Quantum Delocalization of a Levitated Nanoparticle (2408.01264v1)

Abstract: Every massive particle behaves like a wave, according to quantum physics. Yet, this characteristic wave nature has only been observed in double-slit experiments with microscopic systems, such as atoms and molecules. The key aspect is that the wavefunction describing the motion of these systems extends coherently over a distance comparable to the slit separation, much larger than the size of the system itself. Preparing these states of more massive and complex objects remains an outstanding challenge. While the motion of solid-state oscillators can now be controlled at the level of single quanta, their coherence length remains comparable to the zero-point motion, limited to subatomic distances. Here, we prepare a delocalized state of a levitating solid-state nanosphere with coherence length exceeding the zero-point motion. We first cool its motion to the ground state. Then, by modulating the stiffness of the confinement potential, we achieve more than a threefold increment of the initial coherence length with minimal added noise. Optical levitation gives us the necessary control over the confinement that other mechanical platforms lack. Our work is a stepping stone towards the generation of delocalization scales comparable to the object size, a crucial regime for macroscopic quantum experiments, and towards quantum-enhanced force sensing with levitated particles.

• The paper demonstrates quantum delocalization by extending the nanoparticle’s coherence length beyond its zero-point motion using modulated optical trapping.
• The experiment uses a silica nanoparticle cooled to its ground state in an optical tweezer, then applies precision pulse modulation to enhance delocalization.
• The results align with optomechanical models, revealing a peak coherence of 73 pm and indicating potential for quantum-enhanced force sensing and gravitational wave detection.

Quantum Delocalization of a Levitated Nanoparticle

This paper presents an in-depth paper on the quantum delocalization of a levitated nanoparticle, a solid-state realization demonstrating a coherence length exceeding that of zero-point motion. Traditional double-slit experiments have long showcased the wave nature of microscopic systems such as atoms and molecules. However, expanding this phenomenon to more massive, complex objects poses significant challenges due to their short coherence lengths and interactions with the environment. The authors successfully delocalized a nanoscale object far beyond its zero-point motion limitations by leveraging optical levitation.

The experimental approach utilizes a silica nanoparticle levitated within an optical tweezer. The confinement potential of the optical tweezer is controllable, enabling the authors to cool the nanoparticle to its ground state before initiating the delocalization process. By employing a sequence of modulated pulses to manipulate the resonant frequency of the trapping potential, the team achieved over a threefold increase in coherence length with minimal added noise. This coherent increase in position uncertainty while maintaining state purity is evidenced by their quantum-limited position measurement technique, augmented by a retrodiction-based estimation filter.

The experimental results disclose a significant advancement in the coherence length of the levitated nanoparticle, scaling with the square of the frequency modulation factor. With the aid of rigorous optomechanical modeling, the experimental outcomes aligned closely with theoretical predictions, attributing the limited decoherence primarily to photon recoil during the experiments. By optimizing the modulation protocol and minimizing extrinsic noise sources, the authors quantitatively demonstrated a peaked coherence length reaching 73 pm, a twofold increase over the zero-temperature state coherence length.

Significantly, the findings have practical implications for quantum-enhanced force sensing, potentially benefitting precision measurements in gravitational wave detection and exploring fundamental physics laws. Future research could capitalize on these results using alternate “dark” traps to facilitate even larger delocalization scales. Prospective developments include RF traps that could further mitigate decoherence while sustaining the particle in a delocalized quantum state.

This work exemplifies a critical step toward bridging microscopic quantum behaviors to macroscopic regimes. The authors’ control methodologies can be instrumental in probing quantum mechanics on increasing scales, ultimately contributing to the understanding of quantum mechanics' nuances in complex and macro-dimensional systems, including the paper of gravity at a quantum level. Future progress in this domain may lead to new insights existing at the junction of quantum physics and gravitational interaction theories.