During the duration of the project, we have investigated a novel phase of matter known as supersolid. We have created this phase by using light to couple a pair of internal states in a Bose-Einstein condensate, which allowed us to modify the dispersion relation of the resulting dressed states. In this regime, instead of the parabolic dispersion relation of a free particle, the modified dispersion relation takes the form of a double well. If the system populates these wells in momentum space, then in position space, this gives rise to atomic density modulation due to the interference between different momentum states. This crystal-like density modulation and the superfluidity of a Bose-Einstein condensate give rise to the supersolid phase.
We have observed the submicron density modulation in a light-coupled supersolid for the first time using a novel technique using matter-wave optics to magnify the atomic distribution. Moreover, we have explored the configuration space where the formation of the supersolid is possible by adjusting the strength of the light coupling, and we have observed a good quantitative agreement between our measurements and the mixture model, a low-energy model we have developed for this system. Finally, we have shown that the modulation period in the supersolid is not fixed and can depend on the momentum of the atoms and the light-coupling strength, indicating that the light-coupled supersolid is not stiff.
Finally, in an experiment not planned in the initial proposal, we have implemented a condensed-matter topological gauge theory in the continuum for the first time. The quantum simulation of gauge theories is an exciting field which only until recently has become possible due to the exquisite control of internal and external degrees of freedom in ultracold atoms. We have realized this feature by light dressing a Bose mixture in the high coupling regime together with tunable atomic interactions. We have engineered a system which maps to a one-dimensional reduction of the Chern-Simons gauge theory, which provides a low-energy description of the fractional quantum Hall states. In our experiment, we have measured the two main observables of this gauge theory: a density-dependent electric field and chiral solitons (wavepackets that propagate without dispersion only in a particular direction).
