Fabian Brauneis, HansWerner Hammer, Mikhail Lemeshko, Artem G. Volosniev
SciPost Phys. 11, 008 (2021) ·
published 13 July 2021

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A few years ago, flow equations were introduced as a technique for calculating the groundstate energies of cold Bose gases with and without impurities. In this paper, we extend this approach to compute observables other than the energy. As an example, we calculate the densities, and phase fluctuations of onedimensional Bose gases with one and two impurities. For a single mobile impurity, we use flow equations to validate the meanfield results obtained upon the LeeLowPines transformation. We show that the meanfield approximation is accurate for all values of the bosonimpurity interaction strength as long as the phase coherence length is much larger than the healing length of the condensate. For two static impurities, we calculate impurityimpurity interactions induced by the Bose gas. We find that leading order perturbation theory fails when bosonimpurity interactions are stronger than bosonboson interactions. The meanfield approximation reproduces the flow equation results for all values of the bosonimpurity interaction strength as long as bosonboson interactions are weak.
SciPost Phys. 10, 025 (2021) ·
published 3 February 2021

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We employ the GrossPitaevskii equation to study acoustic emission generated
in a uniform Bose gas by a static impurity. The impurity excites a soundwave
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
onedimensional 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 soundwave
packet for a threedimensional Bose gas assuming a spherically symmetric
perturbation.
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