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arXiv:1412.6910 · Physical Review A

Trimer superfluid and supersolid on two-dimensional optical lattices

Wanzhou Zhang, Yuan Yang, Lijuan Guo, Chengxiang Ding, Tony C. Scott

Published Mar 11, 2015• 11 citations
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Abstract

By the photoassociation method, the trimer superfluid phase disappears in the one-dimensional state-dependent optical lattice if the ratio of the three-body interaction $W$ to the trimer tunneling $J$ is kept at $W/J=12$ [W. Z. Zhang et al., Phys. Rev. A 90, 033622 (2014)]. To search for a trimer superfluid and trimer supersolid, we load the cold atom into two-dimensional lattices, whose coordinate number $z$ and kinetic energy $\ensuremath{-}zJ$ are respectively larger and lower than those of a one-dimensional lattice. Herein, we study the Bose-Hubbard model, which has an additional trimer tunneling term, a three-body interaction, and a next-nearest repulsion. The on-site trimer and trimer superfluid exist if the on-site two-body repulsion and three-body repulsion are smaller than some thresholds. With atom-tunneling terms, the phase transitions from trimer superfluid phase to both atom superfluid and atom supersolid phases are first order. With $W/J=12$, in a one-dimensional lattice, the trimer superfluid phase does not exist at all. In contrast, the trimer superfluid phase exists in the lower density regions $0<\ensuremath{\rho}<2$ on the square lattice if $J$ is not very large. The trimer superfluid phase emerges in a wider range $0<\ensuremath{\rho}<3$ in the triangular lattice, or in the cubic lattice $(z=6)$. When the three-body interaction is turned on, a trimer supersolid phase emerges due to the classical degeneracy between the quasitrimer solid and the trimer solid being broken by the quantum fluctuation. The phase transitions from the trimer supersolid phase to the quasitrimer solid are first order and the phase transition from the trimer supersolid phase to trimer solid is continuous. Our results, obtained by mean-field and quantum Monte Carlo methods, will be helpful in realizing the trimer superfluid and supersolid by cold-atom experiments.

