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arXiv:1611.06404 · Physical Review A

Supersolid and pair correlations of the extended Jaynes-Cummings-Hubbard model on triangular lattices

Lijuan Guo, Sebastian Greschner, Siyu Zhu, Wanzhou Zhang

Published Sep 18, 2019• 17 citations
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Abstract

We study the extended Jaynes-Cummings-Hubbard model on triangular cavity lattices and zigzag ladders. By using density-matrix renormalization-group methods, we observe various types of solids with different density patterns and find evidence for light supersolids, which exist in extended regions of the phase diagram of the zigzag ladder. Furthermore, we observe strong pair correlations in the supersolid phase due to the interplay between the atoms in the cavities and atom-photon interaction. By means of cluster mean-field simulations and a scaling of the cluster size extending our analysis to two-dimensional triangular lattices, we present evidence for the emergence of a light supersolid in this case also.

DOI
10.1103/physreva.100.033614

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We study the extended Jaynes-Cummings-Hubbard model on triangular cavity lattices and zigzag ladders. By using density-matrix renormalization-group methods, we observe various types of solids with different density patterns and find evidence for light supersolids, which exist in extended regions of the phase diagram of the zigzag ladder. Furthermore, we observe strong pair correlations in the supersolid phase due to the interplay between the atoms in the cavities and atom-photon interaction. By means of cluster mean-field simulations and a scaling of the cluster size extending our analysis to two-dimensional triangular lattices, we present evidence for the emergence of a light supersolid in this case also.
Searching for and investigating supersolids is a long-term outstanding problem in physics. In addition to the solid element 4He^{4}\mathrm{He}4He and cold atoms as potential candidates for the supersolid, the quantum system of light realized by circuit quantum electrodynamics is also a promising platform. In this paper, we propose a supersolid phase, i.e., a superradiant supersolid of light, where superradiant, superfluid, and solid orders coexist. We theoretically simulate the extended Jaynes-Cummings-Hubbard model describing the circuit quantum electrodynamics systems, mainly by the large-scale worm quantum Monte Carlo method, and find that a superradiant supersolid phase exists on triangular lattices due to the antiferromagnetic correlation between photons via light-atom coupling. We also confirm that the previous supersolid of light given by Bujnowski et al. [Phys. Rev. A 90, 043801 (2014)] is not stable. The phase transition between our superradiant supersolid phase and the superradiant solid phase can be continuous (first order) and above (below) the ``symmetry point.'' This is not the same as the pure Bose-Hubbard model on triangular lattices. The results herein could help in the search for a new superradiant supersolid phase in circuit quantum electrodynamic experiments and other light-matter coupling systems.
Jaynes-Cummings-Hubbard lattices provide unique properties for the study of correlated phases as they exhibit convenient state preparation and measurement, as well as in situ tuning of parameters. We show how to realize charge density and supersolid phases in Jaynes-Cummings-Hubbard lattices in the presence of long-range interactions. The long-range interactions are realized by the consideration of Rydberg states in coupled atom-cavity systems and the introduction of additional capacitive couplings in quantum-electrodynamics circuits. We demonstrate the emergence of supersolid and checkerboard solid phases, for calculations which take into account nearest-neighbor couplings, through a mean-field decoupling.
We have systematically studied the hard-core Bose-Hubbard model with correlated hopping on a triangular lattice using the density-matrix renormalization group method. A rich ground-state phase diagram is determined. In this phase diagram there is a supersolid phase and a pair superfluid phase due to the interplay between the ordinary frustrated boson hopping and an unusual correlated hopping. In particular, we find that the quantum phase transition between the supersolid phase and the pair superfluid phase is continuous.
We systematically study an extended Bose-Hubbard model with atom hopping and atom-pair hopping in the presence of a three-body constraint on the triangular lattice. By means of large-scale quantum Monte Carlo simulations, the ground-state phase diagram is studied. We find a first-order transition between the atomic superfluid phase and the pair superfluid phase when the ratio of the atomic hopping and the atom-pair hopping is adapted. The first-order transition remains unchanged under various conditions. We then focus on the interplay among the atom-pair hopping, the on-site repulsion, and the nearest-neighbor repulsion. With on-site repulsion present, we observe first-order transitions between the Mott insulators and pair superfluid driven by the pair hopping. With the nearest-neighbor repulsion turning on, three typical solid phases with 2/32/32/3, 1, and 4/34/34/3 filling emerge at small atom-pair hopping region. A stable pair supersolid phase is found at small on-site repulsion. This is due to the three-body constraint and the pair hopping, which essentially make the model a quasihardcore boson system. Thus the pair supersolid state emerges basing on the order-by-disorder mechanism, by which hardcore bosons avoid classical frustration on the triangular lattice. Without on-site repulsion, the transitions between the pair supersolid and the atom superfluid or pair superfluid are first order, except for the particle-hole symmetric point. With weak on-site repulsion and atom hopping turning on, the transition between the pair supersolid and pair superfluid phase becomes continuous. The transition between solid and pair supersolid is three-dimensional XYXYXY university, with dynamical exponent z=1z=1z=1 and correlation exponent $\ensuremath{\nu}=0.671\phantom{\rule{0.16em}{0ex}}55$. The thermal melting of pair supersolid belongs to the two-dimensional Ising university. We check both energetic and mechanical balance of pair supersolid phase. Lowering the three-body constraint, no pair supersolid is found due to the absence of degeneracy of pair solids in classical limits. We describe the experimental realization of pair tunneling on state dependent lattice.
We study ground-state properties in a hard-core Bose-Hubbard model on a layered triangular lattice. Combining cluster mean-field theory with the density matrix renormalization group method, we discuss the effect of the interlayer coupling on the supersolid states realized in a single layered model. By examining the distributions for the particle density and superfluid order parameter, the rich phase diagram of the system is obtained. We find that the supersolid states are widely stabilized at a commensurate filling, in contrast to the case of the single layered model. The nature of the supersolid states is also addressed.
Using a state-of-the-art numerical method density-matrix renormalization-group, we study the ground states of one-dimensional spinless Bose-Hubbard model inside a red-detuned cavity. By calculating the superfluid order, density distribution, second and third-order correlation functions, we find that there exist two novel supersolid phases with diagonal, off-diagonal orders beyond mean-field theory. One has package type density modulation along the lattice axis, another exhibits uniform density distribution. Moreover, by calculating the superradiant order parameter and the number of photon inside the cavity, we find that the novel supersolid phases are highly related to cavity-field fluctuation. Our work gives the physics beyond the mean-field theory of the Bose-Hubbard model inside an optical cavity, and provides the complete approach to fully explore the collective state of light and matter inside an optical cavity.