Ultracold atoms in optical lattices provide a versatile platform for studying many-body physics in a defect-free system with tunable parameters. For the analog quantum simulation of the Fermi-Hubbard model, fermionic atoms take on the role of the valence electrons and optical lattices provide the periodic potential in place of the solid-state crystal. The dynamics in the system are described by the tunneling amplitude t between neighboring lattice sites and the interaction energy U of two particles occupying the same lattice site. With the depth of the optical lattices and an external magnetic field, both parameters can be tuned to access a wide range of regimes. Two superimposed lattices with different lattice periods form an optical superlattice, where the most common configuration is a bichromatic superlattice with lattice periods different by a factor of two. Depending on the lattice depths and the relative phase of the lattices, the bichromatic superlattice potential ranges from an array of weakly-coupled double wells to a continuous lattice potential with a staggered energy offset. We developed a calibration technique for measuring the depth of an optical lattice with local resolution. The band structure of the optical lattice is probed by modulating the lattice depth and exciting the atoms to higher bands. However, compared to resolving the band occupations in a time-of-flight measurement, we further excite the atoms to an untrapped band to deplete the optical lattice along equipotential lines where the modulation frequency is resonant with the local band transitions. From the profile of the lattice depth, we obtain the calibration factor for the power regulation, the waist of the underlying lattice beams and the position of the lattice axis. This technique combines several calibration measurements, thereby reducing the measurement time and enabling an automation of the lattice alignment. For the bichromatic superlattice we realized an active stabilization of the superlattice phase that enables long-term measurements with a precise control over the superlattice phase. The instability of the superlattice phase is a result of the different refractive indices for the two lattices in air and the optical elements along the optical path. Using environmental sensors, we monitor the temperature, the pressure, and the relative humidity to apply the expected correction to the superlattice phase. The stabilized superlattice phase enabled the investigation of Floquet-driven double wells by modulating the energy offset through the superlattice phase. We used a near-resonant driving frequency with respect to the interaction energy to enhance the pair-tunneling amplitude in doubly-occupied double wells compared to static double wells and compared to the tunneling amplitude in singly-occupied double wells.
We study how the bosonic atoms on the excited
p band of an optical lattice are coupled to the lowest
s band and the second excited
d band. We find that in some parameter regimes, the atom-atom interactions can cause a dynamical instability of the
p-band atoms toward decay to the
s and
d bands. Furthermore, even when dynamical instability is not expected
s and
d bands can become substantially populated. We also find that the stability properties of the excited bands can be improved in superlattices.
Abstract Faraday or parametric instability has been observed in various contexts in Bose–Einstein condensates. In Rabi-coupled condensates, the instability can arise without explicit modulation of external parameters. We study the dynamics of an interface in a two-component immiscible condensate near the miscible-immiscible threshold, with Rabi coupling between components. We show that a small initial perturbation leads to oscillations that grow in amplitude with increasing Rabi frequency until the interface produces droplet-like structures. We find that the interface oscillations are driven by parametric resonance with density oscillations in the bulk. This parametric instability of the interface provides a link to the walking droplet pilot wave system, which is governed by the Faraday instability. Because walking droplets simulate fundamentally quantum behaviors, and ‘vortex molecules,’ which are hosted by a Rabi-coupled condensate, simulate quark confinement, this observation suggests a mechanism-level connection between these systems and provides a possible bridge between distinct analog models of fundamental particles.