Combining gravity with quantum mechanics remains one of the biggest challenges of physics. In the past years, experiments with optomechanical systems have been proposed that may give indirect clues about the quantum nature of gravity. In a recent variation of such tests [Carney et al., PRX Quantum 2, 030330 (2021)], the authors propose to gravitationally entangle an atom interferometer with a mesoscopic oscillator. The interaction results in periodic drops and revivals of the interferometeric visibility, which under specific assumptions indicate the gravitational generation of entanglement. Here, we study semiclassical models of the atom interferometer that can reproduce the same effect. We show that the core signature---periodic collapses and revivals of the visibility---can appear if the atom is subject to a random unitary channel, including the case where the oscillator is fully classical and situations even without explicit modeling of the oscillator. We also show that the nonclassicality of the oscillator vanishes unless the system is very close to its ground state, and even when the system is in the ground state, the nonclassicality is limited by the coupling strength. Our results thus indicate that deducing entanglement from the proposed experiment is very challenging, since fulfilling and verifying the nonclassicality assumptions constitute a significant challenge in their own right.
Combining gravity with quantum mechanics remains one of the biggest challenges of physics. In the past years, experiments with optomechanical systems have been proposed that may give indirect clues about the quantum nature of gravity. In a recent variation of such tests [Carney et al., PRX Quantum 2, 030330 (2021)], the authors propose to gravitationally entangle an atom interferometer with a mesoscopic oscillator. The interaction results in periodic drops and revivals of the interferometeric visibility, which under specific assumptions indicate the gravitational generation of entanglement. Here, we study semiclassical models of the atom interferometer that can reproduce the same effect. We show that the core signature---periodic collapses and revivals of the visibility---can appear if the atom is subject to a random unitary channel, including the case where the oscillator is fully classical and situations even without explicit modeling of the oscillator. We also show that the nonclassicality of the oscillator vanishes unless the system is very close to its ground state, and even when the system is in the ground state, the nonclassicality is limited by the coupling strength. Our results thus indicate that deducing entanglement from the proposed experiment is very challenging, since fulfilling and verifying the nonclassicality assumptions constitute a significant challenge in their own right.
Finding a feasible scheme for testing the quantum mechanical nature of the gravitational interaction has been attracting an increasing level of attention. Gravity mediated entanglement generation so far appears to be the key ingredient for a potential experiment. In a recent proposal [D. Carney et al., PRX Quantum 2, 030330 (2021)] combining an atom interferometer with a low-frequency mechanical oscillator, a coherence revival test is proposed for verifying this entanglement generation. With measurements performed only on the atoms, this protocol bypasses the need for correlation measurements. Here, we explore formulations of such a protocol, and specifically find that in the envisioned regime of operation with high thermal excitation, semiclassical models, where there is no concept of entanglement, also give the same experimental signatures. We elucidate in a fully quantum mechanical calculation that entanglement is not the source of the revivals in the relevant parameter regime. We argue that, in its current form, the suggested test is only relevant if the oscillator is nearly in a pure quantum state, and in this regime the effects are too small to be measurable. We further discuss potential open ends. The results highlight the importance and subtleties of explicitly considering how the quantum case differs from the classical expectations when testing for the quantum mechanical nature of a physical system.
We show that the atom interferometric coherence revival test suggested in [arXiv:2101.11629 [quant-ph] (2021)] does not test the quantum nature of the gravitational field when the atoms are coupled to a mechanical oscillator prepared in a thermal state. Specifically we clarify that the same coherence revivals take place in a model where the atoms are coupled to a classical oscillator through a classical gravitational field. We further elucidate the quantum mechanical calculation, showing that entanglement is not the source of the revivals. The suggested test is thus only relevant for pure initial quantum states of the oscillator. In this regime, numerical estimates show that it is unfeasible to do a test of the proposed type.
