Pairing and Vortex Lattices for Interacting Fermions in Optical Lattices with a Large Magnetic Field

We study the structure of pairing order parameter for spin-1/2 fermions with attractive interactions in a square lattice under a uniform magnetic field. Because the magnetic translation symmetry gives a unique degeneracy in the single-particle spectrum, the wave function has both zero and finite momentum components co-existing, and their relative phases are determined by a self-consistent mean-field theory. We present a microscopic calculation that can determine the vortex lattice structure in the superfluid phase for different flux densities. Phase transition from a Hofstadter insulator to a superfluid phase is also discussed.Comment: 4 pages, 3 figures, one table, published versio

Probing few-particle Laughlin states of photons via correlation measurements

We propose methods to create and observe Laughlin-like states of photons in a strongly nonlinear optical cavity. Such states of strongly interacting photons can be prepared by pumping the cavity with a Laguerre-Gauss beam, which has a well-defined orbital angular momentum per photon. The Laughlin-like states appear as sharp resonances in the particle-number-resolved transmission spectrum. Power spectrum and second-order correlation function measurements yield unambiguous signatures of these few-particle strongly-correlated states.Comment: 11 pages including appendice

Fractional Quantum Hall states in the vicinity of Mott plateaus

We perform variational Monte-Carlo calculations to show that bosons in a rotating optical lattice will form analogs of fractional quantum Hall states when the tunneling is sufficiently weak compared to the interactions and the deviation of density from an integer is commensurate with the effective magnetic field. We compare the energies of superfluid and correlated states to one-another and to the energies found in full configuration-interaction calculations on small systems. We look at overlaps between our variational states and the exact ground-state, characterizing the ways in which fractional quantum Hall effect correlations manifest themselves near the Mott insulating state. We explore the experimental signatures of these states.Comment: 6 pages, 4 figure

Bulk density signatures of a lattice quasihole with very few particles

Motivated by the recent experimental realization of a two-particle fractional quantum Hall state of ultracold atoms in a small optical lattice [Nature 619, 495 (2023)], we propose a minimal setup to create and observe a quasihole in such a system. Adding a single-site repulsive potential to pin the quasihole and superimposing a harmonic trap on top of the optical lattice to keep the particles away from the system edge, we determine via exact diagonalization an optimal range for system parameters such as the magnetic flux and the strengths of the additional potentials that would favour the creation of the quasihole state. We suggest that clear signatures of such a state with two or three particles can be obtained through a standard density measurement.Comment: 4.5+3 page

Photon condensation in circuit QED by engineered dissipation

We study photon condensation phenomena in a driven and dissipative array of superconducting microwave resonators. Specifically, we show that by using an appropriately designed coupling of microwave photons to superconducting qubits, an effective dissipative mechanism can be engineered, which scatters photons towards low-momentum states while conserving their number. This mimics a tunable coupling of bosons to a low temperature bath, and leads to the formation of a stationary photon condensate in the presence of losses and under continuous-driving conditions. Here we propose a realistic experimental setup to observe this effect in two or multiple coupled cavities, and study the characteristics of such an out-of-equilibrium condensate, which arise from the competition between pumping and dissipation processes