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arXiv:1509.04217 · Physical Review A

Beliaev damping in quasi-two-dimensional dipolar condensates

Ryan Wilson, Stefan S. Natu

Published May 9, 2016• 7 citations

Abstract

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 $^{4}\mathrm{He}$ films.

DOI: 10.1103/physreva.93.053606

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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

^{4}\mathrm{He}

films.

Beliaev damping provides a fundamental mechanism for dissipation of quasiparticles. Previous research has shown that the two-component internal degrees of freedom has no nontrivial effect on Beliaev damping. Here we provide the first example where the spinor nature of Bose gases can manifest itself in the Beliaev damping by way of spin-obit coupling. We identify novel features of the Beliaev decay rate due to spin-orbit coupling; in particular, it shows an explicit dependence on the spin-density interaction and diverges at the interaction-modified phase boundary between the zero-momentum and plane wave phases. This represents a manifestation of the effect of spin-orbit coupling in the beyond-mean-field regime, which by breaking Galilean invariance couples excitations in the density and spin channels. We further show that the measurement of the Beliaev damping rate is experimentally feasible through the measurement of spin polarizability susceptibility, which has been already achieved in spin-orbit-coupled Bose gases.

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 develop a theory of damping of low-energy, collective excitations in a quasi-two-dimensional, homogenous, dipolar Bose gas at zero temperature, via processes whereby an excitation decays into two excitations with lower energy. We find that owing to the nature of the low-energy spectrum of a quasi-two-dimensional dipolar gas, such processes cannot occur unless the momentum of the incoming quasiparticle exceeds a critical value

{\mathbf{k}}_{\text{crit}}

. We find that as the dipolar interaction strength is increased, this critical value shifts to larger momenta. Our predictions can be directly verified in current experiments on dipolar Bose condensates using Bragg spectroscopy, and provide valuable insight into the quantum many-body physics of dipolar gases.

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.

We study the merging and splitting of quasi-two-dimensional Bose-Einstein condensates with strong dipolar interactions. We observe that if the dipoles have a non-zero component in the plane of the condensate, the dynamics of merging or splitting along two orthogonal directions, parallel and perpendicular to the projection of dipoles on the plane of the condensate are different. The anisotropic merging and splitting of the condensate is a manifestation of the anisotropy of the roton-like mode in the dipolar system. The difference in dynamics disappears if the dipoles are oriented at right angles to the plane of the condensate as in this case the Bogoliubov dispersion, despite having roton-like features, is isotropic.

We study quasi-two-dimensional dipolar Bose-Einstein condensates, in which the Bogoliubov excitation spectrum displays, at sufficiently large gas density, a deep roton minimum due to the spatially anisotropic behavior of the dipolar two-body potential. A rapid quench, performed on the speed of sound of excitations propagating on the condensate background, leads to the dynamical Casimir effect, which can be characterized by measuring the density-density correlation function. It is shown, for both zero and finite initial temperatures, that the continuous-variable bipartite quantum state of the created quasiparticle pairs with opposite momenta, resulting from the quench, displays an enhanced potential for the presence of entanglement (represented by nonseparable and steerable quasiparticle states), when compared to a gas with solely repulsive contact interactions. Steerable quasiparticle pairs contain momenta from close to the roton, and hence quantum correlations significantly increase in the presence of a deep roton minimum.