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Di Liberto, M.; Recati, A.; Trivedi, N.; Carusotto, I.; Menotti, C. (2018): Particle-Hole Character of the Higgs and Goldstone Modes in Strongly Interacting Lattice Bosons. In: Physical Review Letters, Vol. 120, No. 7, 73201
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Abstract

We study the low-energy excitations of the Bose-Hubbard model in the strongly interacting superfluid phase using a Gutzwiller approach. We extract the single-particle and single-hole excitation amplitudes for each mode and report emergent mode-dependent particle-hole symmetry on specific arc-shaped lines in the phase diagram connecting the well-known Lorentz-invariant limits of the Bose-Hubbard model. By tracking the in-phase particle-hole symmetric oscillations of the order parameter, we provide an answer to the long-standing question about the fate of the pure amplitude Higgs mode away from the integer-density critical point. Furthermore, we point out that out-of-phase symmetric oscillations in the gapless Goldstone mode are responsible for a full suppression of the condensate density oscillations. Possible detection protocols are also discussed.