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arXiv:1311.1125 · Journal of Physics B Atomic Molecular and Optical Physics

Twisted phonons in Bose–Einstein condensates

J T Mendonça, A Gammal

Published Feb 26, 2014• 4 citations
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Abstract

We consider elementary excitations in a Bose Einstein condensate, carrying a finite amount of angular momentum. We show that these elementary excitations are modified Bogoliubov oscillations, or phonons with an helical wave structure. These twisted phonon modes can contribute to the total vorticity in a quantum fluid, thus complementing the contribution of the traditional quantum vortices. Linear and nonlinear versions of twisted phonon modes will be discussed. New envelope soliton solutions are shown to exist in a condensate.

DOI
10.1088/0953-4075/47/6/065301

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We consider elementary excitations in a Bose Einstein condensate, carrying a finite amount of angular momentum. We show that these elementary excitations are modified Bogoliubov oscillations, or phonons with an helical wave structure. These twisted phonon modes can contribute to the total vorticity in a quantum fluid, thus complementing the contribution of the traditional quantum vortices. Linear and nonlinear versions of twisted phonon modes will be discussed. New envelope soliton solutions are shown to exist in a condensate.
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Abstract We consider the nonlinear coupling between an exact vortex solution in a Bose–Einstein condensate and a spectrum of elementary excitations in the medium. These excitations, or Bogoliubov–de Gennes modes, are indeed a special kind of phonons. We treat the spectrum of elementary excitations in the medium as a gas of quantum particles, sometimes also called bogolons . An exact kinetic equation for the bogolon gas is derived, and an approximate form of this equation, valid in the quasi-classical limit, is also obtained. We study the energy transfer between the vortex and the bogolon gas, and establish conditions for vortex instability and damping.
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Like classical fluids, quantum gases may suffer from hydrodynamic instabilities. Our paper develops a quantum version of the classical stability analysis in fluids, the Bogoliubov theory of elementary excitations in unstable Bose-Einstein condensates. In unstable condensates the excitation modes have complex frequencies. We derive the normalization conditions for unstable modes such that they can serve in a mode decomposition of the non-condensed component. Furthermore, we develop approximative techniques to determine the spectrum and the mode functions. Finally, we apply our theory to a sonic white hole and find that the spectrum of unstable modes is intrinsically discrete.
We investigate tunneling properties of Bogoliubov phonons in a Bose-Einstein condensate. We find the anomalous enhancement of the quasiparticle current JqJ_{\rm q}Jq​ carried by Bogoliubov phonons near a potential barrier, due to the supply of the excess current from the condensate. This effect leads to the increase of quasiparticle transmission probability in the low energy region found by Kovrizhin {\it et al.}. We also show that the quasiparticle current twists the phase of the condensate wavefunction across the barrier, leading to a finite Josephson supercurrent JsJ_{\rm s}Js​ through the barrier. This induced supercurrent flows in the opposite direction to the quasiparticle current so as to cancel out the enhancement of JqJ_{\rm q}Jq​ and conserve the total current J=Jq+JsJ=J_{\rm q}+J_{\rm s}J=Jq​+Js​.
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