A Spin Entanglement Witness for Quantum Gravity (1707.06050v1)

Abstract: Understanding gravity in the framework of quantum mechanics is one of the great challenges in modern physics. Along this line, a prime question is to find whether gravity is a quantum entity subject to the rules of quantum mechanics. It is fair to say that there are no feasible ideas yet to test the quantum coherent behaviour of gravity directly in a laboratory experiment. Here, we introduce an idea for such a test based on the principle that two objects cannot be entangled without a quantum mediator. We show that despite the weakness of gravity, the phase evolution induced by the gravitational interaction of two micron size test masses in adjacent matter-wave interferometers can detectably entangle them even when they are placed far apart enough to keep Casimir-Polder forces at bay. We provide a prescription for witnessing this entanglement, which certifies gravity as a quantum coherent mediator, through simple correlation measurements between two spins: one embedded in each test mass. Fundamentally, the above entanglement is shown to certify the presence of non-zero off-diagonal terms in the coherent state basis of the gravitational field modes.

• The paper introduces a protocol leveraging spin entanglement in matter-wave interferometry to evidence the quantum nature of gravity.
• It details an experimental design using Stern-Gerlach interferometers that measures phase differences between controlled quantum states of test masses.
• The approach implies that observing gravitationally mediated entanglement necessitates a quantum treatment of gravity, challenging classical perspectives.

A Spin Entanglement Witness for Quantum Gravity

This paper proposes a novel approach for investigating the quantum nature of gravity through an experimental setup designed to detect entanglement between two neutral test masses. The primary objective is to determine whether gravity can be described as a quantum entity, capable of mediating entanglement between spatially separated masses through a quantum field—the graviton.

Entanglement As Evidence for Quantum Gravity

Central to this proposal is the assertion that entanglement cannot arise through classical communication or local operations. Therefore, if two spatially separated masses become entangled, the mediating force must inherently possess quantum characteristics. The authors suggest that by employing adjacent matter-wave interferometers, they can demonstrate measurable entanglement between two micron-sized test masses. This entanglement would be mediated by gravity, acting as evidence of its quantization.

The proposed method relies on the formation of superposition states of test masses separated by a distance that allows gravitational interaction without significant influence from forces such as the Casimir-Polder interaction. By assessing the evolution of these mass states via phase correlations, the experiment seeks to observe quantum superposition effects attributed to gravitational interactions, specifically targeting off-diagonal elements in the coherent state basis of gravitational field modes to signify quantum entanglement.

Experimental Design and Theoretical Analysis

The experimental approach involves configuring two Stern-Gerlach (SG) interferometers to facilitate the splitting and later recombination of test mass states. The SG apparatus is engineered to effectuate phase differences between quantum states sheltered within micro-crystals, such as micro-diamonds containing spin qubits like NV centers, which are isolated from macroscopic decoherence sources. By considering feasible masses and separations in this setup, the paper calculates that measurable phase differences can result, indicative of spin entanglement between the test masses.

The work elaborates on the calculation of gravitational phase shifts as a function of variables such as interaction time, mass, and separating distance. It posits that if entanglement is observed through spin correlations, the gravitational field must inherently possess quantum attributes. The authors assert the necessity for the gravitational field to not only facilitate entanglement but also be explicitly quantum—emphasizing that simulating classical gravitational fields results in a loss of coherence, thereby precluding entanglement.

Challenges and Potential Impacts

The successful realization of this protocol hinges upon precision in maintaining minimal decoherence and isolating the system from non-gravitational interactions. The control over internal temperatures, precise measurements of spin correlations, and navigations through the technicalities of interferometry are acknowledged challenges that demand innovation in experimental physics.

The implications of this investigation are significant, as it may define the extent to which classical and quantum theories intersect regarding gravitational phenomena. Observations consistent with the proposed entanglement mediated by the quantized gravitational field could direct theoretical and empirical research, potentially recalibrating classical gravitational theories to integrate quantization. Such implications could also influence models relating to cosmology, high energy physics, and quantum field theories.

Conclusion

Through its approach, using entanglement as a probe for the quantum character of gravity, this paper positions itself as a pioneering attempt to devise feasible laboratory experiments where gravitational interactions reveal quantum features. While primarily a theoretical outline requiring rigorous empirical verification, the research initiates a conceptual framework suggesting that closeness to macroscopic coherence and quantum measurements can furnish valid insights into the nature of gravity as a quantum entity. By providing structured theoretical and experimental guidelines, it fosters momentum towards one of the profound open questions in contemporary physics, potentially altering the course of quantum gravity research.