In this first phase of the project, we have focused on the investigation of two-component Bose-Einstein condensates (BEC) subjected simultaneously to tunable interactions and spin-orbit coupling engineered via optical Raman coupling. We have developed a theoretical framework to describe the system in terms of interacting atom-photon dressed states, and shown how to derive effective field theories for the optically-coupled Bose-Einstein condensate hosting unconventional superfluid phases.
First, exploiting potassium-39 in the regime of large Raman coupling, we have engineered and investigated chiral condensates: exotic superfluids which have momentum-dependent interactions and, as a result, display properties that depend on their propagation direction. This work builds on our preparatory work on controlling interactions in Rabi-coupled BECs [Phys. Rev. Lett. 128, 013201(2022)]. We have theoretically shown that the chiral condensates are described by a one-dimensional topological gauge theory, the so-called chiral BF theory, which corresponds to a one-dimensional reduction of the celebrated Chern-Simons gauge theory effectively describing fractional quantum Hall states. We have experimentally realized these ideas in the laboratory and revealed the key properties of the chiral BF theory: the formation of chiral solitons and the emergence of a density-dependent electric field generated by the system itself. These experimental results have been published in [Nature 608, 293-297 (2022)], while the theoretical framework was published in [Phys. Rev. Research 4, 043088 (2022)] and selected as Editors’ suggestion. Our work on this topic expands the scope of quantum simulation to topological gauge theories, provides a new pathway to investigate anyonic excitations in weakly interacting continuum and lattice systems, and opens a route to the implementation of analogous gauge theories in higher dimensions.
Second, we have explored with potassium-41 the regime of weak Raman coupling, where the dispersion relation of the gas has two minima. When both are occupied, interference between them takes place and the system enters a supersolid phase – a state of matter which spontaneously breaks two continuous symmetries and presents simultaneously the frictionless flow of a superfluid and the crystalline structure of a solid. Taking advantage of the favourable scattering properties of potassium-41, we have been able to reach the previously unexplored regime of large contrast. Combined with matter-wave lensing techniques, this has allowed us to image in situ for the first time the density modulation of the spin-orbit coupled supersolid, the so-called stripe pattern. Moreover, we have directly observed its compression mode, corresponding to a temporal oscillation of the stripe pattern’s period, and exploited its mode softening to reveal the supersolid-to-plane-wave phase transition. We are currently preparing two publications on this topic: one on our experimental results, and one on the theoretical model that we have developed to describe the supersolid collective mode frequencies analytically. Our work on this topic demonstrates a new experimental platform for investigating supersolidity, in which fundamental questions related to it could be addressed.
In parallel, we have performed several theoretical studies to investigate the potential application of these ideas to a broader context, including: i) the investigation of the chiral BF theory in an annular geometry, where a density-dependent magnetic flux arises [in preparation]; ii) the combination of Raman-based spin-orbit coupling, interacting Bose gases and optical lattices, observing the emergence of effective geometrical frustration in synthetic ladder systems [Phys. Rev. Research 5, L042008 (2023)] and of 1D anyon physics [in preparation]. We are currently upgrading our experimental apparatus in order to implement several optical lattice potentials and an improved imaging system, which will allow us to investigate both low dimensional systems and some of these ideas experimentally.
