational field cannot give rise to. reasoning the phenomenology fields restricted to Local Operations and Classical Communication~(LOCC) whereas non-LOCC effect, so gravity must not be channel if can phenomenon. Here, we show Hamiltonian semiclassical results in an evolution coherent states...

A recent analysis by Pikovski et al. [Nat. Phys. 11, 668 (2015)] has triggered interest in the question of how to include relativistic corrections quantum dynamics governing many-particle systems a gravitational field. Here we show center-of-mass motion system subject gravity can be derived more rigorously, addressing ambiguous definition coordinates. We further demonstrate that, contrary prediction al., external forces play crucial role coupling internal and degrees freedom, resulting...