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arXiv:2311.03176 · Journal of Physics A Mathematical and Theoretical

Nonuniform Bose–Einstein condensate: II. Doubly coherent states

Maksim Tomchenko

Published Nov 12, 2024• 2 citations
arXivHTMLPDF

Abstract

Abstract 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 jth stationary excited state of a nonuniform condensate of atoms corresponds to a Bethe-ansatz solution with the quantum numbers n 1 = n 2 = … = n N = j + 1 . On the other hand, such values of n 1 , … , n N correspond to a condensate of N elementary excitations (the Bogoliubov quasiparticles) with the quasimomentum ℏ π j / 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.

DOI
10.1088/1751-8121/ad9188

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