Many theories of quantum gravity can be understood as imposing a minimum length scale the signatures of which can potentially be seen in precise table top experiments. In this work, we inspect the capacity for correlated many-body systems to probe non-classicalities of spacetime through modifications of the commutation relations. We find an analytic derivation of the dynamics for a single mode light field interacting with a single mechanical oscillator and with coupled oscillators to first order corrections to the commutation relations. Our solution is valid for any coupling function as we work out the full Magnus expansion. We numerically show that it is possible to have superquadratic scaling of a nonstandard phase term, arising from the modification to the commutation relations, with coupled mechanical oscillators.
Many theories of quantum gravity can be understood as imposing a minimum length scale the signatures of which can potentially be seen in precise table top experiments. In this work, we inspect the capacity for correlated many-body systems to probe non-classicalities of spacetime through modifications of the commutation relations. We find an analytic derivation of the dynamics for a single mode light field interacting with a single mechanical oscillator and with coupled oscillators to first order corrections to the commutation relations. Our solution is valid for any coupling function as we work out the full Magnus expansion. We numerically show that it is possible to have superquadratic scaling of a nonstandard phase term, arising from the modification to the commutation relations, with coupled mechanical oscillators.
Abstract Phenomenological models aiming to join gravity and quantum mechanics often predict effects that are potentially measurable in refined low-energy experiments. For instance, modified commutation relations between position and momentum, that account for a minimal scale length, yield a dynamics that can be codified in additional Hamiltonian terms. When applied to the paradigmatic case of a mechanical oscillator, such terms, at the lowest order in the deformation parameter, introduce a weak intrinsic nonlinearity and, consequently, deviations from the classical trajectory. This point of view has stimulated several experimental proposals and realizations, leading to meaningful upper limits to the deformation parameter. All such experiments are based on classical mechanical oscillators, i.e., excited from a thermal state. We remark indeed that decoherence, that plays a major role in distinguishing the classical from the quantum behavior of (macroscopic) systems, is not usually included in phenomenological quantum gravity models. However, it would not be surprising if peculiar features that are predicted by considering the joined roles of gravity and quantum physics should manifest themselves just on purely quantum objects. On the basis of this consideration, we propose experiments aiming to observe possible quantum gravity effects on macroscopic mechanical oscillators that are preliminary prepared in a high purity state, and we report on the status of their realization. Graphical abstract
This thesis is about probing aspects of the foundations of quantum mechanics. Firstly, two notions of quantum nonlocality are explored: EPR-steering, the ability to control a remote quantum state, and Bell nonlocality, the inconsistency of a theory with local causality. A necessary and sufficient witness of Einstein-Podolsky- Rosen (EPR) steering is derived for a two qubit system employing only correlations between two arbitrary dichotomic measurements on each party. It is demonstrated that all states that are EPR-steerable with such correlations are also Bell nonlocal, a surprising equivalence between these two fundamental concepts of quantum mechanics. Next, testing modifications of the quantum mechanical canonical commutation relations is addressed. These are properties of some quantum gravity theories that involve an effective minimal length. It is shown that optomechanical probes of position noise spectrum of macroscopic oscillators can produce constraints on these theories. A comparison with current and future realistic experiments reveals the potential to beat constraints from direct experiments on elementary particles. Finally, it is studied how such modifications of quantum mechanics manifest in the theory of general continuous quantum position measurements. Several behaviours are found that deviate strongly from that of standard commutation relations.
Models of quantum gravity imply a fundamental revision of our description of position and momentum that manifests in modifications of the canonical commutation relations. Experimental tests of such modifications remain an outstanding challenge. These corrections scale with the mass of test particles, which motivates experiments using macroscopic composite particles. Here we consider a challenge to such tests, namely that quantum gravity corrections of canonical commutation relations are expected to be suppressed with increasing number of constituent particles. Since the precise scaling of this suppression is unknown, it needs to be bounded experimentally and explicitly incorporated into rigorous analyses of quantum gravity tests. We analyse this scaling based on data from past experiments involving macroscopic pendula, and provide tight bounds that exceed those of current experiments based on quantum mechanical oscillators. Furthermore, we discuss possible experiments that promise even stronger bounds thus bringing rigorous and well-controlled tests of quantum gravity closer to reality.
Models of quantum gravity imply a fundamental revision of our description of position and momentum that manifests in modifications of the canonical commutation relations. Experimental tests of such modifications remain an outstanding challenge. These corrections scale with the mass of test particles, which motivates experiments using macroscopic composite particles. Here we consider a challenge to such tests, namely that quantum gravity corrections of canonical commutation relations are expected to be suppressed with increasing number of constituent particles. Since the precise scaling of this suppression is unknown, it needs to be bounded experimentally and explicitly incorporated into rigorous analyses of quantum gravity tests. We analyse this scaling based on data from past experiments involving macroscopic pendula, and provide tight bounds that exceed those of current experiments based on quantum mechanical oscillators. Furthermore, we discuss possible experiments that promise even stronger bounds thus bringing rigorous and well-controlled tests of quantum gravity closer to reality.
Many quantum-gravity scenarios predict a minute modification of the canonical commutator, known as the generalized uncertainty principle (GUP), whose low-energy signatures are, in principle, accessible to state-of-the-art laboratory tests. We compute first-order minimal-length corrections to the quantum speed limit (QSL) for three cases: uniform superpositions in an infinite square well, coherent harmonic-oscillator states, and squeezed-oscillator states. We identify a universal amplification law: for any pure state, the fractional shift of either speed limit scales linearly with β and algebraically with the state's effective Hilbert-space size. As the effective Hilbert-space dimension can be exceedingly large, the associated minimal-length signatures are amplified by several orders of magnitude. Using high-precision matter-wave timing data, we set a direct bound on the GUP parameter β, which quantifies minimal-length quantum-gravity effects. Our analysis indicates that phase-locked, short-time overlap fits on kilogram-scale optical-spring modes can tighten this bound by orders of magnitude. We outline two implementable measurement pipelines -- continuous back-action-evading single-quadrature readout and stroboscopic, phase-locked pulsed tomography -- that exploit this leverage, making QSL-based timing a practical, near-term probe of minimal-length physics on quantum-optical and optomechanical platforms.
We propose an optomechanics experiment that can search for signatures of a fundamentally classical theory of gravity and in particular of the many-body Schr\"odinger-Newton (SN) equation, which governs the evolution of a crystal under a self-gravitational field. The SN equation predicts that the dynamics of a macroscopic mechanical oscillator's center-of-mass wave function differ from the predictions of standard quantum mechanics [H. Yang, H. Miao, D.-S. Lee, B. Helou, and Y. Chen, Phys. Rev. Lett. 110, 170401 (2013)]. This difference is largest for low-frequency oscillators, and for materials, such as tungsten or osmium, with small quantum fluctuations of the constituent atoms around their lattice equilibrium sites. Light probes the motion of these oscillators and is eventually measured in order to extract valuable information on the pendulum's dynamics. Due to the nonlinearity contained in the SN equation, we analyze the fluctuations of measurement results differently than standard quantum mechanics. We revisit how to model a thermal bath, and the wave-function collapse postulate, resulting in two prescriptions for analyzing the quantum measurement of the light. We demonstrate that both predict features, in the outgoing light's phase fluctuations' spectrum, which are separate from classical thermal fluctuations and quantum shot noise, and which can be clearly resolved with state of the art technology.