Direct observation of deterministic macroscopic entanglement

Abstract: Quantum entanglement of mechanical systems emerges when distinct objects move with such a high degree of correlation that they can no longer be described separately. Although quantum mechanics presumably applies to objects of all sizes, directly observing entanglement becomes challenging as masses increase, requiring measurement and control with a vanishingly small error. Here, using pulsed electromechanics, we deterministically entangle two mechanical drumheads with masses of 70 pg. Through nearly quantum-limited measurements of the position and momentum quadratures of both drums, we perform quantum state tomography and thereby directly observe entanglement. Such entangled macroscopic systems are uniquely poised to serve in fundamental tests of quantum mechanics, enable sensing beyond the standard quantum limit, and function as long-lived nodes of future quantum networks.

• The paper demonstrates deterministic entanglement of two macroscopic oscillators via pulsed electromechanical interactions, achieving a symplectic eigenvalue as low as 0.44.
• It employs advanced quantum state tomography to reconstruct the covariance matrix and confirm entanglement with measurement efficiencies of 26% and 15.3%.
• The study paves the way for fundamental quantum mechanics tests and practical quantum information protocols in hybrid quantum networks.

Direct Observation of Deterministic Macroscopic Entanglement

The study presented in this paper reports the deterministic entanglement of two macroscopic mechanical oscillators, each with a mass of 70 picograms. The significance of this research lies in the direct observation and characterization of entangled states, made possible through pulsed electromechanics and nearly quantum-limited measurements. This advancement could pave the way for both fundamental tests of quantum mechanics and practical applications within quantum networks.

Core Contributions and Methodology

The authors employ a novel approach to entangle two "drumhead" oscillators using simultaneous pulsed electromechanical interactions. The framework involves interacting mechanical modes through a microwave cavity, effectively mediating the dynamical interaction to establish correlations between the oscillators. The success of the entanglement protocol hinges on two key interactions: a beam-splitter interaction that swaps cavity photons with one mechanical mode and a two-mode squeezing interaction that entangles another mechanical mode with the cavity.

The research employs advanced quantum state tomography by measuring the position and momentum quadratures, which allows for the reconstruction of the covariant matrix of the entangled state. The technique used yields clear evidence of continuous-variable entanglement with high efficiency and accuracy, providing new insights into the quantum mechanics of macroscopic systems.

Strong Numerical Results

The study demonstrates entanglement of the two oscillators with high confidence. The smallest symplectic eigenvalue of the partially transposed covariance matrix is consistently measured below unity, indicating the presence of entanglement. Specifically, the lowest observed value is 0.44 with controlled systematic uncertainty, a notable achievement for massive systems. With measurement efficiencies of 26% and 15.3% for the respective drums, the results surpass classical correlation limits firmly.

Implications and Future Directions

The capability to entangle macroscopic objects deterministically opens promising avenues for the exploration of quantum behaviors at scales beyond the microscopic. This work suggests potential applications in quantum information protocols, such as quantum teleportation and entanglement swapping, which are crucial for the functionality of quantum networks. Additionally, the study provides a stepping stone for experimental investigations into the foundations of quantum mechanics, including macroscopic tests of quantum non-locality.

Looking forward, the practical realization of such protocols in hybrid quantum networks, where mechanical systems could serve as intermediaries to entangle various quantum elements, appears promising. Future research could expand upon optimizing measurement efficiencies and scaling the entanglement process to involve larger macroscopic systems or integrate with other quantum technologies such as photon-based networks or spin systems.

In conclusion, this paper presents a significant stride forward in the realization and measurement of deterministic macroscopic entanglement, offering both direct observational evidence and laying foundational groundwork for future technological advancements in quantum mechanics and related fields.