SciPost Phys. 10, 025 (2021) ·
published 3 February 2021
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· pdf
We employ the Gross-Pitaevskii equation to study acoustic emission generated
in a uniform Bose gas by a static impurity. The impurity excites a sound-wave
packet, which propagates through the gas. We calculate the shape of this wave
packet in the limit of long wave lengths, and argue that it is possible to
extract properties of the impurity by observing this shape. We illustrate here
this possibility for a Bose gas with a trapped impurity atom -- an example of a
relevant experimental setup. Presented results are general for all
one-dimensional systems described by the nonlinear Schr\"odinger equation and
can also be used in nonatomic systems, e.g., to analyze light propagation in
nonlinear optical media. Finally, we calculate the shape of the sound-wave
packet for a three-dimensional Bose gas assuming a spherically symmetric
perturbation.
