Abstract No experiment to date has provided evidence for quantum features of the gravitational interaction. Recently proposed tests suggest looking for the generation of quantum entanglement between massive objects as a possible route towards the observation of such features. Motivated by advances in optical cooling of mirrors, here we provide a systematic study of entanglement between two masses that are coupled gravitationally. We first consider the masses trapped at all times in harmonic potentials (optomechanics) and then the masses released from the traps. This leads to the estimate of the experimental parameters required for the observation of gravitationally induced entanglement. The optomechanical setup demands LIGO-like mirrors and squeezing or long coherence times, but the released masses can be light and accumulate detectable entanglement in a timescale shorter than their coherence times. No macroscopic quantum superposition develops during the evolution. We discuss the implications from such thought experiments regarding the nature of the gravitational coupling.
Abstract No experiment to date has provided evidence for quantum features of the gravitational interaction. Recently proposed tests suggest looking for the generation of quantum entanglement between massive objects as a possible route towards the observation of such features. Motivated by advances in optical cooling of mirrors, here we provide a systematic study of entanglement between two masses that are coupled gravitationally. We first consider the masses trapped at all times in harmonic potentials (optomechanics) and then the masses released from the traps. This leads to the estimate of the experimental parameters required for the observation of gravitationally induced entanglement. The optomechanical setup demands LIGO-like mirrors and squeezing or long coherence times, but the released masses can be light and accumulate detectable entanglement in a timescale shorter than their coherence times. No macroscopic quantum superposition develops during the evolution. We discuss the implications from such thought experiments regarding the nature of the gravitational coupling.
We report the feasibility of detecting the gravity-induced entanglement (GIE) with optomechanical systems, which is the first investigation that clarifies the feasible experimental parameters to achieve a signal-to-noise ratio of S/N=1. Our proposal focuses on GIE generation between optomechanical mirrors, coupled via gravitational interactions, under continuous measurement, feedback control, and Kalman filtering process, which matured in connection with the field of gravitational wave observations. We solved the Riccati equation to evaluate the time evolution of the conditional covariance matrix for optomechanical mirrors that estimated the minimum variance of the motions. The results demonstrate that GIE is generated faster than a well-known time scale without optomechanical coupling. The fast generation of entanglement is associated with quantum-state squeezing by the Kalman filtering process, which is an advantage of using optomechanical systems to experimentally detect GIE.
Gravitationally induced entanglement has been proposed as a probe of the quantum nature of gravity. This work analyzes a system of two particles in harmonic traps interacting only through gravity, considering thermal and two-mode squeezed initial states. For thermal states, a maximum temperature is identified above which entanglement cannot be generated, and for fixed system parameters an optimal trap frequency that maximizes the logarithmic negativity is found. Squeezing the initial state does not further enhance the entanglement generation, but increases the temperature range over which it can be observed. Extending the analysis to general Gaussian states, an upper bound on the achievable entanglement is derived and shown to be saturated, for example, by ground and squeezed states. The results show that the amount of entanglement generated in this setup is extremely small, highlighting the experimental challenges of observing gravitationally induced quantum effects.
A promising route to testing quantum gravity in the laboratory is to look for gravitationally induced entanglement (GIE) between two or more quantum matter systems. To date, proposed tests have primarily focused on microsolid platforms prepared in highly nonclassical states, such as N00N states or strongly squeezed states. Here, we instead consider measuring GIE in atom interferometry as evidence of quantum gravity. We propose placing two atom interferometers next to each other in parallel and looking for correlations in the atom-number statistics at their output ports. Importantly, GIE is possible without challenging macroscopic superposition states, such as N00N or Schrödinger-cat states. Instead, GIE can arise using coherent, near-classical atomic states, substantially reducing the experimental complexity. Observing the effect in this regime would require the total mass of the atom interferometers to be near the Planck mass scale. However, we show that state-of-the-art quantum squeezing techniques in cold-atom systems can significantly lower this mass requirement, and outline realistic pathways by which the necessary mass scales could be achieved in the near future, placing laboratory tests of GIE with atom interferometers within reach.
Observation of gravitationally induced quantum entanglement is often interpreted as a direct evidence of non-classical gravity. While the form and the degree of non-classicality have been rigorously studied from a foundational perspective, classical models reproducing experimental signatures of such entanglement remain underexplored. Motivated by the experimental simplicity, nearly all existing optomechanical approaches assume Gaussian initial states, and due to the weakness of gravity the quantum Newtonian potential is truncated at the second order. However, this regime admits a classical description in terms of the Wigner-Weyl representation, including features typically associated with quantum entanglement. A clear distinction between classical and quantum predictions emerges only beyond this setting. We comprehensively analyze the possibilities and provide operational witnesses for detection of non-classicality via Wigner negativity, and detection of non-quantumness via negativity of the Weyl operator. Our results demonstrate that the experimental requirements on certifying gravitational entanglement are more stringent than previously anticipated.
Abstract 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, 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 a toy model composed of two light and two heavy quantum oscillators prepared in the motional ground state, 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 decoherence in the proposed experiment for testing the quantum nature of gravity.
Over the past century, a large community within theoretical physics has been seeking a unified framework for quantum gravity. Yet, to date, there is still no experimental evidence of any non-classical features of gravity. While traditional experimental proposals would usually require immensely challenging Planck scale experiments, recent table-top protocols based on low-energy quantum control have opened a new avenue into the investigation of non-classical gravity. An approach that has sparked high interest, both in terms of experimental feasibility and of theoretical implications, is the indirect witnessing of non-classical gravity through the detection of its capacity to act as an entangling channel. Most discussions have been centred on the entanglement generation between two gravitationally coupled massive systems. In this work, we instead examine the entangling capacity of the gravitational interaction between two light pulses. We explain the main experimental and theoretical advantages of having a photonic protocol, and lay out the steps leading to the determination of the entangling phase, using the path integral formalism and linearised gravity. We establish a closed form formula for the entangling phase and provide an estimated order of magnitude of the average photon number required for the generation of appreciable phase. Using statistical analysis, we show how entanglement may be certified with lower phase signal.