Xue-Feng Zhang

Rydberg Polaritons in a Cavity: A Superradiant Solid

We study an optical cavity coupled to a lattice of Rydberg atoms, which can be represented by a generalized Dicke model. We show that the competition between the atomic interaction and atomlight coupling induces a rich phase diagram. A novel “superradiant solid” (SRS) phase is found, where both the superradiance and crystalline orders coexist. Different from the normal second order superradiance (SR) transition, here both the Solid-1/2 and SRS to SR phase transitions are first order. These results are confirmed by the large scale quantum Monte Carlo simulations.

Supersolid phase transitions for hard-core bosons on a triangular lattice

Hard-core bosons on a triangular lattice with nearest-neighbor repulsion are a prototypical example of a system with supersolid behavior on a lattice. We show that in this model the physical origin of the supersolid phase can be understood quantitatively and analytically by constructing quasiparticle excitations of defects that are moving on an ordered background. The location of the solid to supersolid phase transition line is predicted from the effective model for both positive and negative (frustrated) hopping parameters. For positive hopping parameters the calculations agree very accurately with numerical quantum Monte Carlo simulations. The numerical results indicate that the supersolid to superfluid transition is first order.

Tuning the quantum phase transition of bosons in optical lattices via periodic modulation of the

We consider interacting bosons in a 2D square and a 3D cubic optical lattice with a periodic modulation of the s-wave scattering length. At first we map the underlying periodically driven Bose-Hubbard model for large enough driving frequencies approximately to an effective time-independent Hamiltonian with a conditional hopping. Combining different analytical approaches with quantum Monte Carlo simulations then reveals that the superfluid-Mott insulator quantum phase transition still exists despite the periodic driving and that the location of the quantum phase boundary turns out to depend quite sensitively on the driving amplitude. A more detailed quantitative analysis shows even that the effect of driving can be described within the usual Bose-Hubbard model provided that the hopping is rescaled appropriately with the driving amplitude. This finding indicates that the Bose-Hubbard model with a periodically driven s-wave scattering length and the usual Bose-Hubbard model belong to the same universality class from the point of view of critical phenomena.

s

We study the properties of the Bose-Hubbard model for square and cubic superlattices. To this end we generalize a recently established effective potential Landau theory for a single component to the case of multiple components and not only find the characteristic incompressible solid phases with fractional filling, but also obtain the underlying quantum phase diagram in the whole parameter region at zero temperature. A comparison of our analytic results with corresponding ones from quantum Monte Carlo simulations demonstrates the high accuracy of the generalized effective-potential Landau theory (GEPLT). Finally, we comment on the advantages and disadvantages of the GEPLT in view of a direct comparison with a corresponding decoupled mean-field theory.

-wave scattering length

We study the phase diagram of the Bose-Hubbard model on the kagome lattice with a broken sublattice symmetry. Such a superlattice structure can naturally be created and tuned by changing the potential offset of one sublattice in the optical generation of the frustrated lattice. The superstructure gives rise to a rich quantum phase diagram, which is analyzed by combining Quantum Monte Carlo simulations with the Generalized Effective Potential Landau Theory. Mott phases with non-integer filling and a characteristic order along stripes are found, which show a transition to a superfluid phase with an anisotropic superfluid density. Surprisingly, the direction of the superfluid anisotropy is changing between different symmetry directions as a function of the particle number or the hopping strength. Finally, we discuss characteristic signatures of anisotropic phases in time-of-flight absorption measurements.

Generalized effective-potential Landau theory for bosonic quadratic superlattices

We study the extended Hubbard model on the triangular lattice as a function of filling and interaction strength. The complex interplay of kinetic frustration and strong interactions on the triangular lattice leads to exotic phases where long-range charge order, antiferromagnetic order, and metallic conductivity can coexist. Variational Monte Carlo simulations show that three kinds of ordered metallic states are stable as a function of nearest neighbor interaction and filling. The coexistence of conductivity and order is explained by a separation into two functional classes of particles: part of them contributes to the stable order, while the other part forms a partially filled band on the remaining substructure. The relation to charge ordering in charge transfer salts is discussed.

Tunable anisotropic superfluidity in optical Kagome superlattice

We consider the extended hard-core Bose-Hubbard model on a kagome lattice with boundary conditions on two edges. We find that the sharp edges lift the degeneracy and freeze the system into a striped order at 1/3 and 2/3 filling for zero hopping. At small hopping strengths, holes spontaneously appear and separate into fractional charges which move to the edges of the system. This leads to a novel edge liquid phase, which is characterized by fractional charges near the edges and a finite edge compressibility but no superfluid density. The compressibility is due to excitations on the edge which display a chiral symmetry breaking that is reminiscent of the quantum Hall effect and topological insulators. Large scale Monte Carlo simulations confirm the analytical considerations.

Phase Diagram of the Triangular Extended Hubbard Model

We study the effect of impurities in a supersolid phase in comparison to the behavior in the solid and superfluid phases. A supersolid phase has been established for interacting hard-core bosons on a triangular lattice which may be realizable by ultracold atomic gases. Static vacancies are considered in this model which always lower the magnitude of the order parameter in the solid or superfluid phases. In the supersolid phase, however, the impurities directly affect both order parameters simultaneously and thereby reveal an interesting interplay between them. In particular, the solid order may be enhanced at the cost of a strong reduction in the superfluidity, which shows that the two order parameters cannot be in a simple superposition. We also observe an unusual impurity pinning effect in the solid ordered phase, which results in two distinct states separated by a first-order transition.

Chiral edge states and fractional charge separation in a system of interacting bosons on a kagome lattice.

We analyze the hard-core Bose-Hubbard model with both three-body and nearest-neighbor repulsions on a triangular lattice. The phase diagram is achieved by means of the semiclassical approximation and a quantum Monte Carlo simulation. For a system with only three-body interactions, both the supersolid phase and the one-third solid disappear while the two-thirds solid is stable. As the thermal behavior of the bosons with nearest-neighbor repulsion, the solid and the superfluid undergo the three-state Potts-and Kosterlitz-Thouless-type phase transitions, respectively. In a system with both frustrated nearest-neighbor two-body and three-body interactions, the supersolid and one-third solid are revived. By tuning the strength of the three-body interactions, the phase diagram is distorted because the one-third solid and the supersolid are suppressed.