# Collective excitations of trapped one-dimensional dipolar quantum gases

### P. Pedri 1, S. De Palo 2, 3, Edmond Orignac 4, R. Citro 5, M. L. Chiofalo 6, 7

#### Physical Review A: Atomic, Molecular and Optical Physics 77 (2008) 015601

We calculate the excitation modes of a 1D dipolar quantum gas confined in a harmonic trap with frequency $\omega_0$ and predict how the frequency of the breathing n=2 mode characterizes the interaction strength evolving from the Tonks-Girardeau value $\omega_2=2\omega_0$ to the quasi-ordered, super-strongly interacting value $\omega_2=\sqrt{5}\omega_0$. Our predictions are obtained within a hydrodynamic Luttinger-Liquid theory after applying the Local Density Approximation to the equation of state for the homogeneous dipolar gas, which are in turn determined from Reptation Quantum Monte Carlo simulations. They are shown to be in quite accurate agreement with the results of a sum-rule approach. These effects can be observed in current experiments, revealing the Luttinger-liquid nature of 1D dipolar Bose gases.

• 1. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS),
CNRS : UMR8626 – Université Paris XI - Paris Sud
• 2. Dipartimento di Fisica Teorica,
INFN – Università degli studi di Trieste
• 3. DEMOCRITOS,
Consiglio Nazionale delle Ricerche
• 4. Laboratoire de Physique de l'ENS Lyon (Phys-ENS),
CNRS : UMR5672 – École Normale Supérieure - Lyon
• 5. Dipartimento di Fisica "E. R. Caianiello" and CNISM,
Università degli studi di Salerno
• 6. INFN Dipartimento di Matematica,,
Università di Pisa
• 7. Centre Emile Borel,
Institut Henri Poincaré