Fractional Chern insulators (FCIs) are lattice analogs of fractional quantum Hall systems, where the interplay of strong interactions with a frustrated tunnelling kinetics leads tothe emergence of a gapped ground state with long-range entanglement and anyonic excitations. The highly correlated nature of such systems makes their adiabatic preparation challenging already beyond the minimal system size of two particles. Considering Floquet implementations of the bosonic Harper-Hofstadter-Hubbard model of few photons in superconducting circuits, we design protocols for the driven-dissipative stabilization of its FCI ground state at half filling via quantum bath engineering. Dissipation control is achieved through the coupling to driven leaky cavity modes, which realize a tuneable artificial environment having the Floquet-FCI as its approximate fixed point. For systems of two, three and six particles, we show numerically how the flexibility of the control scheme further allows for the detection of fractional quantum Hall signatures in the stabilized steady states, including bulk incompressibility, Hall response and the trapping of fractional charges. Our results provide a concrete pathway to dissipation-assisted preparation of strongly correlated states in quantum simulators.
Quantum many-body scars are energy eigenstates which fail to reproduce thermal expectation values of local observables in systems, where the rest of the many-body spectrum fulfils eigenstatethermalization. Experimental observation of quantum many-body scars has so far been limited to models with multiple scar states. Here we propose protocols to observe single scars in architectures of fixed-frequency, fixed-coupling superconducting qubits. We first adapt known models possessing the desired features into a form particularly suited for the experimental platform. We develop protocols for the implementation of these models, through trotterized sequences of two-qubit cross-resonance interactions, and verify the existence of the approximate scar state in the stroboscopic effective Hamiltonian. Since a single scar cannot be detected from coherent revivals in the dynamics, differently from towers of scar states, we propose and numerically investigate alternative and experimentally-accessible signatures. These include the dynamical response of the scar to local state deformations, to controlled noise, and to the resolution of the Lie-Suzuki-Trotter digitization.
By periodically driving a quantum system at a high frequency, it can acquire novel properties that are captured by an effective time-independent Hamiltonian. An important applicationof such Floquet engineering is, e.g., the realization of effective gauge fields for charge-neutral particles. Here we consider driven Bose-Hubbard systems, as they can be realized as arrays of artificial atoms in superconducting circuits, and show that the ground state of the effective Hamiltonian can be prepared with high fidelity using reservoir engineering. For this purpose, some artificial atoms are coupled to driven leaky cavities. We derive an effective description of the open system by employing degenerate perturbation theory in the extended Floquet space with respect to both the periodic drive and the system-cavity coupling. Applying this theory to different Floquet-engineered flux ladders, we find both that it allows to cool the systems and that it shows excellent agreement with the full driven-dissipative evolution of system and cavities.