We experimentally realize a Peierls phase in the hopping amplitude of excitations carried by Rydberg atoms, and observe the resulting characteristic chiral motion in a minimal setup of three sites. Our demonstration relies on the intrinsic spin-orbit coupling of the dipolar exchange interaction combined with time-reversal symmetry breaking by a homogeneous external magnetic field. Remarkably, the phase of the hopping amplitude between two sites strongly depends on the occupancy of the third site, thus leading to a correlated hopping associated with a density-dependent Peierls phase. We experimentally observe this density-dependent hopping and show that the excitations behave as anyonic particles with a nontrivial phase under exchange. Finally, we confirm the dependence of the Peierls phase on the geometrical arrangement of the Rydberg atoms.

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We consider a minimal model to describe the quantum phases of ultracold dipolar bosons in two-dimensional (2D) square optical lattices. The model is a variation of the extended Bose-Hubbard model and apt to study the quantum phases arising from the variation in the tilt angle θ of the dipolar bosons. At low tilt angles 0 • θ 25 • , the ground state of the system are phases with checkerboard order, which could be either checkerboard supersolid or checkerboard density wave. For high tilt angles 55 • θ 35 • , phases with striped order of supersolid or density wave are preferred. In the intermediate domain 25 • θ 35 • an emulsion or SF phase intervenes the transition between the checkerboard and striped phases. The attractive interaction dominates for θ 55 • , which renders the system unstable and there is a density collapse. For our studies we use Gutzwiller mean-field theory to obtain the quantum phases and the phase boundaries. In addition, we calculate the phase boundaries between an incompressible and a compressible phase of the system by considering second order perturbation analysis of the mean-field theory. The analytical results, where applicable, are in excellent agreement with the numerical results.

Quantum Hall (QH) states of two dimensional (2D) single layer optical lattices are examined using Bose-Hubbard model (BHM) in presence of artificial gauge field. We study the QH states of both the homogeneous and inhomogeneous systems. For the homogeneous case we use cluster Gutzwiller mean-field (CGMF) theory with cluster sizes ranging from 2 × 2 to 5 × 5. We, then, consider the inhomogeneous case, which is relevant to experimental realization. In this case, we use CGMF and exact diagonalization (ED). The ED studies are using lattice sizes ranging from 3 × 3 to 4 × 12. Our results show that the geometries of the QH states are sensitive to the magnetic flux α and cluster sizes. For homogeneous system, among various combinations of 1/5 α 1/2 and filling factor ν, only the QH state of α = 1/4 with ν = 1/2, 1, 3/2 and 2 occur as ground states. For other combinations, the competing superfluid (SF) state is the ground state and QH state is metastable. For BHM with envelope potential, all the QH states observed in homogeneous system exist for box potentials, but none for the harmonic potential. The QH states also persist for very shallow Gaussian envelope potential. As a possible experimental signature we study the two-point correlations of the QH and SF states.

We examine the effects of an artificial gauge field and finite temperature in a two-dimensional disordered Bose-Hubbard model. The disorder considered is diagonal and quenched in nature. A signature of disorder in the Bose-Hubbard model is the Bose glass phase. Our work shows that the introduction of an artificial gauge field enhances the domain of the Bose glass phase in the phase diagram. Most importantly, the size of the domain can be tuned with the strength of the artificial gauge field. The introduction of the finite temperature effects is essential to relate theoretical results with the experimental realizations. For our studies we use the single site and cluster Gutzwiller mean-field theories. The results from the latter are more reliable as it better describes the correlation effects. Our results show that the Bose glass phase has a larger domain with the latter method.arXiv:1807.00269v2 [cond-mat.quant-gas]

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We demonstrate an enhancement in the vortex generation when artificial gauge potential is introduced to condensates confined in a double well potential. This is due to the lower energy required to create a vortex in the low condensate density region within the barrier. Furthermore, we study the transport of vortices between the two wells, and show that the traverse time for vortices is longer for the lower height of the well. We also show that the critical value of synthetic magnetic field to inject vortices into the bulk of the condensate is lower in the double-well potential compared to the harmonic confining potential. arXiv:1705.06493v2 [cond-mat.quant-gas]