On the origin of force sensitivity in tests of quantum gravity with delocalised mechanical systems

The detection of the quantum nature of gravity in the low-energy limit hinges on achieving an unprecedented degree of force sensitivity with mechanical systems. Against this background, we explore the relationship between the sensitivity of mechanical systems to external forces and the properties of the quantum states they are prepared in. We establish that the main determinant of the force sensitivity in pure quantum states is their spatial delocalisation and we link the force sensitivity to the rate at which two mechanical systems become entangled under a quantum force. We exemplify this at the hand of two commonly considered configurations. One that involves gravitationally interacting objects prepared in non-Gaussian states such as Schr\"odinger-cat states, where the generation of entanglement is typically ascribed to the accumulation of a dynamical phase between components in superposition. The other prepares particles in Gaussian states that are strongly squeezed in momentum and delocalised in position where entanglement generation is attributed to accelerations. We offer a unified description of these two arrangements using the phase-space representation and link their entangling rate to their force sensitivity, showing that both configurations get entangled at the same rate provided that they are equally delocalised in space. Our description in phase space and the established relation between force sensitivity and entanglement sheds light on the intricacies of why the equivalence between these two configurations holds, something that is not always evident in the literature, due to the distinct physical and analytical methods employed to study each of them. Notably, we demonstrate that while the conventional computation of entanglement via the dynamical phase remains accurate for Schr\"odinger-cat states, it yields erroneous estimations for systems in squeezed cat states.Comment: Invited contribution to Contemporary Physics. 16 pages (+ bibliography), 6 figure

Testing the quantum nature of gravity without entanglement

Given a unitary evolution $U$ on a multi-partite quantum system and an ensemble of initial states, how well can $U$ be simulated by local operations and classical communication (LOCC) on that ensemble? We answer this question by establishing a general, efficiently computable upper bound on the maximal LOCC simulation fidelity -- what we call an "LOCC inequality". We then apply our findings to the fundamental setting where $U$ implements a quantum Newtonian Hamiltonian over a gravitationally interacting system. Violation of our LOCC inequality can rule out the LOCCness of the underlying evolution, thereby establishing the non-classicality of the gravitational dynamics, which can no longer be explained by a local classical field. As a prominent application of this scheme we study systems of quantum harmonic oscillators initialised in coherent states following a normal distribution and interacting via Newtonian gravity, and discuss a possible physical implementation with torsion pendula. One of our main technical contributions is the analytical calculation of the above LOCC inequality for this family of systems. As opposed to existing tests based on the detection of gravitationally mediated entanglement, our proposal works with coherent states alone, and thus it does not require the generation of largely delocalised states of motion nor the detection of entanglement, which is never created at any point in the process.Comment: 25+20 pages, 7 figures. In v2 we improved the presentation considerabl

Motional dynamical decoupling for interferometry with macroscopic particles

We extend the concept of dynamical decoupling from spin to mechanical degrees of freedom of macroscopic objects, for application in interferometry. In this manner, the superposition of matter waves can be made resilient to many important sources of noise when these are driven along suitable paths in space. As a concrete implementation, we present the case of levitated (or free falling) nanodiamonds hosting a color center in a magnetic field gradient. We point out that these interferometers are inherently affected by diamagnetic forces, which restrict the separation of the superposed states to distances that scale with the inverse of the magnetic field gradient. Periodic forcing of the mechanical degree of freedom is shown to overcome this limitation, achieving a linear-in-time growth of the separation distance independent of the magnetic field gradient, while simultaneously protecting the coherence of the superposition from environmental perturbations

