Quantum dark solitons in the 1D Bose gas: From single to double
dark-solitons
- URL: http://arxiv.org/abs/2111.02686v1
- Date: Thu, 4 Nov 2021 08:43:30 GMT
- Title: Quantum dark solitons in the 1D Bose gas: From single to double
dark-solitons
- Authors: Kayo Kinjo, Eriko Kaminishi, Takashi Mori, Jun Sato, Rina Kanamoto and
Tetsuo Deguchi
- Abstract summary: We study quantum double dark-solitons by constructing corresponding quantum states in the Lieb-Liniger model for the one-dimensional Bose gas.
The Gross-Pitaevskii equation should play a central role in the long distance mean-field behavior of the 1D Bose gas.
- Score: 3.170887683719515
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: We study quantum double dark-solitons by constructing corresponding quantum
states in the Lieb-Liniger model for the one-dimensional Bose gas. Here we
expect that the Gross-Pitaevskii (GP) equation should play a central role in
the long distance mean-field behavior of the 1D Bose gas. We first introduce
novel quantum states of a single dark soliton with a nonzero winding number. We
show them by exactly evaluating not only the density profile but also the
profiles of the square amplitude and phase of the matrix element of the field
operator between the $N$-particle and $(N-1)$-particle states. For elliptic
double dark-solitons, the density and phase profiles of the corresponding
states almost perfectly agree with those of the classical solutions,
respectively, in the weak coupling regime. We then show that the scheme of the
mean-field product state is quite effective for the quantum states of double
dark solitons. Assigning the ideal Gaussian weights to a sum of the excited
states with two particle-hole excitations we obtain double dark-solitons of
distinct narrow notches with different depths. We suggest that the mean-field
product state should be well approximated by the ideal Gaussian weighted sum of
the low excited states with a pair of particle-hole excitations. The results of
double dark-solitons should be fundamental and useful for constructing quantum
multiple dark-solitons.
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