Dispersion Law for a One-Dimensional Weakly Interacting Bose Gas with Zero Boundary Conditions

Tomchenko, Maksim

doi:10.1007/s10909-024-03136-8

J Low Temp Phys

2024

DOI: 10.1007/s10909-024-03136-8

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Dispersion Law for a One-Dimensional Weakly Interacting Bose Gas with Zero Boundary Conditions

Maksim Tomchenko

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Nonuniform Bose–Einstein condensate: II. Doubly coherent states

Tomchenko

2024

J. Phys. A: Math. Theor.

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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 values of$n_{1},\ldots,n_{N}$ correspond to a condensate of $N$ elementaryexcitations (the Bogoliubov quasiparticles) with the quasimomentum$\hbar \pi j/L$, where $L$ is the system size. Thus, eachstationary excited state of the condensate is \textquotedblleftdoubly coherent\textquotedblright, 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 $\rho (x)$ for such states. The possibility ofexperimental production of these states is alsodiscussed.

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Nonuniform Bose–Einstein condensate: II. Doubly coherent states

Tomchenko

2024

J. Phys. A: Math. Theor.

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Dispersion Law for a One-Dimensional Weakly Interacting Bose Gas with Zero Boundary Conditions

Cited by 1 publication

References 40 publications

Nonuniform Bose–Einstein condensate: II. Doubly coherent states

Nonuniform Bose–Einstein condensate: II. Doubly coherent states

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