We demonstrate the paired state of bosons in optical lattices, namely the formation of paired superfluids (PSFs) and paired supersolids (PSSs) in the presence of next-nearest neighbor (NNN) interactions that mimic pair hopping and long-range forces. study the Both zero-temperature and finite-temperature phase diagrams are obtained using cluster mean field theory, which systematically includes the effects of correlation. We also compute low-energy excitations that capture the features of such paired states and their transitions. Apart from gapless sound modes due to the PSF ordering, gapped modes also appear in He PSF phases, similar to the Higgs mode in normal atomic superfluidity (ASF). The transition from PSF to ASF exhibits interesting behavior due to the presence of a ‘triple-critical’ point where the nature of the transition changes. As a result of continuous PSF-ASF transitions, the gap modes of both phases become gapless at the critical points. For sufficiently strong NNN interaction strength, the PSS phase appears with coexistence of pairwise superfluidity and stripe density order. The softening of roton modes as precursors of density ordering and the emergence of low-energy gap modes serve as robust features associated with the formation of the PSS phase. He also investigates the melting of PSF and PSS phases into ordinary fluids at finite temperatures, especially the melting pathways of PSS that occur in at least two steps due to coexisting ordering. Finally, we discuss the possibility of emulating such exotic phases in ongoing cold atom experiments.
