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arXiv:1606.09089 · Physical Review A

Synthetic dimensions in the strong-coupling limit: Supersolids and pair superfluids

Thomas Bilitewski, Nigel R. Cooper

Published Aug 25, 2016• 41 citations
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Abstract

We study the many-body phases of bosonic atoms with $N$ internal states confined to a one-dimensional (1D) optical lattice under the influence of a synthetic magnetic field and strong repulsive interactions. The $N$ internal states of the atoms are coupled via Raman transitions creating the synthetic magnetic field in the space of internal spin states corresponding to recent experimental realizations. We focus on the case of strong $\text{SU}(N)$ invariant local density-density interactions in which each site of the 1D lattice is at most singly occupied, and strong Raman coupling, in distinction to previous work which has focused on the weak Raman coupling case. This allows us to keep only a single state per site and derive a low-energy effective spin-$1/2$ model. The effective model contains first-order nearest-neighbor tunneling terms, second-order nearest-neighbor interactions, and correlated next-nearest-neighbor tunneling terms. By adjusting the flux $\ensuremath{\phi}$, one can tune the relative importance of first-order and second-order terms in the effective Hamiltonian. In particular, first-order terms can be set to zero, realizing a model with dominant second-order terms. We show that the resulting competition between density-dependent tunneling and repulsive density-density interaction leads to an interesting phase diagram including a phase with long-range pair-superfluid correlations. The method can be straightforwardly extended to higher dimensions and lattices of arbitrary geometry, including geometrically frustrated lattices where the interplay of frustration, interactions, and kinetic terms is expected to lead to even richer physics.

DOI
10.1103/physreva.94.023630

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We study the many-body phases of bosonic atoms with NNN internal states confined to a one-dimensional (1D) optical lattice under the influence of a synthetic magnetic field and strong repulsive interactions. The NNN internal states of the atoms are coupled via Raman transitions creating the synthetic magnetic field in the space of internal spin states corresponding to recent experimental realizations. We focus on the case of strong SU(N)\text{SU}(N)SU(N) invariant local density-density interactions in which each site of the 1D lattice is at most singly occupied, and strong Raman coupling, in distinction to previous work which has focused on the weak Raman coupling case. This allows us to keep only a single state per site and derive a low-energy effective spin-1/21/21/2 model. The effective model contains first-order nearest-neighbor tunneling terms, second-order nearest-neighbor interactions, and correlated next-nearest-neighbor tunneling terms. By adjusting the flux \ensuremathϕ\ensuremath{\phi}\ensuremathϕ, one can tune the relative importance of first-order and second-order terms in the effective Hamiltonian. In particular, first-order terms can be set to zero, realizing a model with dominant second-order terms. We show that the resulting competition between density-dependent tunneling and repulsive density-density interaction leads to an interesting phase diagram including a phase with long-range pair-superfluid correlations. The method can be straightforwardly extended to higher dimensions and lattices of arbitrary geometry, including geometrically frustrated lattices where the interplay of frustration, interactions, and kinetic terms is expected to lead to even richer physics.
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We study Hubbard models for ultracold bosonic or fermionic atoms loaded into an optical lattice. The atoms carry a high spin F> 1/2, and interact on site via strong repulsive Van der Waals forces. Making convenient rearrangements of the interaction terms, and exploiting their symmetry properties, we derive low-energy effective models with nearest-neighbor interactions, and their properties. We apply our method to F =3/2, and 5/2 fermions on two-dimensional square lattice at quarter, and 1/6 fillings, respectively, and investigate mean-field equations for repulsive couplings. We find for F =3/2 fermions that the plaquette state appearing in the highly symmetric SU (4) case does not require fine tuning, and is stable in an extended region of the phase diagram. This phase competes with an SU (2) flux state, that is always suppressed for repulsive interactions in the absence of external magnetic field. The SU (2) flux state has, however, lower energy than the plaquette phase, and stabilizes in the presence of weak applied magnetic field. For F =5/2 fermions a similar SU (2) plaquette phase is found to be the ground state without external magnetic field.
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.
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.