Levitated Oscillator Amplifies Subtle Deviations From Standard Quantum Mechanics

The subtle interplay between quantum mechanics and gravity remains one of the most challenging frontiers in physics, with experimental verification of theoretical predictions proving exceptionally difficult. Researchers now propose a method to amplify the minuscule deviations from standard quantum behaviour predicted by the Schrödinger-Newton equation, a modification of the Schrödinger equation incorporating self-gravitational effects. Davide Giordano, Ario Altamura, and colleagues, from the University of Trieste and the University of Southampton, detail their approach in a new article entitled ‘Enhancement of the effects due to the Schrödinger-Newton equation’, demonstrating how periodic modulation of a levitated mechanical oscillator’s trapping frequency can enhance these effects by up to six orders of magnitude, bringing a viable experimental test of the equation within reach.

Research details a method to enhance the detection of deviations from standard quantum mechanics, predicted by the Schrödinger-Newton (SN) equation, a theoretical model incorporating self-gravitational effects into quantum mechanics. The challenge in testing the SN equation lies in the typically minuscule deviations it predicts from established quantum behaviour, and researchers address this through periodic modulation of the trapping frequency of a levitated mechanical oscillator. Calculations demonstrate that this periodic modulation significantly enhances SN-induced effects on the system’s second moments, achieving an amplification of up to six orders of magnitude compared to unmodulated systems.

The approach centres on manipulating the dynamics of second moments, quantities describing the spread and correlation of position and momentum. These moments provide a sensitive measure of the uncertainty inherent in quantum systems. The methodology relies on a detailed mathematical framework, calculating the time evolution of expectation values – the average value of a quantity – and utilising Green’s functions, mathematical tools used to solve differential equations, to express these averages in terms of initial conditions and the applied forcing function, the periodic modulation of the trapping frequency.

The analysis incorporates the influence of thermal fluctuations, random movements caused by temperature, and includes terms that account for their contribution to the system’s dynamics. This ensures the proposed protocol remains feasible within the constraints of current magnetic levitation technologies, where a particle is suspended using magnetic fields. The method enables the distinction between standard quantum dynamics and the predictions of the SN equation through measurable quantities, notably the position variance, a measure of the spread of the particle’s position.

This provides a pathway for a viable experimental test of the SN equation, offering a novel approach to investigate the interface between mechanics and quantum phenomena. The amplified deviations provide a pathway to experimentally verify the SN equation, a longstanding goal in fundamental physics, and offers a novel route to test the limits of standard quantum mechanics and explore potential modifications that may be necessary to reconcile it with general relativity, Einstein’s theory of gravity. Future work will focus on refining the experimental setup and exploring the limits of this technique.