A consistent theory including gravitational effects in quantum mechanics has not been found. Although many different approaches have been proposed for theory of quantum gravity, several authors have suggested that gravity may be fundamentally classical. As there is no experimental evidence for a fundamentally quantum vs. fundamentally classical theory of gravity, it is hoped that investigating the consequences of semiclassical gravity, one may propose an experiment to distinguish between the quantum or classical nature of gravity. As opto- and electromechanical devices allow quantum limited measurement and control over massive, mechanical degrees of freedom, they are ideal systems to test violations of standard quantum mechanics arising from gravitational effects. After a brief introduction to the background theory and literature review, we begin by introducing a semiclassical model of gravity based on quantum measurement and control. We show under which conditions the theory behaves like a collapse model, and how a Newtonian potential is recovered in the multi particle case.We then go on to analyse our semiclassical model in two scenarios: firstly in a cosmological setting, and secondly by considering quantum clocks on the surface of the earth. In the cosmological description, we show that a violation of energy conservation, resulting from our model, can be reinterpreted as a dark energy fluid in the spacetime, suggesting that perhaps local violations of conservations of energy may be resolved in a cosmological framework. Secondly, we derive a minimum, gravitational dephasing rate for quantum clocks under the semiclassical model, which unsurprisingly, is is well below the resolution of current state of the art clocks. The next chapters diverge from analysing the gravitational model, and instead focus on novel methods of manipulating and measuring micromechanical devices, that may be used to experimentally probe the results of the semi-classical theory. Firstly we show that a sequence of coherently controlled pulses in an optomechanical system can be used to directly probe the momentum of an oscillator - opening up the possibility for direct detection of momentum diffusion, which is a consequence of the semiclassical gravity model. Secondly, we introduce an electro-mechanical device, and sequence of control operations, that may be understood as an interferometer for the wave function of a mechanical oscillator coupled to a qubit. We show how the resulting interference pattern can distinguish between unitary evolution, thermalisation/decoherence, and a purely classical description of the mechanical oscillator. We also show how the qubit-oscillator interaction can be used generate arbitrary wave functions of the mechanical oscillator, using only classical qubit driving.
We propose an experiment to test the non-classicality of the gravitational interaction. We consider two optomechanical systems that are perfectly isolated, except for a weak gravitational coupling. If a suitable resonance condition is satisfied, an optical signal can be transmitted from one system to the other over a narrow frequency band, a phenomenon that we call gravitationally induced transparency. In this framework, the challenging problem of testing the quantum nature of gravity is mapped to the easier task of determining the non-classicality of the gravitationally-induced optical channel: If the optical channel is not entanglement-breaking, then gravity must have a quantum nature. This approach is applicable without making any assumption on the, currently unknown, correct model of gravity in the quantum regime. In the second part of this work, we model gravity as a quadratic Hamiltonian interaction (e.g. a weak Newtonian force), resulting in a Gaussian thermal attenuator channel between the two systems. Depending on the strength of thermal noise, the system presents a sharp transition from an entanglement-breaking to a non-classical channel capable not only of entanglement preservation but also of asymptotically perfect quantum communication.
We suggest a test of a central prediction of perturbatively quantized general relativity: the coherent communication of quantum information between massive objects through gravity. To do this, we introduce the concept of interactive quantum information sensing, a protocol tailored to the verification of dynamical entanglement generation between a pair of systems. Concretely, we propose to monitor the periodic wavefunction collapse and revival in an atomic interferometer which is gravitationally coupled to a mechanical oscillator. We prove a theorem which shows that, under the assumption of time-translation invariance, this collapse and revival is possible if and only if the gravitational interaction forms an entangling channel. Remarkably, as this approach improves at moderate temperatures and relies primarily upon atomic coherence, our numerical estimates indicate feasibility with current devices.
We investigate how to entangle an atom interferometer and a macroscopic mechanical oscillator to create nonclassical states of the oscillator. This work is done in the context of an experimental-theoretical collaboration that aims to implement the proposal in the paper “Using an Atom Interferometer to Infer Gravitational Entanglement Generation,” written by Carney . []. Here, we propose an entanglement witness (EW), from whose violation the generation of entanglement can be determined. We do this for three scenarios: the noiseless case, when including thermal noise, and with atomic dephasing. Thermal noise can arise from two sources: the first being when the oscillator starts in a thermal state, and the second when a continuous thermal bath is in contact with the oscillator. We find that for the appropriate oscillator quality factor Q , violation always exists for any value of coupling λ and thermal occupancy n ¯ . Cooling the oscillator to its ground state provides an O ( n ¯ ) improvement in the EW violation than when starting in a thermal state; in this case, we find that couplings of λ = 10 − 4.5 require at least ∼ 10 5.2 measurements for violation to be observed. For atomic dephasing, we find that EW violation can exist for an atom interferometer with a coherence time of 600 s, which is the parameter our experimental collaborators hope to reach. Finally, we consider how to use magnetic interactions to realize this idea within the context of the torsional pendulum that has been planned for our collaboration.