Leggett-Garg Inequality Violation Demonstrates Nonclassicality in Photon-Graviton Conversion Experiments

Scientists are increasingly exploring the boundaries between quantum mechanics and gravity, and a new study demonstrates a potential pathway to test fundamental aspects of both. Kimihiro Nomura from Kyoto University, Akira Taniguchi from Kyushu University, and Kazushige Ueda from the National Institute of Technology, Tokuyama College, et al., present analytical evidence for violation of the Leggett-Garg inequality within the process of photon-graviton conversion in a magnetic field. This research is significant because it proposes a method to probe the nonclassicality of gravity by examining the temporal correlations arising from a superposition of photon and graviton states, potentially offering a novel approach to understanding the quantum nature of gravitational perturbations.

The team analytically investigated the LGI violation arising from the conversion of photons into gravitons in the presence of a magnetic field, establishing a theoretical framework for observing nonclassical correlations. The study meticulously models photon-graviton conversion within a quantum-mechanical framework, beginning with the derivation of a Lagrangian describing the interaction. Crucially, the researchers show that temporal correlations obtained from successive projective measurements on this photon-graviton system demonstrably violate the LGI.

This violation serves as a quantitative test of the nonclassicality of the system, implying a failure of either macroscopic realism or noninvasive measurability, assumptions consistent with classical intuition. The analytical approach allows for precise calculations of the conversion probability of a photon into a graviton, essential for predicting the magnitude of the LGI violation. This breakthrough reveals a potential avenue for probing gravity at the quantum level, circumventing the challenges associated with direct graviton detection. The team’s calculations, performed in natural units where ħ= c = 1, detail the conditions under which these violations are expected to occur, providing specific parameters for future experimental investigations.
This approach is particularly well-suited to two-level systems exhibiting oscillatory dynamics, mirroring similar analyses conducted in areas like neutrino oscillations. Furthermore, the work connects to existing research exploring gravitational radiation in squeezed states and graviton-magnon or photon conversion schemes. By focusing on the LGI, the scientists provide a criterion for identifying nonclassical behaviour, building upon the established foundation of Bell’s inequality and its temporal analogue. This detailed analysis paves the way for designing experiments aimed at detecting these subtle quantum gravitational effects and furthering our understanding of the universe at its most fundamental level.

Photon-graviton superposition and Leggett-Garg inequality violation

This engineered superposition was central to demonstrating the potential for LGI violation. The study pioneered a theoretical framework to predict LGI violation based on the specific characteristics of photon-graviton interactions. Calculations detailed how the superposition state evolves over time, enabling the prediction of correlation functions necessary for evaluating the LGI. Specifically, the team derived expressions for the probability amplitudes of detecting either a photon or a graviton at different points in time, forming the basis for the correlation analysis. This analytical approach bypasses the need for complex numerical simulations, offering a direct pathway to assess nonclassicality.

Experiments employing this methodology would require precise control over the magnetic field and the initial photon state. Detecting gravitons remains a significant technological challenge, but the theoretical framework developed in this work establishes a clear signature for nonclassicality if such detection becomes feasible. The team demonstrated that the predicted LGI violation arises directly from the quantum superposition and the temporal correlations it induces, providing a novel avenue for probing the nature of gravity. Furthermore, the research highlights the potential for utilising photon-graviton conversion as a unique platform for testing fundamental aspects of quantum mechanics. The analytical results show that the degree of LGI violation is sensitive to the strength of the magnetic field and the initial photon state, offering parameters for optimising the experiment. Observation of this violation would not only confirm the nonclassicality of the system but also provide insights into the interplay between quantum mechanics and general relativity.

Leggett-Garg inequality violation via photon-graviton conversion suggests nonlocal

The team defined the temporal correlation function, Cab, between two distinct times, ta and tb, as the ensemble average of the product of measurement outcomes, Qa and Qb, weighted by the joint probability Pab(Qa, Qb). Specifically, measurements at times t1, t2, and t3 yielded correlation functions C12, C23, and C13, which were then combined to calculate K3 ≡ C12 + C23 − C13. Measurements confirm that a violation of the LGI occurs when K3 exceeds 1, indicating a nonclassical system. Researchers established a quadratic action, S(2), representing the system’s dynamics, incorporating terms up to second order in the dynamical variables.

This action included contributions from both the photon and graviton fields, as well as a mixing term proportional to λ, the coupling strength between the two. The mixing strength is defined as λ ≡ √ 2 MP εijl e+ i (k) kj k Bl, where MP represents the Planck mass and B is the magnitude of the background magnetic field. When electromagnetic waves propagate perpendicular to the magnetic field, the mixing strength simplifies to λ = √ 2B/MP, maximizing the photon-graviton conversion rate. Data shows that the Lagrangian can be diagonalized to reveal the decoupled dynamics of the photon and graviton modes, simplifying the analysis of their temporal behavior. The resulting oscillatory behavior of the transition probabilities between photon and graviton states is crucial for observing the LGI violation., The authors acknowledge that their analysis relies on the assumptions of macroscopic realism and noninvasive measurability, which, if invalidated, would explain the observed LGI violation. Future research could focus on exploring the practical feasibility of observing this LGI violation in experimental settings and refining the theoretical model to account for potential sources of decoherence.