Tunable optical lattices for the creation of matter-wave lattice solitons

TL;DR

This work presents an optical accordion lattice with tunable spacing to create and study bright matter-wave lattice solitons in a one-dimensional lattice. It combines precise lattice-spacing and depth calibration, site-resolved state preparation via microwave addressing, and a quench protocol that converts repulsive lattice solitons into stable attractive solitons, with optimization of the quench duration and final interaction strength. The approach yields controlled, high-fidelity initialization and imaging of solitons and provides a versatile platform for exploring nonlinear dynamics in discretized quantum gases. The methods open avenues for implementing complex lattice geometries and topological states, including superlattices and higher-dimensional or synthetic gauge-field systems, in future work.

Abstract

We present experimental techniques that employ an optical accordion lattice with dynamically tunable spacing to create and study bright matter-wave solitons in optical lattices. The system allows precise control of lattice parameters over a wide range of lattice spacings and depths. We detail calibration methods for the lattice parameters that are adjusted to the varying lattice spacing, and we demonstrate site-resolved atom number preparation via microwave addressing. Lattice solitons are generated through rapid quenches of the atomic interaction strength and the external trapping potential. We systematically optimize the quench parameters, such as duration and final scattering length, to maximize soliton stability. Our results provide insight into nonlinear matter-wave dynamics in discretized systems and establish a versatile platform for the controlled study of lattice solitons.

Figures (8)

• Figure 1: Experimental setup and preparation schemes. (a) Configuration of laser beams and coils, and (b) of the accordion lattice. A beam is diffracted by an acousto-optic deflector (AOD) and split into two parallel beams by polarizing beam splitters (PBS). These beams are focused by a lens (L1) onto the atomic cloud and interfere creating the accordion lattice potential. (c) Schematic of the optical lattice and occupied lattice sites. (d-g) In situ absorption images of the initially prepared states. (d) Full cloud in approximately twenty lattice sites with $d_\text{L} =3\,\upmu$m, which is below the optical resolution limit. (e) Preparation of a wave packet in one lattice site by selectively removing atoms with microwave sweeps, followed by an increase of the lattice spacing to $d_\text{L} =27(1)\,\upmu$m. Preparation for (f) a multi-site soliton in 3-5 lattice sites, and for (g) a gray soliton with a single unoccupied site.
• Figure 2: Magnification of density profile. (a) Absorption images of density profile in the optical lattice after a short expansion time of $2$ ms. Parameters $V_0>200\, E_\text{r}$, ramp $\Delta t=400\,$ms. Shift of center position of $0.87\, d_\text{L}$. (b) Oscillation of wave packet in central lattice site after magnification to $d_\text{L} =30\,\upmu$m in $150$ ms (orange circles) and $600\,$ms (blue squares). Solid lines denote damped sine fits to the data. Inset: measured oscillation amplitude for varying ramp duration $\Delta t$, error bars denote the $2\sigma$ error, line is a guide to the eye.
• Figure 3: Calibration of lattice spacing $d_\text{L}$. (a) Measurement of lattice spacing by determining the atom position (blue squares) and the momentum after expansion from the lattice (orange circles). Insets show absorption images after an expansion time 122 ms for deflector frequency $f_\text{D}=82.7$ MHz, 94.2 MHz, 101.6 MHz, and in position space for 104.9 MHz (left to right). (b) Numerical simulation of the time evolution shows the density distribution for parameters $V_0=20\, E_\text{r}$, $d_\text{L} =3\,\upmu$m, $a_\text{s}=10\,a_0$, $N=10,000$ atoms. Panels, from top to bottom, show the evolution during 1 ms lattice pulse, the initial evolution with Talbot revivals, and the full evolution over 150 ms. Black dotted lines indicate the $\pm 2\mathchar'26\mkern-9mu h k_\text{L}$ momentum. Bottom: The final momentum peaks of the density distribution show a small dependence on pulse duration: 1.00 ms (blue line), 1.45 ms (green line), 1.70 ms (red line), and 2.00 ms (black line).
• Figure 4: Calibration of lattice depth $V_0$. Determination of $V_0$ by measuring the trap frequency $\omega_\text{L}$ at each lattice site via center-of-mass oscillations (blue circles), and by measuring oscillations between energy bands (orange squares). The gray shaded area indicates the range of depths achievable using the method described in Ref. huckans2009, with black dots showing the data points ($d_\text{L} =3\,\upmu$m throughout). Inset shows measured oscillation for $P_0=0.75\,$mW, solid line is a damped sinusoidal fit.
• Figure 5: Atom number preparation in central lattice site. (a) Atom number reduction by loading into a lattice with spacing $d_\text{L}$ and depth $V_0\approx30\, E_\text{r}$ (gray squares), where $E_\text{r}$ is defined at $d_\text{L} =3\,\upmu$m. $N_\text{tot}=13.0(4)\times10^4$ atoms, error bars denote the standard deviation over five repetitions, solid line is a linear fit to the data. (b) Atom number in central site after a time delay between switching off the dipole trap D1 and adding the accordion lattice. Time $t=0$ ms is the moment immediately after the dipole trap is removed. (Top panel) Absorption images of corresponding density profile of central three lattice sites, dashed red lines delineate center site. (lower panel) Extracted atom number in the central site, error bars denote the standard deviation over seven repetitions.