We chart out possible phases of ultracold Rydberg atoms in an hypercubic optical
lattice within mean field description. We introduce effective spin degrees of
freedom for Rydberg atom in Mott Insulator Phase with filling one to provide a
clear picture for Canted Ising Anti-ferromagnetic Mott phase and Canted Density
Wave phase. Including Next Nearest Neighbour interaction the ground state of
the system shows translational symmetry broken Density Wave phase with p/q
type filling. In presence of harmonic trap ground state of the system shows incompressible
plateaus with compressible edges. We also study the system with decay
and provide the phase diagram based on the steady states of the non-equilibrium
system. We show that unlike equilibrium case several homogeneous phases are
possible as a stable steady state of the non-equilibrium system.
We chart out possible phases of ultracold Rydberg atoms in an hypercubic optical
lattice within mean field description. We introduce effective spin degrees of
freedom for Rydberg atom in Mott Insulator Phase with filling one to provide a
clear picture for Canted Ising Anti-ferromagnetic Mott phase and Canted Density
Wave phase. Including Next Nearest Neighbour interaction the ground state of
the system shows translational symmetry broken Density Wave phase with p/q
type filling. In presence of harmonic trap ground state of the system shows incompressible
plateaus with compressible edges. We also study the system with decay
and provide the phase diagram based on the steady states of the non-equilibrium
system. We show that unlike equilibrium case several homogeneous phases are
possible as a stable steady state of the non-equilibrium system.
We chart out the possible phases of laser-driven Rydberg atoms in the presence of a hypercubic optical lattice. We define a pseudospin degree of freedom whose up (down) components correspond to the excited (ground) states of the Rydberg atoms and use them to demonstrate the realization of a canted Ising antiferromagnetic (CIAF) Mott phase of the atoms in these systems. We also show that, on lowering the lattice depth, the quantum melting of the CIAF and density-wave Mott states (which are also realized in these systems) leads to supersolid phases of the atoms. We provide analytical expressions for the phase boundaries and collective excitations of these phases in the hard-core limit within mean-field theory and discuss possible experiments to test our theory.
The superfluid--Mott-insulator phase transition of ultracold spin-1 bosons with ferromagnetic and antiferromagnetic interactions in an optical lattice is theoretically investigated. Two counterpropagating linearly polarized laser beams with the angle $\ensuremath{\theta}$ between the polarization vectors ($\mathrm{lin}\text{\ensuremath{-}}\ensuremath{\theta}\text{\ensuremath{-}}\mathrm{lin}$ configuration), driving an Fg=1 to Fe=1 internal atomic transition, create the optical lattice and at the same time couple atomic ground states with magnetic quantum numbers $m=\ifmmode\pm\else\textpm\fi{}1$. Due to the coupling the system can be described as a two-component one. At $\ensuremath{\theta}=0$ the system has a continuous isospin symmetry, which can be spontaneously broken, thereby fixing the number of particles in the atomic components. The phase diagram of the system and the spectrum of collective excitations, which are density waves and isospin waves, are worked out. In the case of ferromagnetic interactions, the superfluid--Mott-insulator phase transition is always second order, but in the case of antiferromagnetic interactions for some values of system parameters it is first order and the superfluid and Mott phases can coexist. Varying the angle $\ensuremath{\theta}$ one can control the populations of atomic components and continuously turn on and tune their asymmetry.
The plethora of possible ground states of spinor bosons placed in an external lattice and a cavity is revisited. We discuss the simplest configuration when the external lattice nodes coincide with the antinodes of the cavity field. We analyze the problem within the grand-canonical mean-field approach, considering both the homogeneous system and the nonhomogeneous case with a harmonic trapping potential. Due to the spin degree of freedom, in the homogeneous case, we treat the system in a twofold manner: we impose the physically relevant total-magnetization constraint, while also discussing the minimization landscape for the full unconstrained problem. In the latter, by combining analytical arguments with numerical calculations based on the Gutzwiller ansatz, we show that the system exhibits two types of magnetic phases: an antiferromagnetic Mott insulator (AFM) and a ferromagnetic density wave (FDW). In addition, two distinct supersolid phases emerge, characterized by different patterns of spin and density imbalances. In the case of zero total magnetization, the FDW phases are replaced by charge density waves (CDWs) that lack net magnetic ordering. Finally, we establish the phase diagram of the trapped system, providing direct guidance for future experiments.
Engineering quantum phases with spontaneously broken symmetries is a major goal of research in different fields. Trapped ultracold Rydberg-excited atoms in optical lattices are a promising platform for realizing quantum phases with broken lattice translational symmetry since they are interacting over distances larger than the lattice constant. Although numerous theoretical works on trapped Rydberg-excited gases have predicted such phases, in particular, density wave or supersolid phases, their experimental observation proves to be difficult due to challenges such as scattering processes and the limited experimentally achievable coupling strength. Most of these previous studies have focused on isotropically interacting gases dressed with Rydberg s states, while the effect of anisotropic interactions due to Rydberg-excited p states in trapped quantum gases remains much less investigated. Additionally, it was shown that the excitation scheme used to excite Rydberg p states possesses advantages regarding achievable coupling strengths and limitation of scattering processes compared to its s-state counterpart, which makes the investigation of Rydberg p-state dressed quantum gases even more interesting. In the present work we study the extended two-component Bose-Hubbard model, realized with a bosonic quantum gas with Rydberg-excited p states trapped in an optical lattice, within the Gutzwiller mean-field theory. We compute the ground-state phase diagram and investigate its different regimes. By comparison to the phase diagram of the isotropic case, we find the anisotropic interaction to be more advantageous for the observation of supersolid phases.
In this work we consider a system of spinless fermions with nearest and next-to-nearest neighbor repulsive Hubbard interactions on a honeycomb lattice, and propose and analyze a realistic scheme for analog quantum simulation of this model with cold atoms in a two-dimensional hexagonal optical lattice. To this end, we first derive the zero-temperature phase diagram of the interacting model within a mean-field theory treatment. We show that besides a semimetallic and a charge-density-wave ordered phase, the system exhibits a quantum anomalous Hall phase, which is generated dynamically, i.e., purely as a result of the repulsive fermionic interactions and in the absence of any external gauge fields. We establish the topological nature of this dynamically created Mott-insulating phase by the numerical calculation of a Chern number, and we study the possibility of coexistence of this phase with any of the other phases characterized by local order parameters. Based on the knowledge of the mean-field phase diagram, we then discuss in detail how the interacting Hamiltonian can be engineered effectively by state-of-the-art experimental techniques for laser dressing of cold fermionic ground-state atoms with electronically excited Rydberg states that exhibit strong dipolar interactions.
We propose a realistic scheme to quantum simulate the so-far experimentally unobserved topological Mott insulator phase---an interaction-driven topological insulator---using cold atoms in an optical Lieb lattice. To this end, we study a system of spinless fermions in a Lieb lattice, exhibiting repulsive nearest- and next-to-nearest-neighbor interactions and derive the associated zero-temperature phase diagram within mean-field approximation. In particular, we analyze how the interactions can dynamically generate a charge density wave ordered, a nematic, and a topologically nontrivial quantum anomalous Hall phase. We characterize the topology of the different phases by the Chern number and discuss the possibility of phase coexistence. Based on the identified phases, we propose a realistic implementation of this model using cold Rydberg-dressed atoms in an optical lattice. The scheme, which allows one to access, in particular, the topological Mott insulator phase, robustly and independently of its exact position in parameter space, merely requires global, always-on off-resonant laser coupling to Rydberg states and is feasible with state-of-the-art experimental techniques that have already been demonstrated in the laboratory.