DOI
10.1103/physreva.91.033613

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By the photoassociation method, the trimer superfluid phase disappears in the one-dimensional state-dependent optical lattice if the ratio of the three-body interaction WWW to the trimer tunneling JJJ is kept at W/J=12W/J=12W/J=12 [W. Z. Zhang et al., Phys. Rev. A 90, 033622 (2014)]. To search for a trimer superfluid and trimer supersolid, we load the cold atom into two-dimensional lattices, whose coordinate number zzz and kinetic energy \ensuremath−zJ\ensuremath{-}zJ\ensuremath−zJ are respectively larger and lower than those of a one-dimensional lattice. Herein, we study the Bose-Hubbard model, which has an additional trimer tunneling term, a three-body interaction, and a next-nearest repulsion. The on-site trimer and trimer superfluid exist if the on-site two-body repulsion and three-body repulsion are smaller than some thresholds. With atom-tunneling terms, the phase transitions from trimer superfluid phase to both atom superfluid and atom supersolid phases are first order. With W/J=12W/J=12W/J=12, in a one-dimensional lattice, the trimer superfluid phase does not exist at all. In contrast, the trimer superfluid phase exists in the lower density regions 0<\ensuremathρ<20<\ensuremath{\rho}<20<\ensuremathρ<2 on the square lattice if JJJ is not very large. The trimer superfluid phase emerges in a wider range 0<\ensuremathρ<30<\ensuremath{\rho}<30<\ensuremathρ<3 in the triangular lattice, or in the cubic lattice (z=6)(z=6)(z=6). When the three-body interaction is turned on, a trimer supersolid phase emerges due to the classical degeneracy between the quasitrimer solid and the trimer solid being broken by the quantum fluctuation. The phase transitions from the trimer supersolid phase to the quasitrimer solid are first order and the phase transition from the trimer supersolid phase to trimer solid is continuous. Our results, obtained by mean-field and quantum Monte Carlo methods, will be helpful in realizing the trimer superfluid and supersolid by cold-atom experiments.
We use the mean-field method, the quantum Monte Carlo method and the density-matrix-renormalization-group method to study the trimer superfluid phase and the quantum phase diagram of the Bose-Hubbard model in a one-dimensional optical lattice, with an explicit trimer-tunneling term. Theoretically, we derive the explicit trimer hopping terms, such as ${a}_{i}^{3\ifmmode\dagger\else\textdagger\fi{}}{a}_{j}^{3}$, by the Schrieffer-Wolf transformation. In practice, the trimer superfluid described by these terms is driven by photoassociation. The phase transition between the trimer superfluid phase and other phases are also studied. Without the on-site interaction, the phase transition between the trimer superfluid phase and the Mott insulator phase is continuous. Turning on the on-site interaction, the phase transitions are first order with Mott insulators of atoms filling 1 and 2. With nonzero atom tunneling, the phase transition is first order from the atom superfluid to the trimer superfluid. In the trimer superfluid phase, the winding numbers can be divided by three without any remainder. The power-law decay exponent is 1/21/21/2 for the nondiagonal correlation ${a}_{i}^{\ifmmode\dagger\else\textdagger\fi{}3}{a}_{j}^{3}$, i.e., the same as the exponent of the correlation ${a}_{i}^{\ifmmode\dagger\else\textdagger\fi{}}{a}_{j}$ in hardcore bosons. The density-dependent atom-tunneling term ${n}_{i}^{2}{a}_{i}^{\ifmmode\dagger\else\textdagger\fi{}}{a}_{j}$ and pair-tunneling term ${n}_{i}{a}_{i}^{\ifmmode\dagger\else\textdagger\fi{}2}{a}_{j}^{2}$ are also studied. With these terms, the phase transition from the empty phase to atom superfluid is first order and different from the cases without the density-dependent terms. The effects of finite three-body interactions and finite temperatures are also studied. Our results will be helpful in realizing the trimer superfluid by a cold-atom experiment.
The Bose–Hubbard model with an effective off-site three-body tunneling, characterized by jumps towards one another, between one atom on a site and a pair atoms on the neighborhood site, is studied systematically on a one-dimensional (1D) lattice, by using the density matrix renormalization group method. The off-site trimer superfluid, condensing at momentum k = 0 , emerges in the softcore Bose–Hubbard model but it disappears in the hardcore Bose–Hubbard model. Our results numerically verify that the off-site trimer superfluid phase derived in the momentum space from [ Phys. Rev. A 81 , 011601(R) (2010)] is stable in the thermodynamic limit. The off-site trimer superfluid phase, the partially off-site trimer superfluid phase and the Mott insulator phase are found, as well as interesting phase transitions, such as the continuous or first-order phase transition from the trimer superfluid phase to the Mott insulator phase. Our results are helpful in realizing this novel off-site trimer superfluid phase by cold atom experiments.
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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 the nature of the ground state of the two-dimensional extended boson Hubbard model on a square lattice by quantum Monte Carlo methods. We demonstrate that strong but finite on-site interaction U along with a comparable nearest-neighbor repulsion V result in a thermodynamically stable supersolid ground state for densities larger than 1/2, in contrast to fillings less than 1/2 or for very large U, where the checkerboard supersolid is unstable towards phase separation. We discuss the relevance of our results to realizations of supersolids using cold bosonic atoms in optical lattices.
Motivated by a recent experiment that realizes nearest-neighbor dipolar couplings in an optical lattice [C. Lagoin et al., Nature (London) 609, 485 (2022)], we study a one-dimensional version of the two-component extended Bose-Hubbard model via the density-matrix renormalization group method. By using the nearest-neighbor and on-site interaction parameters from the experiment, we start by mapping the quantum phase diagram in the hopping parameter ${t}_{A}\text{\ensuremath{-}}{t}_{B}$ plane with boson densities ${\ensuremath{\rho}}_{A}={\ensuremath{\rho}}_{B}=1/2$. In addition to the density-wave phase reported in the experiment, we find several regimes of superfluidity when one or both hopping parameters are large enough, and interestingly there is a supercounterfluid phase at moderate and comparable hopping parameters. The universality classes of these phase transitions are analyzed from the correlation functions, excitation gaps, and entanglement entropy. In particular, a Berezinskii-Kosterlitz-Thouless type is recognized for several gapped-to-gapless transitions. In addition, we also study the quantum phase transitions by varying ${\ensuremath{\rho}}_{B}$ from 0 to 1 while keeping ${\ensuremath{\rho}}_{A}=1/2$. We identify a supersolid phase in a wide range of $1/2<{\ensuremath{\rho}}_{B}<1$. Our work paves the way for realizing exotic many-body phases in cold-atom experiments upon proper tuning of experimental parameters.