Damping of elementary excitations in one-dimensional dipolar Bose gases
Résumé
In the presence of dipolar interactions the excitation spectrum of a Bose gas can acquire a local minimum. The corresponding quasiparticles are known as rotons. They are gaped and do not decay at zero temperature. Here we study the decay of rotons in one-dimensional Bose gases at low temperatures. It predominantly occurs due to the backscattering of thermal phonons on rotons. The resulting rate scales with the third power of temperature and is inversely proportional to the sixth power of the roton gap near the solidification phase transition. The hydrodynamic approach used here enables us to find the decay rate for quasiparticles at practically any mo-menta, with minimal assumptions on the exact form of the interparticle interactions. Our results are an essential prerequisite for the description of all the dissipative phenomena in dipolar gases and have direct experimental relevance. Introduction.-At low pressures and temperatures, helium-4 is a remarkable quantum liquid that is superfluid. Lan-dau characterized the latter state by a dissipationless flow of macroscopic objects at small velocities [1]. Another particular feature of the superfluid helium is seen in its spectrum of elementary excitations. While at lowest momenta it is linear, the spectrum possesses a local minimum. The corresponding quasiparticles are known as rotons and have the wavelengths that practically coincide with the mean interparticle distance. Since the interaction between helium atoms is strong, the ro-ton can be visualized as yet undeveloped Goldstone mode due to an instability toward the crystallization [2]. However, such so-called supersolid state that unifies superfluidity with crystalline order has not been so far observed in helium, despite some controversies [3-5]. Another system that shows some similarities with super-fluid helium are dipolar Bose gases. They can be realized with atoms possessing large dipolar moments, such as chromium, dysprosium, and erbium. Bose-Einstein condensates of those atoms are realized [6-9], which opened new avenues for studying various phenomena that originate from the dipolar interaction [10, 11]. Some of them are the striped states [12], the quantum droplets [13, 14], and the elusive supersolid state [15-20]. Trapped dipolar Bose gases can exhibit a quasiparticle spectrum with a roton minimum [21, 22]. This occurs because the dipolar interaction cannot be described only by a short-range pseudopotential, but it must also include an anisotropic long-range part, in order to correctly describe the low-energy scattering between bosons [11]. The quasiparticle spectrum in weakly-interacting Bose gases is determined by the Bogoli-ubov theory [23] and depends on the Fourier transform of the pseudopotential. Since it is described by the two parameters, one for the short-range and the other the long-range part, when they are properly tuned, the local minimum can develop in the spectrum. A recent experiment [24] have confirmed the presence of rotons in the dipolar Bose gas. The current understanding of the properties and the dynam
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