Quantum simulation of the quantum Rabi model in a trapped ion

The quantum Rabi model, involving a two-level system and a bosonic field mode, is arguably the simplest and most fundamental model describing quantum light-matter interactions. Historically, due to the restricted parameter regimes of natural light-matter processes, the richness of this model has been elusive in the lab. Here, we experimentally realize a quantum simulation of the quantum Rabi model in a single trapped ion, where the coupling strength between the simulated light mode and atom can be tuned at will. The versatility of the demonstrated quantum simulator enables us to experimentally explore the quantum Rabi model in detail, including a wide range of otherwise unaccessible phenomena, as those happening in the ultrastrong and deep strong coupling regimes. In this sense, we are able to adiabatically generate the ground state of the quantum Rabi model in the deep strong coupling regime, where we are able to detect the nontrivial entanglement between the bosonic field mode and the two-level system. Moreover, we observe the breakdown of the rotating-wave approximation when the coupling strength is increased, and the generation of phonon wave packets that bounce back and forth when the coupling reaches the deep strong coupling regime. Finally, we also measure the energy spectrum of the quantum Rabi model in the ultrastrong coupling regime.Comment: 8 pages, 4 figure

Measuring Entanglement in a Photonic Embedding Quantum Simulator

Measuring entanglement is a demanding task that usually requires full tomography of a quantum system, involving a number of observables that grows exponentially with the number of parties. Recently, it was suggested that adding a single ancillary qubit would allow for the efficient measurement of concurrence, and indeed any entanglement monotone associated to antilinear operations. Here, we report on the experimental implementation of such a device---an embedding quantum simulator---in photonics, encoding the entangling dynamics of a bipartite system into a tripartite one. We show that bipartite concurrence can be efficiently extracted from the measurement of merely two observables, instead of fifteen, without full tomographic information.Comment: Updated versio

Quantum Simulation Of The Quantum Rabi Model In A Trapped Ion

The quantum Rabi model, involving a two-level system and a bosonic field mode, is arguably the simplest and most fundamental model describing quantum light-matter interactions. Historically, due to the restricted parameter regimes of natural light-matter processes, the richness of this model has been elusive in the lab. Here, we experimentally realize a quantum simulation of the quantum Rabi model in a single trapped ion, where the coupling strength between the simulated light mode and atom can be tuned at will. The versatility of the demonstrated quantum simulator enables us to experimentally explore the quantum Rabi model in detail, including a wide range of otherwise unaccessible phenomena, as those happening in the ultrastrong and deep strong-coupling regimes. In this sense, we are able to adiabatically generate the ground state of the quantum Rabi model in the deep strong-coupling regime, where we are able to detect the nontrivial entanglement between the bosonic field mode and the two-level system. Moreover, we observe the breakdown of the rotating-wave approximation when the coupling strength is increased, and the generation of phonon wave packets that bounce back arid forth when the coupling reaches the deep strong-coupling regime. Finally, we also measure the energy spectrum of the quantum Rabi model in the ultrastrong-coupling regime.We thank Xiao Yuan, Xiongfeng Ma, Hyunchul Nha, Jiyong Park, Jaehak Lee, and M. S. Kim for useful discussions on the entanglement verification of the ground state. This work was supported by the National Key Research and Development Program of China under Grants No. 2016YFA0301900 and No. 2016YFA0301901 and the National Natural Science Foundation of China Grants No. 11374178, No. 11574002, and No. 11504197, MINECO/FEDER FIS2015-69983-P, Ramon y Cajal Grant No. RYC-2012-11391, and Basque Government IT986-16

A Study on Fast Gates for Large-Scale Quantum Simulation with Trapped Ions

Large-scale digital quantum simulations require thousands of fundamental entangling gates to construct the simulated dynamics. Despite success in a variety of small-scale simulations, quantum information processing platforms have hitherto failed to demonstrate the combination of precise control and scalability required to systematically outmatch classical simulators. We analyse how fast gates could enable trapped-ion quantum processors to achieve the requisite scalability to outperform classical computers without error correction. We analyze the performance of a large-scale digital simulator, and find that fidelity of around 70% is realizable for π-pulse infidelities below 10−5 in traps subject to realistic rates of heating and dephasing. This scalability relies on fast gates: entangling gates faster than the trap perio