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arXiv:2112.06835 · Physical Review A

Rotons and their damping in elongated dipolar Bose-Einstein condensates

Sergey I. Matveenko, M. S. Bahovadinov, M. A. Baranov, Georgy V. Shlyapnikov

Published Jul 26, 2022• 2 citations
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Abstract

We discuss finite-temperature damping of rotons in elongated Bose-condensed dipolar gases, which are in the Thomas-Fermi regime in the tightly confined directions. The presence of many branches of excitations, which can participate in the damping process, is crucial for the Landau damping and results in significant increase of the damping rate. It is found, however, that even rotons with energies close to the roton gap may remain fairly stable in systems with the roton gap as small as $1\phantom{\rule{0.28em}{0ex}}\mathrm{nK}$.

DOI
10.1103/physreva.106.013319

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We discuss finite-temperature damping of rotons in elongated Bose-condensed dipolar gases, which are in the Thomas-Fermi regime in the tightly confined directions. The presence of many branches of excitations, which can participate in the damping process, is crucial for the Landau damping and results in significant increase of the damping rate. It is found, however, that even rotons with energies close to the roton gap may remain fairly stable in systems with the roton gap as small as 1nK1\phantom{\rule{0.28em}{0ex}}\mathrm{nK}1nK.
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 gapped 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 momenta, 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.
We consider Landau damping of elementary excitations in Bose-Einstein condensates (BECs) with dipolar interactions. We discuss quantum and quasiclassical regimes of Landau damping. We use a generalized wave-kinetic description of BECs which, apart from the long-range dipolar interactions, also takes into account the quantum fluctuations and the finite-energy corrections to short-range interactions. Such a description is therefore more general than the usual mean-field approximation. The present wave-kinetic approach is well suited for the study of kinetic effects in BECs, such as those associated with Landau damping, atom trapping, and turbulent diffusion. The inclusion of quantum fluctuations and energy corrections changes the dispersion relation and the damping rates, leading to possible experimental signatures of these effects. Quantum Landau damping is described with generality, and particular examples of dipolar condensates in two and three dimensions are studied. The occurrence of roton-maxon excitations, and their relevance to Landau damping, are also considered in detail. The present approach is mainly based on a linear perturbative procedure, but the nonlinear regime of Landau damping, which includes atom trapping and atom diffusion, is also briefly discussed.
Roton excitations constitute a key feature of dipolar gases, connecting these gases with superfluid helium. We show that the density dependence of the roton minimum results in a spatial roton confinement, particularly relevant in pancake dipolar condensates with large aspect ratios. We show that roton confinement plays a crucial role in the dynamics after roton instability, and that arresting the instability may create a trapped roton gas revealed by confined density modulations. We discuss the local susceptibility against density perturbations, which we illustrate for the case of vortices. Roton confinement is expected to play a key role in experiments.
We study the effects of quasiparticle interactions in a quasi-two-dimensional (quasi-2D), zero-temperature Bose-Einstein condensate of dipolar atoms, which can exhibit a roton-maxon feature in its quasiparticle spectrum. Our focus is the Beliaev damping process, in which a quasiparticle collides with the condensate and resonantly decays into a pair of quasiparticles. Remarkably, the rate for this process exhibits a highly nontrivial dependence on the quasiparticle momentum and the dipolar interaction strength. For weak interactions, low-energy phonons experience no damping, and higher-energy quasiparticles undergo anomalously weak damping. In contrast, the Beliaev damping rates become anomalously large for stronger dipolar interactions, as rotons become energetically accessible as final states. When the dipoles are tilted off the axis of symmetry, the damping rates acquire an anisotropic character. Surprisingly, this anisotropy does not simply track the anisotropy of the dipolar interactions, rather, the mechanisms for damping are qualitatively modified in the anisotropic case. Our study reveals the unconventional nature of Beliaev damping in dipolar condensates, and has important implications for ongoing studies of equilibrium and nonequilibrium dynamics in these systems. Further, our results are relevant for other 2D superfluids with roton excitations, including spin-orbit-coupled Bose gases, magnon condensates, and 4He^{4}\mathrm{He}4He films.
By using a mean-field approximation which describes the coupled oscillations of condensate and noncondensate atoms in the collisionless regime, Landau damping in a dilute dipolar Bose–Fermi mixture in the BEC limit where Fermi superfluid is treated as tightly bounded molecules, is investigated. In the case of a uniform quasi-two-dimensional (2D) case, the results for the Landau damping due to the Bose–Fermi interaction are obtained at low and high temperatures. It is shown that at low temperatures, the Landau damping rate is exponentially suppressed. By increasing the strength of dipolar interaction, and the energy of boson quasiparticles, Landau damping is suppressed over a broader temperature range.
We present a theory for the Landau damping of low-energy quasiparticles in a collisionless, quasi-two-dimensional dipolar Bose gas and produce expressions for the damping rate in uniform and nonuniform systems. Using simple energy-momentum conservation arguments, we show that in the homogeneous system, the nature of the low-energy dispersion in a dipolar Bose gas severely inhibits Landau damping of long wavelength excitations. For a gas with contact and dipolar interactions, the damping rate for phonons tends to decrease with increasing dipolar interactions; for strong dipole-dipole interactions, phonons are virtually undamped over a broad range of temperature. The damping rate for maxon-roton excitations is found to be significantly larger than the damping rate for phonons.