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| Format: | Preprint |
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2023
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| Online Access: | https://arxiv.org/abs/2311.03176 |
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| _version_ | 1866917846567616512 |
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| author | Tomchenko, Maksim |
| author_facet | Tomchenko, Maksim |
| contents | We find stationary excited states of a one-dimensional system of $N$ spinless point bosons with repulsive interaction and zero boundary conditions by numerically solving the time-independent Gross-Pitaevskii equation. The solutions are compared with the exact ones found in the Bethe-ansatz approach. We show that the $j$th stationary excited state of a nonuniform condensate of atoms corresponds to a Bethe-ansatz solution with the quantum numbers $n_{1}=n_{2}=\ldots =n_{N}=j+1$. On the other hand, such $n_{1},\ldots,n_{N}$ correspond to a condensate of $N$ elementary excitations (in the present case the latter are the Bogoliubov quasiparticles with the quasimomentum $\hbar πj/L$, where $L$ is the system size). Thus, each stationary excited state of the condensate is ``doubly coherent'', since it corresponds simultaneously to a condensate of $N$ atoms and a condensate of $N$ elementary excitations. We find the energy $E$ and the particle density profile $ρ(x)$ for such states. The possibility of experimental production of these states is also discussed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_03176 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Nonuniform Bose-Einstein condensate. II. Doubly coherent states Tomchenko, Maksim Quantum Gases We find stationary excited states of a one-dimensional system of $N$ spinless point bosons with repulsive interaction and zero boundary conditions by numerically solving the time-independent Gross-Pitaevskii equation. The solutions are compared with the exact ones found in the Bethe-ansatz approach. We show that the $j$th stationary excited state of a nonuniform condensate of atoms corresponds to a Bethe-ansatz solution with the quantum numbers $n_{1}=n_{2}=\ldots =n_{N}=j+1$. On the other hand, such $n_{1},\ldots,n_{N}$ correspond to a condensate of $N$ elementary excitations (in the present case the latter are the Bogoliubov quasiparticles with the quasimomentum $\hbar πj/L$, where $L$ is the system size). Thus, each stationary excited state of the condensate is ``doubly coherent'', since it corresponds simultaneously to a condensate of $N$ atoms and a condensate of $N$ elementary excitations. We find the energy $E$ and the particle density profile $ρ(x)$ for such states. The possibility of experimental production of these states is also discussed. |
| title | Nonuniform Bose-Einstein condensate. II. Doubly coherent states |
| topic | Quantum Gases |
| url | https://arxiv.org/abs/2311.03176 |