In-situ Imaging of a Single-Atom Wave Packet in Continuous Space (2404.05699v1)

Abstract: The wave nature of matter remains one of the most striking aspects of quantum mechanics. Since its inception, a wealth of experiments has demonstrated the interference, diffraction or scattering of massive particles. More recently, experiments with ever increasing control and resolution have allowed imaging the wavefunction of individual atoms. Here, we use quantum gas microscopy to image the in-situ spatial distribution of deterministically prepared single-atom wave packets as they expand in a plane. We achieve this by controllably projecting the expanding wavefunction onto the sites of a deep optical lattice and subsequently performing single-atom imaging. The protocol established here for imaging extended wave packets via quantum gas microscopy is readily applicable to the wavefunction of interacting many-body systems in continuous space, promising a direct access to their microscopic properties, including spatial correlation functions up to high order and large distances.

• The paper demonstrates the use of quantum gas microscopy to capture the ballistic expansion of a single-atom wave packet.
• It employs Raman sideband cooling and optical lattices to prepare and control Lithium-6 atoms with near-ground state precision.
• The findings validate theoretical predictions and open avenues for exploring wavefunction dynamics and many-body quantum systems.

In-situ Imaging of a Single-Atom Wave Packet in Continuous Space

This paper explores the observation of a single-atom wave packet's expansion dynamics using advanced quantum gas microscopy techniques. The research presented focuses on in-situ imaging of wave packets in continuous space, leveraging the ability to project the wavefunction of atoms onto an optical lattice. Such visualization extends to monitoring the dynamics of a deterministically prepared single-atom wave packet, providing significant insights into fundamental quantum mechanical behaviors.

Key Contributions and Methodology

The paper builds on foundational principles of wave-particle duality, as initially proposed by de Broglie, and experimentally observes the ballistic expansion of Gaussian wave packets. By employing quantum gas microscopy, the authors achieve atomic resolution imaging by projecting expanding wavefunctions onto the sites of a deep optical lattice. This methodology allows real-time monitoring of wave packet dynamics, paving the way for exploring wavefunctions of many-body systems in their natural continuous space.

Key experimental steps involve the preparation of Lithium 6 ($^6$Li) atoms in an optical lattice, achieving near-ground state conditions using Raman sideband cooling (RSC). The experimental setup includes a triangular optical lattice within a highly controlled trap, ensuring vertical confinement while probing in the $x-y$ plane. The research meticulously adjusts the initial momentum spread and employs time-of-flight expansion measurements to observe the dynamics governed by the Schrödinger equation.

Numerical Results and Observations

Experimental results presented in the paper align the dynamics of the atoms with theoretical predictions. The wave packets expand linearly with time, conforming to the equation $$\sigma(t) = \sqrt{\frac{\hbar \omega}{2m}\sqrt{2\langle n \rangle+1} \cdot t}$$ for large times $t$, where $\sigma(t)$ represents the wave packet width. The paper accurately determines the average harmonic oscillator eigenvalues for different initial conditions, showcasing a consistency of extracted values with theoretical models. These observations validate the precise control over quantum states achieved in the experimental setup.

Implications and Future Directions

The implications of this research are profound for quantum mechanics and experimental physics. The ability to project and image atomic wave packets with such precision offers a powerful tool for investigating the properties of many-body systems in quantum simulations. The methodologies outlined can be extended to probe spatially-resolved correlation functions, thus providing insights into complex quantum phenomena.

Furthermore, the flexibility of the experimental setup suggests potential applications in exploring fermionic systems, quantum gases, and related quantum field theories. As quantum technology and quantum computing continue to advance, the techniques refined in this paper could become pivotal in understanding and harnessing quantum systems that exhibit wave-like properties at macroscopic scales.

Overall, this work represents an important technical advancement in the field, offering a bridge between theoretical quantum mechanics and experimental realization. The paper's thorough investigation and rigorous methodology ensure its place as a foundational paper for future explorations in quantum system imaging and beyond.