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We determine the excitation spectrum of a bosonic dipolar quantum gas in aone-dimensional geometry, from the dynamical density-density correlationfunctions simulated by means of Reptation Quantum Monte Carlo techniques. Theexcitation energy is always vanishing at the first vector of the reciprocallattice in the whole crossover from the liquid-like at low density to thequasi-ordered state at high density, demonstrating the absence of a rotonminimum. Gaps at higher reciprocal lattice vectors are seen to progressivelyclose with increasing density, while the quantum state evolves into aquasi-periodic structure. The simulational data together with theuncertainty-principle inequality also provide a rigorous proof of the absenceof long-range order in such a super-strongly correlated system. Our conclusionsconfirm that the dipolar gas is in a Luttinger-liquid state, significantlyaffected by the dynamical correlations. The connection with ongoing experimentsis also discussed.

The low-energy excitation spectrum of one-dimensional dipolar quantum gases