Ground-state Properties and Bogoliubov Modes of a Harmonically Trapped
One-Dimensional Quantum Droplet
- URL: http://arxiv.org/abs/2309.05245v1
- Date: Mon, 11 Sep 2023 05:39:53 GMT
- Title: Ground-state Properties and Bogoliubov Modes of a Harmonically Trapped
One-Dimensional Quantum Droplet
- Authors: Xucong Du, Yifan Fei, Xiao-Long Chen, and Yunbo Zhang
- Abstract summary: We study the stationary and excitation properties of a one-dimensional quantum droplet in a Bose mixture trapped in a harmonic potential.
We explicitly show how the spectrum of the excitation is split into discrete modes, and finally taken over by the harmonic trap.
- Score: 4.864202986612716
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: We study the stationary and excitation properties of a one-dimensional
quantum droplet in the two-component Bose mixture trapped in a harmonic
potential. By constructing the energy functional for the inhomogeneous mixture,
we elaborate the extended the Gross-Pitaevskii equation applicable to both
symmetric and asymmetric mixtures into a universal form, and the equations in
two different dimensionless schemes are in a duality relation, i.e. the unique
parameters left are inverse of each other. The Bogoliubov equations for the
trapped droplet are obtained by linearizing the small density fluctuation
around the ground state and the low-lying excitation modes are calculated
numerically.It is found that the confinement trap changes easily the flat-top
structure for large droplets and alters the mean square radius and the chemical
potential intensively. The breathing mode of the confined droplet connects the
self-bound and ideal gas limits, with the excitation in the weakly interacting
Bose condensate for large particle numbers lying in between. We explicitly show
how the continuum spectrum of the excitation is split into discrete modes, and
finally taken over by the harmonic trap. Two critical particle numbers are
identified by the minimum size of the trapped droplet and the maximum breathing
mode energy, both of which are found to decrease exponentially with the
trapping parameter.
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