Reproducing Superlattice BEC Loading

The groundbreaking paper, “Patterned loading of a Bose-Einstein condensate into an optical lattice” [1], introduced a novel technique for manipulating atom placement within an optical lattice. Their approach utilized a “superlattice” (groans from those familiar with my doctoral research😅) — a combination of two overlapping optical lattices with differing periodicities — to selectively load atoms into specific sites of the main lattice. This allows for precise control over where individual atoms reside within the lattice, offering exciting possibilities for quantum computing and other applications.

The basic model for Patterned Loading. The goal is to get “wide separation yet tight confinement” [1]. The orange ovals represent the BEC atoms. Using a Long lattice only (green line) we get wide separation but loose confinement. With the Short lattice (blue line) we get close separation with tight confinement. A combination of both, a “Superlattice”, if carefully sequenced, can achieve the goal. In the paper, the authors demonstrate selective loading of atoms into every third site of the lattice.

This article details my experience replicating these concepts using the Oqtant platform. Oqtant, with its user-friendly Python API, empowers researchers to design intricate experimental sequences, including those involving superlattices.

One of Oqtant’s key strengths lies in its Python integration. This allows for the creation of sophisticated control sequences using familiar Python syntax. In the context of this experiment, I leveraged this capability to develop the superlattice sequence.

The “Superlattice” sequence. The graph on the left shows the evolution of the individual long and short potentials with time. On the right, is an “animation” of the potentials evolving with time in the BEC trap. Since the total barriers available is limited to 10 (for now) I restricted the covered section to [-6, 6] μm.

The approach involved employing a series of evolving Gaussian barriers to mimic the desired cosine waveforms that define the optical lattice potentials [2]. My Github project (PatternedLoading), offers the actual Jupyter notebooks used for these experiments, allowing you to delve deeper into the code.

However, there’s a current limitation within Oqtant — users can only utilize a maximum of 10 barriers. While I could mimic the superlattice effect, the limited barrier count restricted the range spanned by the simulated lattice. Ideally, 80 barriers would be needed to fully encompass the extent of the BEC. This limitation necessitated a smaller-scale implementation, with the barriers limited to the span [-6, 6] μm.

Despite the barrier limitation, the results were encouraging.

In-Trap images from running the Patterned Loading experiment on Oqtant. The red square zooms into a section covering [-10, 10] μm. The zoomed in section also include a line plot of a slice taken at y = 0. The Short lattice only results shows 5 narrow peaks indicating loading of atoms evenly at each trough of the Short lattice. In comparison, the Superlattice result shows 2 narrow peaks, with the second peak at the third trough from the first (in trough units of the Short lattice). This result is a good replication of the Patterned Loading effect discussed in [1].

The implemented superlattice sequence successfully demonstrated a partial replication of the patterned loading effect observed in the Peil et al. paper.

The next steps involve exploring the remaining aspects of the paper, particularly the concept of adiabaticity — the gradual transition between potential landscapes. Even such a detailed investigation is practically possible on Oqtant.

Explore the Quantum World with Oqtant

If you’re looking for a user-friendly platform to delve into the fascinating realm of quantum physics, check out Oqtant. With its intuitive Python interface and powerful control tools, Oqtant empowers researchers to explore concepts like patterned BEC loading. As the platform evolves, the possibilities for exploring complex quantum phenomena become even more exciting.

References

1. Peil, S. & Porto, J. & Tolra, & Laburthe, B. & Obrecht, John & King, B. & Subbotin, M. & Rolston, Steven & Phillips, William. (2003). Patterned loading of a Bose-Einstein condensate into an optical lattice. Phys. Rev. A. 67. 051603. 10.1103/PhysRevA.67.051603.
2. functional analysis — Is it possible to approximate $\cos(x)$ with a linear combination of Gaussians $e^{-x²}$? — Mathematics Stack Exchange