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

TL;DR

This paper investigates the phases of strongly interacting bosonic atoms with multiple internal states in a 1D optical lattice under synthetic magnetic fields, revealing novel phases like pair-superfluids through an effective spin model.

Contribution

It derives a low-energy effective spin model for strongly coupled multi-state bosons in 1D lattices with synthetic magnetic fields, highlighting the emergence of pair-superfluid phases.

Findings

Identification of a phase with long-range pair-superfluid correlations.

Derivation of an effective spin model with tunable first- and second-order terms.

Potential extension of the method to higher-dimensional and frustrated lattices.

Abstract

We study the many-body phases of bosonic atoms with $N$ internal states confined to a 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 realisations. We focus on the case of strong $\mbox{SU}(N)$ 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 neighbour tunnelling terms, and second-order nearest neighbour interactions and correlated next-nearest neighbour tunnelling terms. By adjusting the flux $\phi$ 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, realising a novel model with dominant second-order terms. We show that the resulting competition between density-dependent tunnelling and repulsive density-density interaction leads to an interesting phase diagram including a phase with long-ranged 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.