Deterministic multi-phonon entanglement between two mechanical resonators on separate substrates

Abstract: Mechanical systems have emerged as a compelling platform for applications in quantum information, leveraging recent advances in the control of phonons, the quanta of mechanical vibrations. Several experiments have demonstrated control and measurement of phonon states in mechanical resonators integrated with superconducting qubits, and while entanglement of two mechanical resonators has been demonstrated in some approaches, a full exploitation of the bosonic nature of phonons, such as multi-phonon entanglement, remains a challenge. Here, we describe a modular platform capable of rapid multi-phonon entanglement generation and subsequent tomographic analysis, using two surface acoustic wave resonators on separate substrates, each connected to a superconducting qubit. We generate a mechanical Bell state between the two mechanical resonators, achieving a fidelity of $\mathcal{F} = 0.872\pm 0.002$, and further demonstrate the creation of a multi-phonon entangled state (N=2 N00N state), shared between the two resonators, with fidelity $\mathcal{F} = 0.748\pm 0.008$. This approach promises the generation and manipulation of more complex phonon states, with potential future applications in bosonic quantum computing in mechanical systems. The compactness, modularity, and scalability of our platform further promises advances in both fundamental science and advanced quantum protocols, including quantum random access memory and quantum error correction.

• The paper presents a novel modular platform enabling rapid generation and tomographic analysis of multi-phonon entanglement between two separate mechanical resonators on distinct substrates.
• Using this platform, the researchers experimentally achieved a mechanical Bell state with 0.872 fidelity and a multi-phonon N=2 N00N state with 0.748 fidelity.
• This research demonstrates a significant step towards distributed quantum computing with mechanical systems, highlighting potential for quantum memory and error correction applications.

Deterministic Multi-Phonon Entanglement in Mechanical Resonators

The paper under discussion advances the field of quantum information processing utilizing mechanical systems, particularly through the exploration of phonons and their entanglement. The research presents a novel modular platform designed to enable rapid generation and tomographic analysis of multi-phonon entanglement between two surface acoustic wave (SAW) resonators that are physically separated. Located on distinct substrates, each resonator is coupled with a superconducting qubit. This setup is demonstrated to successfully generate multi-phonon states, highlighting a significant stride forward in quantum information applications via mechanical systems.

One of the central achievements of this study is the creation of a mechanical Bell state with a fidelity of 0.872±0.002 and the realization of a multi-phonon entangled state, specifically an N=2 N00N state, with a fidelity of 0.748 ± 0.008. These findings underscore the potential of the platform to handle more complex phonon states, critical for future developments in bosonic quantum computing within mechanical frameworks.

The experimental effectiveness of the platform derives from a combination of compactness, modularity, and scalability. It is posited that such a framework could enhance both fundamental science and quantum protocols, with potential contributions to areas such as quantum random access memory and quantum error correction. Compared to circuit quantum electrodynamics (cQED) systems, mechanical systems present a reduced physical footprint, prolonged lifetimes, and enhanced access to microwave-frequency modes. This investigation reports the deterministic generation and distribution of entanglement in spatially separated mechanical resonators—a substantial accomplishment towards interconnecting microwave qubits and optical photons, facilitating long-distance quantum communication.

The researchers utilize a three-substrate architecture where two mechanical resonators are situated on individual lithium niobate (LN) chips, and the qubits are located on a sapphire substrate. This architectural choice supports the efficient generation of complex entangled states and facilitates quantum tomography. In particular, surface acoustic waves (SAW) offer distinct advantages for achieving entanglement in mechanical systems owing to their highly linear modes and ease in quantum measurement.

The experimental procedure involves inducing Rabi swaps between the qubits and the acoustic modes of the resonators, preserving coherence to ensure entangled state generation and measurement via simultaneous vacuum-Rabi swaps. Additionally, the authors detail the intricacies of realizing and analyzing N00N states, addressing challenges such as qubit decay due to unintended phonon emission and proposing mitigative strategies.

The implications of this research are broad. The demonstrated capacity for superposition and entanglement of mechanical phonons suggests new horizons in distributed quantum computing. The authors project that with extended coherence lifetimes and device enhancements, the demonstrated mechanisms could underpin more sophisticated operations such as GHZ and W states synthesis and quantum sensing applications.

Looking forward, further advancements in material science, especially concerning improved lithium niobate substrate growth, and refined resonator designs may alleviate current limitations on coherence lifetimes, thus broadening practical applications in quantum mechanics and computing. Such progress could unlock complex algorithms and quantum protocols currently beyond reach using state-of-the-art technology. This research lays a significant foundation for future exploration and development of entangled mechanical systems, ushering a promising frontier in quantum technologies.